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Classification of MRI data using Deep Learning and Gaussian Process-based Model Selection
cs.LG stat.ML
The classification of MRI images according to the anatomical field of view is a necessary task to solve when faced with the increasing quantity of medical images. In parallel, advances in deep learning makes it a suitable tool for computer vision problems. Using a common architecture (such as AlexNet) provides quite good results, but not sufficient for clinical use. Improving the model is not an easy task, due to the large number of hyper-parameters governing both the architecture and the training of the network, and to the limited understanding of their relevance. Since an exhaustive search is not tractable, we propose to optimize the network first by random search, and then by an adaptive search based on Gaussian Processes and Probability of Improvement. Applying this method on a large and varied MRI dataset, we show a substantial improvement between the baseline network and the final one (up to 20\% for the most difficult classes).
Hadrien Bertrand, Matthieu Perrot, Roberto Ardon, Isabelle Bloch
null
1701.04355
null
null
The Incredible Shrinking Neural Network: New Perspectives on Learning Representations Through The Lens of Pruning
cs.NE cs.LG
How much can pruning algorithms teach us about the fundamentals of learning representations in neural networks? And how much can these fundamentals help while devising new pruning techniques? A lot, it turns out. Neural network pruning has become a topic of great interest in recent years, and many different techniques have been proposed to address this problem. The decision of what to prune and when to prune necessarily forces us to confront our assumptions about how neural networks actually learn to represent patterns in data. In this work, we set out to test several long-held hypotheses about neural network learning representations, approaches to pruning and the relevance of one in the context of the other. To accomplish this, we argue in favor of pruning whole neurons as opposed to the traditional method of pruning weights from optimally trained networks. We first review the historical literature, point out some common assumptions it makes, and propose methods to demonstrate the inherent flaws in these assumptions. We then propose our novel approach to pruning and set about analyzing the quality of the decisions it makes. Our analysis led us to question the validity of many widely-held assumptions behind pruning algorithms and the trade-offs we often make in the interest of reducing computational complexity. We discovered that there is a straightforward way, however expensive, to serially prune 40-70% of the neurons in a trained network with minimal effect on the learning representation and without any re-training. It is to be noted here that the motivation behind this work is not to propose an algorithm that would outperform all existing methods, but to shed light on what some inherent flaws in these methods can teach us about learning representations and how this can lead us to superior pruning techniques.
Aditya Sharma, Nikolas Wolfe, Bhiksha Raj
null
1701.04465
null
null
Towards a New Interpretation of Separable Convolutions
cs.LG stat.ML
In recent times, the use of separable convolutions in deep convolutional neural network architectures has been explored. Several researchers, most notably (Chollet, 2016) and (Ghosh, 2017) have used separable convolutions in their deep architectures and have demonstrated state of the art or close to state of the art performance. However, the underlying mechanism of action of separable convolutions are still not fully understood. Although their mathematical definition is well understood as a depthwise convolution followed by a pointwise convolution, deeper interpretations such as the extreme Inception hypothesis (Chollet, 2016) have failed to provide a thorough explanation of their efficacy. In this paper, we propose a hybrid interpretation that we believe is a better model for explaining the efficacy of separable convolutions.
Tapabrata Ghosh
null
1701.04489
null
null
Deep Learning for Computational Chemistry
stat.ML cs.AI cs.CE cs.LG physics.chem-ph
The rise and fall of artificial neural networks is well documented in the scientific literature of both computer science and computational chemistry. Yet almost two decades later, we are now seeing a resurgence of interest in deep learning, a machine learning algorithm based on multilayer neural networks. Within the last few years, we have seen the transformative impact of deep learning in many domains, particularly in speech recognition and computer vision, to the extent that the majority of expert practitioners in those field are now regularly eschewing prior established models in favor of deep learning models. In this review, we provide an introductory overview into the theory of deep neural networks and their unique properties that distinguish them from traditional machine learning algorithms used in cheminformatics. By providing an overview of the variety of emerging applications of deep neural networks, we highlight its ubiquity and broad applicability to a wide range of challenges in the field, including QSAR, virtual screening, protein structure prediction, quantum chemistry, materials design and property prediction. In reviewing the performance of deep neural networks, we observed a consistent outperformance against non-neural networks state-of-the-art models across disparate research topics, and deep neural network based models often exceeded the "glass ceiling" expectations of their respective tasks. Coupled with the maturity of GPU-accelerated computing for training deep neural networks and the exponential growth of chemical data on which to train these networks on, we anticipate that deep learning algorithms will be a valuable tool for computational chemistry.
Garrett B. Goh, Nathan O. Hodas, Abhinav Vishnu
null
1701.04503
null
null
Online Learning with Regularized Kernel for One-class Classification
cs.LG
This paper presents an online learning with regularized kernel based one-class extreme learning machine (ELM) classifier and is referred as online RK-OC-ELM. The baseline kernel hyperplane model considers whole data in a single chunk with regularized ELM approach for offline learning in case of one-class classification (OCC). Further, the basic hyper plane model is adapted in an online fashion from stream of training samples in this paper. Two frameworks viz., boundary and reconstruction are presented to detect the target class in online RKOC-ELM. Boundary framework based one-class classifier consists of single node output architecture and classifier endeavors to approximate all data to any real number. However, one-class classifier based on reconstruction framework is an autoencoder architecture, where output nodes are identical to input nodes and classifier endeavor to reconstruct input layer at the output layer. Both these frameworks employ regularized kernel ELM based online learning and consistency based model selection has been employed to select learning algorithm parameters. The performance of online RK-OC-ELM has been evaluated on standard benchmark datasets as well as on artificial datasets and the results are compared with existing state-of-the art one-class classifiers. The results indicate that the online learning one-class classifier is slightly better or same as batch learning based approaches. As, base classifier used for the proposed classifiers are based on the ELM, hence, proposed classifiers would also inherit the benefit of the base classifier i.e. it will perform faster computation compared to traditional autoencoder based one-class classifier.
Chandan Gautam, Aruna Tiwari, Sundaram Suresh and Kapil Ahuja
null
1701.04508
null
null
On The Construction of Extreme Learning Machine for Online and Offline One-Class Classification - An Expanded Toolbox
cs.LG stat.ML
One-Class Classification (OCC) has been prime concern for researchers and effectively employed in various disciplines. But, traditional methods based one-class classifiers are very time consuming due to its iterative process and various parameters tuning. In this paper, we present six OCC methods based on extreme learning machine (ELM) and Online Sequential ELM (OSELM). Our proposed classifiers mainly lie in two categories: reconstruction based and boundary based, which supports both types of learning viz., online and offline learning. Out of various proposed methods, four are offline and remaining two are online methods. Out of four offline methods, two methods perform random feature mapping and two methods perform kernel feature mapping. Kernel feature mapping based approaches have been tested with RBF kernel and online version of one-class classifiers are tested with both types of nodes viz., additive and RBF. It is well known fact that threshold decision is a crucial factor in case of OCC, so, three different threshold deciding criteria have been employed so far and analyses the effectiveness of one threshold deciding criteria over another. Further, these methods are tested on two artificial datasets to check there boundary construction capability and on eight benchmark datasets from different discipline to evaluate the performance of the classifiers. Our proposed classifiers exhibit better performance compared to ten traditional one-class classifiers and ELM based two one-class classifiers. Through proposed one-class classifiers, we intend to expand the functionality of the most used toolbox for OCC i.e. DD toolbox. All of our methods are totally compatible with all the present features of the toolbox.
Chandan Gautam, Aruna Tiwari and Qian Leng
10.1016/j.neucom.2016.04.070
1701.04516
null
null
Towards prediction of rapid intensification in tropical cyclones with recurrent neural networks
cs.LG stat.AP
The problem where a tropical cyclone intensifies dramatically within a short period of time is known as rapid intensification. This has been one of the major challenges for tropical weather forecasting. Recurrent neural networks have been promising for time series problems which makes them appropriate for rapid intensification. In this paper, recurrent neural networks are used to predict rapid intensification cases of tropical cyclones from the South Pacific and South Indian Ocean regions. A class imbalanced problem is encountered which makes it very challenging to achieve promising performance. A simple strategy was proposed to include more positive cases for detection where the false positive rate was slightly improved. The limitations of building an efficient system remains due to the challenges of addressing the class imbalance problem encountered for rapid intensification prediction. This motivates further research in using innovative machine learning methods.
Rohitash Chandra
null
1701.04518
null
null
Faster K-Means Cluster Estimation
cs.LG cs.IR
There has been considerable work on improving popular clustering algorithm `K-means' in terms of mean squared error (MSE) and speed, both. However, most of the k-means variants tend to compute distance of each data point to each cluster centroid for every iteration. We propose a fast heuristic to overcome this bottleneck with only marginal increase in MSE. We observe that across all iterations of K-means, a data point changes its membership only among a small subset of clusters. Our heuristic predicts such clusters for each data point by looking at nearby clusters after the first iteration of k-means. We augment well known variants of k-means with our heuristic to demonstrate effectiveness of our heuristic. For various synthetic and real-world datasets, our heuristic achieves speed-up of up-to 3 times when compared to efficient variants of k-means.
Siddhesh Khandelwal, Amit Awekar
null
1701.046
null
null
Incremental Learning for Robot Perception through HRI
cs.RO cs.HC cs.LG
Scene understanding and object recognition is a difficult to achieve yet crucial skill for robots. Recently, Convolutional Neural Networks (CNN), have shown success in this task. However, there is still a gap between their performance on image datasets and real-world robotics scenarios. We present a novel paradigm for incrementally improving a robot's visual perception through active human interaction. In this paradigm, the user introduces novel objects to the robot by means of pointing and voice commands. Given this information, the robot visually explores the object and adds images from it to re-train the perception module. Our base perception module is based on recent development in object detection and recognition using deep learning. Our method leverages state of the art CNNs from off-line batch learning, human guidance, robot exploration and incremental on-line learning.
Sepehr Valipour, Camilo Perez, Martin Jagersand
null
1701.04693
null
null
Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks
cs.LG
Variational Autoencoders (VAEs) are expressive latent variable models that can be used to learn complex probability distributions from training data. However, the quality of the resulting model crucially relies on the expressiveness of the inference model. We introduce Adversarial Variational Bayes (AVB), a technique for training Variational Autoencoders with arbitrarily expressive inference models. We achieve this by introducing an auxiliary discriminative network that allows to rephrase the maximum-likelihood-problem as a two-player game, hence establishing a principled connection between VAEs and Generative Adversarial Networks (GANs). We show that in the nonparametric limit our method yields an exact maximum-likelihood assignment for the parameters of the generative model, as well as the exact posterior distribution over the latent variables given an observation. Contrary to competing approaches which combine VAEs with GANs, our approach has a clear theoretical justification, retains most advantages of standard Variational Autoencoders and is easy to implement.
Lars Mescheder, Sebastian Nowozin and Andreas Geiger
null
1701.04722
null
null
On the Sample Complexity of Graphical Model Selection for Non-Stationary Processes
cs.LG stat.ML
We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting of i.i.d. samples as well as the case of samples forming a stationary or underspread (non-stationary) processes. More generally, our model applies to any process model for which an efficient decorrelation can be obtained. By analyzing a particular model selection method, we derive a sufficient condition on the required sample size for accurate graphical model selection based on non-stationary data.
Nguyen Q. Tran and Oleksii Abramenko and Alexander Jung
null
1701.04724
null
null
Summoning Demons: The Pursuit of Exploitable Bugs in Machine Learning
cs.CR cs.LG
Governments and businesses increasingly rely on data analytics and machine learning (ML) for improving their competitive edge in areas such as consumer satisfaction, threat intelligence, decision making, and product efficiency. However, by cleverly corrupting a subset of data used as input to a target's ML algorithms, an adversary can perturb outcomes and compromise the effectiveness of ML technology. While prior work in the field of adversarial machine learning has studied the impact of input manipulation on correct ML algorithms, we consider the exploitation of bugs in ML implementations. In this paper, we characterize the attack surface of ML programs, and we show that malicious inputs exploiting implementation bugs enable strictly more powerful attacks than the classic adversarial machine learning techniques. We propose a semi-automated technique, called steered fuzzing, for exploring this attack surface and for discovering exploitable bugs in machine learning programs, in order to demonstrate the magnitude of this threat. As a result of our work, we responsibly disclosed five vulnerabilities, established three new CVE-IDs, and illuminated a common insecure practice across many machine learning systems. Finally, we outline several research directions for further understanding and mitigating this threat.
Rock Stevens, Octavian Suciu, Andrew Ruef, Sanghyun Hong, Michael Hicks, Tudor Dumitra\c{s}
null
1701.04739
null
null
Joint Deep Modeling of Users and Items Using Reviews for Recommendation
cs.LG cs.IR
A large amount of information exists in reviews written by users. This source of information has been ignored by most of the current recommender systems while it can potentially alleviate the sparsity problem and improve the quality of recommendations. In this paper, we present a deep model to learn item properties and user behaviors jointly from review text. The proposed model, named Deep Cooperative Neural Networks (DeepCoNN), consists of two parallel neural networks coupled in the last layers. One of the networks focuses on learning user behaviors exploiting reviews written by the user, and the other one learns item properties from the reviews written for the item. A shared layer is introduced on the top to couple these two networks together. The shared layer enables latent factors learned for users and items to interact with each other in a manner similar to factorization machine techniques. Experimental results demonstrate that DeepCoNN significantly outperforms all baseline recommender systems on a variety of datasets.
Lei Zheng, Vahid Noroozi, Philip S. Yu
null
1701.04783
null
null
Towards Principled Methods for Training Generative Adversarial Networks
stat.ML cs.LG
The goal of this paper is not to introduce a single algorithm or method, but to make theoretical steps towards fully understanding the training dynamics of generative adversarial networks. In order to substantiate our theoretical analysis, we perform targeted experiments to verify our assumptions, illustrate our claims, and quantify the phenomena. This paper is divided into three sections. The first section introduces the problem at hand. The second section is dedicated to studying and proving rigorously the problems including instability and saturation that arize when training generative adversarial networks. The third section examines a practical and theoretically grounded direction towards solving these problems, while introducing new tools to study them.
Martin Arjovsky, L\'eon Bottou
null
1701.04862
null
null
3D Morphology Prediction of Progressive Spinal Deformities from Probabilistic Modeling of Discriminant Manifolds
cs.LG stat.ML
We introduce a novel approach for predicting the progression of adolescent idiopathic scoliosis from 3D spine models reconstructed from biplanar X-ray images. Recent progress in machine learning have allowed to improve classification and prognosis rates, but lack a probabilistic framework to measure uncertainty in the data. We propose a discriminative probabilistic manifold embedding where locally linear mappings transform data points from high-dimensional space to corresponding low-dimensional coordinates. A discriminant adjacency matrix is constructed to maximize the separation between progressive and non-progressive groups of patients diagnosed with scoliosis, while minimizing the distance in latent variables belonging to the same class. To predict the evolution of deformation, a baseline reconstruction is projected onto the manifold, from which a spatiotemporal regression model is built from parallel transport curves inferred from neighboring exemplars. Rate of progression is modulated from the spine flexibility and curve magnitude of the 3D spine deformation. The method was tested on 745 reconstructions from 133 subjects using longitudinal 3D reconstructions of the spine, with results demonstrating the discriminatory framework can identify between progressive and non-progressive of scoliotic patients with a classification rate of 81% and prediction differences of 2.1$^{o}$ in main curve angulation, outperforming other manifold learning methods. Our method achieved a higher prediction accuracy and improved the modeling of spatiotemporal morphological changes in highly deformed spines compared to other learning methods.
Samuel Kadoury, William Mandel, Marjolaine Roy-Beaudry, Marie-Lyne Nault, Stefan Parent
null
1701.04869
null
null
Agglomerative Info-Clustering
cs.IT cs.LG math.IT
An agglomerative clustering of random variables is proposed, where clusters of random variables sharing the maximum amount of multivariate mutual information are merged successively to form larger clusters. Compared to the previous info-clustering algorithms, the agglomerative approach allows the computation to stop earlier when clusters of desired size and accuracy are obtained. An efficient algorithm is also derived based on the submodularity of entropy and the duality between the principal sequence of partitions and the principal sequence for submodular functions.
Chung Chan, Ali Al-Bashabsheh, Qiaoqiao Zhou
null
1701.04926
null
null
A Machine Learning Alternative to P-values
stat.ML cs.LG
This paper presents an alternative approach to p-values in regression settings. This approach, whose origins can be traced to machine learning, is based on the leave-one-out bootstrap for prediction error. In machine learning this is called the out-of-bag (OOB) error. To obtain the OOB error for a model, one draws a bootstrap sample and fits the model to the in-sample data. The out-of-sample prediction error for the model is obtained by calculating the prediction error for the model using the out-of-sample data. Repeating and averaging yields the OOB error, which represents a robust cross-validated estimate of the accuracy of the underlying model. By a simple modification to the bootstrap data involving "noising up" a variable, the OOB method yields a variable importance (VIMP) index, which directly measures how much a specific variable contributes to the prediction precision of a model. VIMP provides a scientifically interpretable measure of the effect size of a variable, we call the "predictive effect size", that holds whether the researcher's model is correct or not, unlike the p-value whose calculation is based on the assumed correctness of the model. We also discuss a marginal VIMP index, also easily calculated, which measures the marginal effect of a variable, or what we call "the discovery effect". The OOB procedure can be applied to both parametric and nonparametric regression models and requires only that the researcher can repeatedly fit their model to bootstrap and modified bootstrap data. We illustrate this approach on a survival data set involving patients with systolic heart failure and to a simulated survival data set where the model is incorrectly specified to illustrate its robustness to model misspecification.
Min Lu and Hemant Ishwaran
null
1701.04944
null
null
A Deep Convolutional Auto-Encoder with Pooling - Unpooling Layers in Caffe
cs.NE cs.CV cs.LG
This paper presents the development of several models of a deep convolutional auto-encoder in the Caffe deep learning framework and their experimental evaluation on the example of MNIST dataset. We have created five models of a convolutional auto-encoder which differ architecturally by the presence or absence of pooling and unpooling layers in the auto-encoder's encoder and decoder parts. Our results show that the developed models provide very good results in dimensionality reduction and unsupervised clustering tasks, and small classification errors when we used the learned internal code as an input of a supervised linear classifier and multi-layer perceptron. The best results were provided by a model where the encoder part contains convolutional and pooling layers, followed by an analogous decoder part with deconvolution and unpooling layers without the use of switch variables in the decoder part. The paper also discusses practical details of the creation of a deep convolutional auto-encoder in the very popular Caffe deep learning framework. We believe that our approach and results presented in this paper could help other researchers to build efficient deep neural network architectures in the future.
Volodymyr Turchenko, Eric Chalmers, Artur Luczak
null
1701.04949
null
null
Multilayer Perceptron Algebra
stat.ML cs.LG
Artificial Neural Networks(ANN) has been phenomenally successful on various pattern recognition tasks. However, the design of neural networks rely heavily on the experience and intuitions of individual developers. In this article, the author introduces a mathematical structure called MLP algebra on the set of all Multilayer Perceptron Neural Networks(MLP), which can serve as a guiding principle to build MLPs accommodating to the particular data sets, and to build complex MLPs from simpler ones.
Zhao Peng
null
1701.04968
null
null
Highly Efficient Hierarchical Online Nonlinear Regression Using Second Order Methods
cs.LG
We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used. For nonlinear modeling we use a hierarchical piecewise linear approach based on the notion of decision trees where the space of the regressor vectors is adaptively partitioned based on the performance. As the first time in the literature, we learn both the piecewise linear partitioning of the regressor space as well as the linear models in each region using highly effective second order methods, i.e., Newton-Raphson Methods. Hence, we avoid the well known over fitting issues by using piecewise linear models, however, since both the region boundaries as well as the linear models in each region are trained using the second order methods, we achieve substantial performance compared to the state of the art. We demonstrate our gains over the well known benchmark data sets and provide performance results in an individual sequence manner guaranteed to hold without any statistical assumptions. Hence, the introduced algorithms address computational complexity issues widely encountered in real life applications while providing superior guaranteed performance in a strong deterministic sense.
Burak C. Civek, Ibrahim Delibalta and Suleyman S. Kozat
null
1701.05053
null
null
Lipschitz Properties for Deep Convolutional Networks
cs.LG math.FA
In this paper we discuss the stability properties of convolutional neural networks. Convolutional neural networks are widely used in machine learning. In classification they are mainly used as feature extractors. Ideally, we expect similar features when the inputs are from the same class. That is, we hope to see a small change in the feature vector with respect to a deformation on the input signal. This can be established mathematically, and the key step is to derive the Lipschitz properties. Further, we establish that the stability results can be extended for more general networks. We give a formula for computing the Lipschitz bound, and compare it with other methods to show it is closer to the optimal value.
Radu Balan, Maneesh Singh, Dongmian Zou
null
1701.05217
null
null
Parsimonious Inference on Convolutional Neural Networks: Learning and applying on-line kernel activation rules
cs.CV cs.AI cs.LG cs.NE
A new, radical CNN design approach is presented in this paper, considering the reduction of the total computational load during inference. This is achieved by a new holistic intervention on both the CNN architecture and the training procedure, which targets to the parsimonious inference by learning to exploit or remove the redundant capacity of a CNN architecture. This is accomplished, by the introduction of a new structural element that can be inserted as an add-on to any contemporary CNN architecture, whilst preserving or even improving its recognition accuracy. Our approach formulates a systematic and data-driven method for developing CNNs that are trained to eventually change size and form in real-time during inference, targeting to the smaller possible computational footprint. Results are provided for the optimal implementation on a few modern, high-end mobile computing platforms indicating a significant speed-up of up to x3 times.
I. Theodorakopoulos, V. Pothos, D. Kastaniotis and N. Fragoulis
null
1701.05221
null
null
Recommendation under Capacity Constraints
stat.ML cs.IR cs.LG
In this paper, we investigate the common scenario where every candidate item for recommendation is characterized by a maximum capacity, i.e., number of seats in a Point-of-Interest (POI) or size of an item's inventory. Despite the prevalence of the task of recommending items under capacity constraints in a variety of settings, to the best of our knowledge, none of the known recommender methods is designed to respect capacity constraints. To close this gap, we extend three state-of-the art latent factor recommendation approaches: probabilistic matrix factorization (PMF), geographical matrix factorization (GeoMF), and bayesian personalized ranking (BPR), to optimize for both recommendation accuracy and expected item usage that respects the capacity constraints. We introduce the useful concepts of user propensity to listen and item capacity. Our experimental results in real-world datasets, both for the domain of item recommendation and POI recommendation, highlight the benefit of our method for the setting of recommendation under capacity constraints.
Konstantina Christakopoulou, Jaya Kawale, Arindam Banerjee
null
1701.05228
null
null
Online Structure Learning for Sum-Product Networks with Gaussian Leaves
stat.ML cs.LG
Sum-product networks have recently emerged as an attractive representation due to their dual view as a special type of deep neural network with clear semantics and a special type of probabilistic graphical model for which inference is always tractable. Those properties follow from some conditions (i.e., completeness and decomposability) that must be respected by the structure of the network. As a result, it is not easy to specify a valid sum-product network by hand and therefore structure learning techniques are typically used in practice. This paper describes the first online structure learning technique for continuous SPNs with Gaussian leaves. We also introduce an accompanying new parameter learning technique.
Wilson Hsu, Agastya Kalra, Pascal Poupart
null
1701.05265
null
null
Validity of Clusters Produced By kernel-$k$-means With Kernel-Trick
cs.LG stat.ML
This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper \cite{Gower:1986}. The first correction is needed in order to establish the existence of the kernel function used commonly in the kernel trick e.g. for $k$-means clustering algorithm, on the grounds of distance matrix. The correction encompasses the missing if-part proof and dropping unnecessary conditions. The second correction deals with transformation of the kernel matrix into a one embeddable in Euclidean space.
Mieczys{\l}aw A. K{\l}opotek
null
1701.05335
null
null
Stochastic Subsampling for Factorizing Huge Matrices
stat.ML cs.LG math.OC q-bio.NC
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors. At each iteration, the row dimension of a new sample is reduced by subsampling, resulting in lower time complexity compared to a simple streaming algorithm. Our method comes with convergence guarantees to reach a stationary point of the matrix-factorization problem. We demonstrate its efficiency on massive functional Magnetic Resonance Imaging data (2 TB), and on patches extracted from hyperspectral images (103 GB). For both problems, which involve different penalties on rows and columns, we obtain significant speed-ups compared to state-of-the-art algorithms.
Arthur Mensch (PARIETAL, NEUROSPIN), Julien Mairal (Thoth), Bertrand Thirion (PARIETAL, NEUROSPIN), Gael Varoquaux (NEUROSPIN, PARIETAL)
10.1109/TSP.2017.2752697
1701.05363
null
null
Variational Dropout Sparsifies Deep Neural Networks
stat.ML cs.LG
We explore a recently proposed Variational Dropout technique that provided an elegant Bayesian interpretation to Gaussian Dropout. We extend Variational Dropout to the case when dropout rates are unbounded, propose a way to reduce the variance of the gradient estimator and report first experimental results with individual dropout rates per weight. Interestingly, it leads to extremely sparse solutions both in fully-connected and convolutional layers. This effect is similar to automatic relevance determination effect in empirical Bayes but has a number of advantages. We reduce the number of parameters up to 280 times on LeNet architectures and up to 68 times on VGG-like networks with a negligible decrease of accuracy.
Dmitry Molchanov, Arsenii Ashukha and Dmitry Vetrov
null
1701.05369
null
null
Learning first-order definable concepts over structures of small degree
cs.LG cs.LO
We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some background structure. We show that within this framework, concepts defined by first-order formulas over a background structure of at most polylogarithmic degree can be learned in polylogarithmic time in the "probably approximately correct" learning sense.
Martin Grohe and Martin Ritzert
null
1701.05487
null
null
Fisher consistency for prior probability shift
stat.ML cs.LG stat.CO
We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver precise estimates in test datasets under prior probability and more general dataset shift. The usefulness of this unbiasedness concept is demonstrated with three examples of classifiers used for quantification: Adjusted Classify & Count, EM-algorithm and CDE-Iterate. We find that Adjusted Classify & Count and EM-algorithm are Fisher consistent. A counter-example shows that CDE-Iterate is not Fisher consistent and, therefore, cannot be trusted to deliver reliable estimates of class probabilities.
Dirk Tasche
null
1701.05512
null
null
PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications
cs.LG stat.ML
PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a number of modifications to the original model that both simplify its structure and improve its performance. 1) We use a discretized logistic mixture likelihood on the pixels, rather than a 256-way softmax, which we find to speed up training. 2) We condition on whole pixels, rather than R/G/B sub-pixels, simplifying the model structure. 3) We use downsampling to efficiently capture structure at multiple resolutions. 4) We introduce additional short-cut connections to further speed up optimization. 5) We regularize the model using dropout. Finally, we present state-of-the-art log likelihood results on CIFAR-10 to demonstrate the usefulness of these modifications.
Tim Salimans, Andrej Karpathy, Xi Chen, Diederik P. Kingma
null
1701.05517
null
null
Deep Neural Networks - A Brief History
cs.NE cs.CV cs.LG
Introduction to deep neural networks and their history.
Krzysztof J. Cios
null
1701.05549
null
null
Poisson--Gamma Dynamical Systems
stat.ML cs.LG
We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties and shrinks the model parameters, thus avoiding overfitting. We present an efficient MCMC inference algorithm that advances recent work on augmentation schemes for inference in negative binomial models. Finally, we demonstrate the model's inductive bias using a variety of real-world data sets, showing that it exhibits superior predictive performance over other models and infers highly interpretable latent structure.
Aaron Schein, Mingyuan Zhou, Hanna Wallach
null
1701.05573
null
null
Rare Disease Physician Targeting: A Factor Graph Approach
stat.ML cs.LG
In rare disease physician targeting, a major challenge is how to identify physicians who are treating diagnosed or underdiagnosed rare diseases patients. Rare diseases have extremely low incidence rate. For a specified rare disease, only a small number of patients are affected and a fractional of physicians are involved. The existing targeting methodologies, such as segmentation and profiling, are developed under mass market assumption. They are not suitable for rare disease market where the target classes are extremely imbalanced. The authors propose a graphical model approach to predict targets by jointly modeling physician and patient features from different data spaces and utilizing the extra relational information. Through an empirical example with medical claim and prescription data, the proposed approach demonstrates better accuracy in finding target physicians. The graph representation also provides visual interpretability of relationship among physicians and patients. The model can be extended to incorporate more complex dependency structures. This article contributes to the literature of exploring the benefit of utilizing relational dependencies among entities in healthcare industry.
Yong Cai, Yunlong Wang, Dong Dai
null
1701.05644
null
null
Git Blame Who?: Stylistic Authorship Attribution of Small, Incomplete Source Code Fragments
cs.LG cs.CR
Program authorship attribution has implications for the privacy of programmers who wish to contribute code anonymously. While previous work has shown that complete files that are individually authored can be attributed, we show here for the first time that accounts belonging to open source contributors containing short, incomplete, and typically uncompilable fragments can also be effectively attributed. We propose a technique for authorship attribution of contributor accounts containing small source code samples, such as those that can be obtained from version control systems or other direct comparison of sequential versions. We show that while application of previous methods to individual small source code samples yields an accuracy of about 73% for 106 programmers as a baseline, by ensembling and averaging the classification probabilities of a sufficiently large set of samples belonging to the same author we achieve 99% accuracy for assigning the set of samples to the correct author. Through these results, we demonstrate that attribution is an important threat to privacy for programmers even in real-world collaborative environments such as GitHub. Additionally, we propose the use of calibration curves to identify samples by unknown and previously unencountered authors in the open world setting. We show that we can also use these calibration curves in the case that we do not have linking information and thus are forced to classify individual samples directly. This is because the calibration curves allow us to identify which samples are more likely to have been correctly attributed. Using such a curve can help an analyst choose a cut-off point which will prevent most misclassifications, at the cost of causing the rejection of some of the more dubious correct attributions.
Edwin Dauber, Aylin Caliskan, Richard Harang, Gregory Shearer, Michael Weisman, Frederica Nelson, Rachel Greenstadt
10.2478/popets-2019-0053
1701.05681
null
null
Real-time Traffic Accident Risk Prediction based on Frequent Pattern Tree
stat.AP cs.LG
Traffic accident data are usually noisy, contain missing values, and heterogeneous. How to select the most important variables to improve real-time traffic accident risk prediction has become a concern of many recent studies. This paper proposes a novel variable selection method based on the Frequent Pattern tree (FP tree) algorithm. First, all the frequent patterns in the traffic accident dataset are discovered. Then for each frequent pattern, a new criterion, called the Relative Object Purity Ratio (ROPR) which we proposed, is calculated. This ROPR is added to the importance score of the variables that differentiate one frequent pattern from the others. To test the proposed method, a dataset was compiled from the traffic accidents records detected by only one detector on interstate highway I-64 in Virginia in 2005. This dataset was then linked to other variables such as real-time traffic information and weather conditions. Both the proposed method based on the FP tree algorithm, as well as the widely utilized, random forest method, were then used to identify the important variables or the Virginia dataset. The results indicate that there are some differences between the variables deemed important by the FP tree and those selected by the random forest method. Following this, two baseline models (i.e. a nearest neighbor (k-NN) method and a Bayesian network) were developed to predict accident risk based on the variables identified by both the FP tree method and the random forest method. The results show that the models based on the variable selection using the FP tree performed better than those based on the random forest method for several versions of the k-NN and Bayesian network models.The best results were derived from a Bayesian network model using variables from FP tree. That model could predict 61.11% of accidents accurately while having a false alarm rate of 38.16%.
Lei Lin, Qian Wang, Adel W. Sadek
null
1701.05691
null
null
Empirical Study of Drone Sound Detection in Real-Life Environment with Deep Neural Networks
cs.SD cs.LG
This work aims to investigate the use of deep neural network to detect commercial hobby drones in real-life environments by analyzing their sound data. The purpose of work is to contribute to a system for detecting drones used for malicious purposes, such as for terrorism. Specifically, we present a method capable of detecting the presence of commercial hobby drones as a binary classification problem based on sound event detection. We recorded the sound produced by a few popular commercial hobby drones, and then augmented this data with diverse environmental sound data to remedy the scarcity of drone sound data in diverse environments. We investigated the effectiveness of state-of-the-art event sound classification methods, i.e., a Gaussian Mixture Model (GMM), Convolutional Neural Network (CNN), and Recurrent Neural Network (RNN), for drone sound detection. Our empirical results, which were obtained with a testing dataset collected on an urban street, confirmed the effectiveness of these models for operating in a real environment. In summary, our RNN models showed the best detection performance with an F-Score of 0.8009 with 240 ms of input audio with a short processing time, indicating their applicability to real-time detection systems.
Sungho Jeon, Jong-Woo Shin, Young-Jun Lee, Woong-Hee Kim, YoungHyoun Kwon, and Hae-Yong Yang
null
1701.05779
null
null
Disentangling group and link persistence in Dynamic Stochastic Block models
cs.SI cs.LG physics.soc-ph stat.ML
We study the inference of a model of dynamic networks in which both communities and links keep memory of previous network states. By considering maximum likelihood inference from single snapshot observations of the network, we show that link persistence makes the inference of communities harder, decreasing the detectability threshold, while community persistence tends to make it easier. We analytically show that communities inferred from single network snapshot can share a maximum overlap with the underlying communities of a specific previous instant in time. This leads to time-lagged inference: the identification of past communities rather than present ones. Finally we compute the time lag and propose a corrected algorithm, the Lagged Snapshot Dynamic (LSD) algorithm, for community detection in dynamic networks. We analytically and numerically characterize the detectability transitions of such algorithm as a function of the memory parameters of the model and we make a comparison with a full dynamic inference.
Paolo Barucca, Fabrizio Lillo, Piero Mazzarisi, Daniele Tantari
null
1701.05804
null
null
Neural Offset Min-Sum Decoding
cs.IT cs.LG math.IT
Recently, it was shown that if multiplicative weights are assigned to the edges of a Tanner graph used in belief propagation decoding, it is possible to use deep learning techniques to find values for the weights which improve the error-correction performance of the decoder. Unfortunately, this approach requires many multiplications, which are generally expensive operations. In this paper, we suggest a more hardware-friendly approach in which offset min-sum decoding is augmented with learnable offset parameters. Our method uses no multiplications and has a parameter count less than half that of the multiplicative algorithm. This both speeds up training and provides a feasible path to hardware architectures. After describing our method, we compare the performance of the two neural decoding algorithms and show that our method achieves error-correction performance within 0.1 dB of the multiplicative approach and as much as 1 dB better than traditional belief propagation for the codes under consideration.
Loren Lugosch, Warren J. Gross
null
1701.05931
null
null
Learning Policies for Markov Decision Processes from Data
math.OC cs.LG stat.ML
We consider the problem of learning a policy for a Markov decision process consistent with data captured on the state-actions pairs followed by the policy. We assume that the policy belongs to a class of parameterized policies which are defined using features associated with the state-action pairs. The features are known a priori, however, only an unknown subset of them could be relevant. The policy parameters that correspond to an observed target policy are recovered using $\ell_1$-regularized logistic regression that best fits the observed state-action samples. We establish bounds on the difference between the average reward of the estimated and the original policy (regret) in terms of the generalization error and the ergodic coefficient of the underlying Markov chain. To that end, we combine sample complexity theory and sensitivity analysis of the stationary distribution of Markov chains. Our analysis suggests that to achieve regret within order $O(\sqrt{\epsilon})$, it suffices to use training sample size on the order of $\Omega(\log n \cdot poly(1/\epsilon))$, where $n$ is the number of the features. We demonstrate the effectiveness of our method on a synthetic robot navigation example.
Manjesh K. Hanawal, Hao Liu, Henghui Zhu, Ioannis Ch. Paschalidis
null
1701.05954
null
null
Label Propagation on K-partite Graphs with Heterophily
cs.LG cs.AI cs.SI
In this paper, for the first time, we study label propagation in heterogeneous graphs under heterophily assumption. Homophily label propagation (i.e., two connected nodes share similar labels) in homogeneous graph (with same types of vertices and relations) has been extensively studied before. Unfortunately, real-life networks are heterogeneous, they contain different types of vertices (e.g., users, images, texts) and relations (e.g., friendships, co-tagging) and allow for each node to propagate both the same and opposite copy of labels to its neighbors. We propose a $\mathcal{K}$-partite label propagation model to handle the mystifying combination of heterogeneous nodes/relations and heterophily propagation. With this model, we develop a novel label inference algorithm framework with update rules in near-linear time complexity. Since real networks change over time, we devise an incremental approach, which supports fast updates for both new data and evidence (e.g., ground truth labels) with guaranteed efficiency. We further provide a utility function to automatically determine whether an incremental or a re-modeling approach is favored. Extensive experiments on real datasets have verified the effectiveness and efficiency of our approach, and its superiority over the state-of-the-art label propagation methods.
Dingxiong Deng, Fan Bai, Yiqi Tang, Shuigeng Zhou, Cyrus Shahabi, Linhong Zhu
null
1701.06075
null
null
Lyrics-to-Audio Alignment by Unsupervised Discovery of Repetitive Patterns in Vowel Acoustics
cs.SD cs.AI cs.IR cs.LG eess.AS
Most of the previous approaches to lyrics-to-audio alignment used a pre-developed automatic speech recognition (ASR) system that innately suffered from several difficulties to adapt the speech model to individual singers. A significant aspect missing in previous works is the self-learnability of repetitive vowel patterns in the singing voice, where the vowel part used is more consistent than the consonant part. Based on this, our system first learns a discriminative subspace of vowel sequences, based on weighted symmetric non-negative matrix factorization (WS-NMF), by taking the self-similarity of a standard acoustic feature as an input. Then, we make use of canonical time warping (CTW), derived from a recent computer vision technique, to find an optimal spatiotemporal transformation between the text and the acoustic sequences. Experiments with Korean and English data sets showed that deploying this method after a pre-developed, unsupervised, singing source separation achieved more promising results than other state-of-the-art unsupervised approaches and an existing ASR-based system.
Sungkyun Chang, Kyogu Lee
10.1109/ACCESS.2017.2738558
1701.06078
null
null
Neurogenesis-Inspired Dictionary Learning: Online Model Adaption in a Changing World
cs.LG cs.AI cs.CV cs.NE stat.ML
In this paper, we focus on online representation learning in non-stationary environments which may require continuous adaptation of model architecture. We propose a novel online dictionary-learning (sparse-coding) framework which incorporates the addition and deletion of hidden units (dictionary elements), and is inspired by the adult neurogenesis phenomenon in the dentate gyrus of the hippocampus, known to be associated with improved cognitive function and adaptation to new environments. In the online learning setting, where new input instances arrive sequentially in batches, the neuronal-birth is implemented by adding new units with random initial weights (random dictionary elements); the number of new units is determined by the current performance (representation error) of the dictionary, higher error causing an increase in the birth rate. Neuronal-death is implemented by imposing l1/l2-regularization (group sparsity) on the dictionary within the block-coordinate descent optimization at each iteration of our online alternating minimization scheme, which iterates between the code and dictionary updates. Finally, hidden unit connectivity adaptation is facilitated by introducing sparsity in dictionary elements. Our empirical evaluation on several real-life datasets (images and language) as well as on synthetic data demonstrates that the proposed approach can considerably outperform the state-of-art fixed-size (nonadaptive) online sparse coding of Mairal et al. (2009) in the presence of nonstationary data. Moreover, we identify certain properties of the data (e.g., sparse inputs with nearly non-overlapping supports) and of the model (e.g., dictionary sparsity) associated with such improvements.
Sahil Garg, Irina Rish, Guillermo Cecchi, Aurelie Lozano
null
1701.06106
null
null
Effective and Extensible Feature Extraction Method Using Genetic Algorithm-Based Frequency-Domain Feature Search for Epileptic EEG Multi-classification
cs.LG cs.IT math.IT stat.ML
In this paper, a genetic algorithm-based frequency-domain feature search (GAFDS) method is proposed for the electroencephalogram (EEG) analysis of epilepsy. In this method, frequency-domain features are first searched and then combined with nonlinear features. Subsequently, these features are selected and optimized to classify EEG signals. The extracted features are analyzed experimentally. The features extracted by GAFDS show remarkable independence, and they are superior to the nonlinear features in terms of the ratio of inter-class distance and intra-class distance. Moreover, the proposed feature search method can additionally search for features of instantaneous frequency in a signal after Hilbert transformation. The classification results achieved using these features are reasonable, thus, GAFDS exhibits good extensibility. Multiple classic classifiers (i.e., $k$-nearest neighbor, linear discriminant analysis, decision tree, AdaBoost, multilayer perceptron, and Na\"ive Bayes) achieve good results by using the features generated by GAFDS method and the optimized selection. Specifically, the accuracies for the two-classification and three-classification problems may reach up to 99% and 97%, respectively. Results of several cross-validation experiments illustrate that GAFDS is effective in feature extraction for EEG classification. Therefore, the proposed feature selection and optimization model can improve classification accuracy.
Tingxi Wen, Zhongnan Zhang
null
1701.0612
null
null
Optimization on Product Submanifolds of Convolution Kernels
cs.CV cs.LG cs.NE
Recent advances in optimization methods used for training convolutional neural networks (CNNs) with kernels, which are normalized according to particular constraints, have shown remarkable success. This work introduces an approach for training CNNs using ensembles of joint spaces of kernels constructed using different constraints. For this purpose, we address a problem of optimization on ensembles of products of submanifolds (PEMs) of convolution kernels. To this end, we first propose three strategies to construct ensembles of PEMs in CNNs. Next, we expound their geometric properties (metric and curvature properties) in CNNs. We make use of our theoretical results by developing a geometry-aware SGD algorithm (G-SGD) for optimization on ensembles of PEMs to train CNNs. Moreover, we analyze convergence properties of G-SGD considering geometric properties of PEMs. In the experimental analyses, we employ G-SGD to train CNNs on Cifar-10, Cifar-100 and Imagenet datasets. The results show that geometric adaptive step size computation methods of G-SGD can improve training loss and convergence properties of CNNs. Moreover, we observe that classification performance of baseline CNNs can be boosted using G-SGD on ensembles of PEMs identified by multiple constraints.
Mete Ozay, Takayuki Okatani
null
1701.06123
null
null
Predicting Demographics of High-Resolution Geographies with Geotagged Tweets
cs.LG cs.SI stat.ML
In this paper, we consider the problem of predicting demographics of geographic units given geotagged Tweets that are composed within these units. Traditional survey methods that offer demographics estimates are usually limited in terms of geographic resolution, geographic boundaries, and time intervals. Thus, it would be highly useful to develop computational methods that can complement traditional survey methods by offering demographics estimates at finer geographic resolutions, with flexible geographic boundaries (i.e. not confined to administrative boundaries), and at different time intervals. While prior work has focused on predicting demographics and health statistics at relatively coarse geographic resolutions such as the county-level or state-level, we introduce an approach to predict demographics at finer geographic resolutions such as the blockgroup-level. For the task of predicting gender and race/ethnicity counts at the blockgroup-level, an approach adapted from prior work to our problem achieves an average correlation of 0.389 (gender) and 0.569 (race) on a held-out test dataset. Our approach outperforms this prior approach with an average correlation of 0.671 (gender) and 0.692 (race).
Omar Montasser and Daniel Kifer
null
1701.06225
null
null
What the Language You Tweet Says About Your Occupation
cs.CY cs.AI cs.CL cs.LG
Many aspects of people's lives are proven to be deeply connected to their jobs. In this paper, we first investigate the distinct characteristics of major occupation categories based on tweets. From multiple social media platforms, we gather several types of user information. From users' LinkedIn webpages, we learn their proficiencies. To overcome the ambiguity of self-reported information, a soft clustering approach is applied to extract occupations from crowd-sourced data. Eight job categories are extracted, including Marketing, Administrator, Start-up, Editor, Software Engineer, Public Relation, Office Clerk, and Designer. Meanwhile, users' posts on Twitter provide cues for understanding their linguistic styles, interests, and personalities. Our results suggest that people of different jobs have unique tendencies in certain language styles and interests. Our results also clearly reveal distinctive levels in terms of Big Five Traits for different jobs. Finally, a classifier is built to predict job types based on the features extracted from tweets. A high accuracy indicates a strong discrimination power of language features for job prediction task.
Tianran Hu, Haoyuan Xiao, Thuy-vy Thi Nguyen, Jiebo Luo
null
1701.06233
null
null
A Multichannel Convolutional Neural Network For Cross-language Dialog State Tracking
cs.CL cs.AI cs.LG
The fifth Dialog State Tracking Challenge (DSTC5) introduces a new cross-language dialog state tracking scenario, where the participants are asked to build their trackers based on the English training corpus, while evaluating them with the unlabeled Chinese corpus. Although the computer-generated translations for both English and Chinese corpus are provided in the dataset, these translations contain errors and careless use of them can easily hurt the performance of the built trackers. To address this problem, we propose a multichannel Convolutional Neural Networks (CNN) architecture, in which we treat English and Chinese language as different input channels of one single CNN model. In the evaluation of DSTC5, we found that such multichannel architecture can effectively improve the robustness against translation errors. Additionally, our method for DSTC5 is purely machine learning based and requires no prior knowledge about the target language. We consider this a desirable property for building a tracker in the cross-language context, as not every developer will be familiar with both languages.
Hongjie Shi, Takashi Ushio, Mitsuru Endo, Katsuyoshi Yamagami, Noriaki Horii
null
1701.06247
null
null
dna2vec: Consistent vector representations of variable-length k-mers
q-bio.QM cs.CL cs.LG stat.ML
One of the ubiquitous representation of long DNA sequence is dividing it into shorter k-mer components. Unfortunately, the straightforward vector encoding of k-mer as a one-hot vector is vulnerable to the curse of dimensionality. Worse yet, the distance between any pair of one-hot vectors is equidistant. This is particularly problematic when applying the latest machine learning algorithms to solve problems in biological sequence analysis. In this paper, we propose a novel method to train distributed representations of variable-length k-mers. Our method is based on the popular word embedding model word2vec, which is trained on a shallow two-layer neural network. Our experiments provide evidence that the summing of dna2vec vectors is akin to nucleotides concatenation. We also demonstrate that there is correlation between Needleman-Wunsch similarity score and cosine similarity of dna2vec vectors.
Patrick Ng
null
1701.06279
null
null
Comparative study on supervised learning methods for identifying phytoplankton species
stat.ML cs.LG
Phytoplankton plays an important role in marine ecosystem. It is defined as a biological factor to assess marine quality. The identification of phytoplankton species has a high potential for monitoring environmental, climate changes and for evaluating water quality. However, phytoplankton species identification is not an easy task owing to their variability and ambiguity due to thousands of micro and pico-plankton species. Therefore, the aim of this paper is to build a framework for identifying phytoplankton species and to perform a comparison on different features types and classifiers. We propose a new features type extracted from raw signals of phytoplankton species. We then analyze the performance of various classifiers on the proposed features type as well as two other features types for finding the robust one. Through experiments, it is found that Random Forest using the proposed features gives the best classification results with average accuracy up to 98.24%.
Thi-Thu-Hong Phan (LISIC), Emilie Poisson Caillault (LISIC), Andr\'e Bigand (LISIC)
10.1109/CCE.2016.7562650
1701.06421
null
null
Learning what to look in chest X-rays with a recurrent visual attention model
stat.ML cs.CV cs.LG
X-rays are commonly performed imaging tests that use small amounts of radiation to produce pictures of the organs, tissues, and bones of the body. X-rays of the chest are used to detect abnormalities or diseases of the airways, blood vessels, bones, heart, and lungs. In this work we present a stochastic attention-based model that is capable of learning what regions within a chest X-ray scan should be visually explored in order to conclude that the scan contains a specific radiological abnormality. The proposed model is a recurrent neural network (RNN) that learns to sequentially sample the entire X-ray and focus only on informative areas that are likely to contain the relevant information. We report on experiments carried out with more than $100,000$ X-rays containing enlarged hearts or medical devices. The model has been trained using reinforcement learning methods to learn task-specific policies.
Petros-Pavlos Ypsilantis and Giovanni Montana
null
1701.06452
null
null
Aggressive Sampling for Multi-class to Binary Reduction with Applications to Text Classification
stat.ML cs.LG
We address the problem of multi-class classification in the case where the number of classes is very large. We propose a double sampling strategy on top of a multi-class to binary reduction strategy, which transforms the original multi-class problem into a binary classification problem over pairs of examples. The aim of the sampling strategy is to overcome the curse of long-tailed class distributions exhibited in majority of large-scale multi-class classification problems and to reduce the number of pairs of examples in the expanded data. We show that this strategy does not alter the consistency of the empirical risk minimization principle defined over the double sample reduction. Experiments are carried out on DMOZ and Wikipedia collections with 10,000 to 100,000 classes where we show the efficiency of the proposed approach in terms of training and prediction time, memory consumption, and predictive performance with respect to state-of-the-art approaches.
Bikash Joshi, Massih-Reza Amini, Ioannis Partalas, Franck Iutzeler, Yury Maximov
null
1701.06511
null
null
ENIGMA: Efficient Learning-based Inference Guiding Machine
cs.LO cs.AI cs.LG
ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, using fast feature-based characterization of the clauses . The learned model is then tightly linked with the core prover and used as a basis of a new parameterized evaluation heuristic that provides fast ranking of all generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E's performance.
Jan Jakub\r{u}v, Josef Urban
null
1701.06532
null
null
Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer
cs.LG cs.CL cs.NE stat.ML
The capacity of a neural network to absorb information is limited by its number of parameters. Conditional computation, where parts of the network are active on a per-example basis, has been proposed in theory as a way of dramatically increasing model capacity without a proportional increase in computation. In practice, however, there are significant algorithmic and performance challenges. In this work, we address these challenges and finally realize the promise of conditional computation, achieving greater than 1000x improvements in model capacity with only minor losses in computational efficiency on modern GPU clusters. We introduce a Sparsely-Gated Mixture-of-Experts layer (MoE), consisting of up to thousands of feed-forward sub-networks. A trainable gating network determines a sparse combination of these experts to use for each example. We apply the MoE to the tasks of language modeling and machine translation, where model capacity is critical for absorbing the vast quantities of knowledge available in the training corpora. We present model architectures in which a MoE with up to 137 billion parameters is applied convolutionally between stacked LSTM layers. On large language modeling and machine translation benchmarks, these models achieve significantly better results than state-of-the-art at lower computational cost.
Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc Le, Geoffrey Hinton, Jeff Dean
null
1701.06538
null
null
Regularizing Neural Networks by Penalizing Confident Output Distributions
cs.NE cs.LG
We systematically explore regularizing neural networks by penalizing low entropy output distributions. We show that penalizing low entropy output distributions, which has been shown to improve exploration in reinforcement learning, acts as a strong regularizer in supervised learning. Furthermore, we connect a maximum entropy based confidence penalty to label smoothing through the direction of the KL divergence. We exhaustively evaluate the proposed confidence penalty and label smoothing on 6 common benchmarks: image classification (MNIST and Cifar-10), language modeling (Penn Treebank), machine translation (WMT'14 English-to-German), and speech recognition (TIMIT and WSJ). We find that both label smoothing and the confidence penalty improve state-of-the-art models across benchmarks without modifying existing hyperparameters, suggesting the wide applicability of these regularizers.
Gabriel Pereyra, George Tucker, Jan Chorowski, {\L}ukasz Kaiser, Geoffrey Hinton
null
1701.06548
null
null
On the Parametric Study of Lubricating Oil Production using an Artificial Neural Network (ANN) Approach
cs.LG
In this study, an Artificial Neural Network (ANN) approach is utilized to perform a parametric study on the process of extraction of lubricants from heavy petroleum cuts. To train the model, we used field data collected from an industrial plant. Operational conditions of feed and solvent flow rate, Temperature of streams and mixing rate were considered as the input to the model, whereas the flow rate of the main product was considered as the output of the ANN model. A feed-forward Multi-Layer Perceptron Neural Network was successfully applied to capture the relationship between inputs and output parameters.
Masood Tehrani and Mary Ahmadi
null
1701.06551
null
null
Identifying Nonlinear 1-Step Causal Influences in Presence of Latent Variables
cs.IT cs.LG math.IT stat.ME
We propose an approach for learning the causal structure in stochastic dynamical systems with a $1$-step functional dependency in the presence of latent variables. We propose an information-theoretic approach that allows us to recover the causal relations among the observed variables as long as the latent variables evolve without exogenous noise. We further propose an efficient learning method based on linear regression for the special sub-case when the dynamics are restricted to be linear. We validate the performance of our approach via numerical simulations.
Saber Salehkaleybar and Jalal Etesami and Negar Kiyavash
null
1701.06605
null
null
Revenue Forecasting for Enterprise Products
q-fin.GN cs.LG
For any business, planning is a continuous process, and typically business-owners focus on making both long-term planning aligned with a particular strategy as well as short-term planning that accommodates the dynamic market situations. An ability to perform an accurate financial forecast is crucial for effective planning. In this paper, we focus on providing an intelligent and efficient solution that will help in forecasting revenue using machine learning algorithms. We experiment with three different revenue forecasting models, and here we provide detailed insights into the methodology and their relative performance measured on real finance data. As a real-world application of our models, we partner with Microsoft's Finance organization (department that reports Microsoft's finances) to provide them a guidance on the projected revenue for upcoming quarters.
Amita Gajewar, Gagan Bansal
null
1701.06624
null
null
Convex Parameterizations and Fidelity Bounds for Nonlinear Identification and Reduced-Order Modelling
cs.SY cs.LG math.OC
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error minimization, leads to optimization problems that are generally non-convex in the model parameters and suffer from multiple local minima. In this work we present methods which address these problems through convex optimization, based on Lagrangian relaxation, dissipation inequalities, contraction theory, and semidefinite programming. We demonstrate the proposed methods with a model order reduction task for electronic circuit design and the identification of a pneumatic actuator from experiment.
Mark M. Tobenkin and Ian R. Manchester and Alexandre Megretski
null
1701.06652
null
null
Patchwork Kriging for Large-scale Gaussian Process Regression
cs.LG stat.ML
This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region. Unlike existing local partitioned GP approaches, we introduce a technique for patching together the local GP models nearly seamlessly to ensure that the local GP models for two neighboring regions produce nearly the same response prediction and prediction error variance on the boundary between the two regions. This largely mitigates the well-known discontinuity problem that degrades the boundary accuracy of existing local partitioned GP methods. Our main innovation is to represent the continuity conditions as additional pseudo-observations that the differences between neighboring GP responses are identically zero at an appropriately chosen set of boundary input locations. To predict the response at any input location, we simply augment the actual response observations with the pseudo-observations and apply standard GP prediction methods to the augmented data. In contrast to heuristic continuity adjustments, this has an advantage of working within a formal GP framework, so that the GP-based predictive uncertainty quantification remains valid. Our approach also inherits a sparse block-like structure for the sample covariance matrix, which results in computationally efficient closed-form expressions for the predictive mean and variance. In addition, we provide a new spatial partitioning scheme based on a recursive space partitioning along local principal component directions, which makes the proposed approach applicable for regression domains having more than two dimensions. Using three spatial datasets and three higher dimensional datasets, we investigate the numerical performance of the approach and compare it to several state-of-the-art approaches.
Chiwoo Park and Daniel Apley
null
1701.06655
null
null
A Contextual Bandit Approach for Stream-Based Active Learning
cs.LG
Contextual bandit algorithms -- a class of multi-armed bandit algorithms that exploit the contextual information -- have been shown to be effective in solving sequential decision making problems under uncertainty. A common assumption adopted in the literature is that the realized (ground truth) reward by taking the selected action is observed by the learner at no cost, which, however, is not realistic in many practical scenarios. When observing the ground truth reward is costly, a key challenge for the learner is how to judiciously acquire the ground truth by assessing the benefits and costs in order to balance learning efficiency and learning cost. From the information theoretic perspective, a perhaps even more interesting question is how much efficiency might be lost due to this cost. In this paper, we design a novel contextual bandit-based learning algorithm and endow it with the active learning capability. The key feature of our algorithm is that in addition to sending a query to an annotator for the ground truth, prior information about the ground truth learned by the learner is sent together, thereby reducing the query cost. We prove that by carefully choosing the algorithm parameters, the learning regret of the proposed algorithm achieves the same order as that of conventional contextual bandit algorithms in cost-free scenarios, implying that, surprisingly, cost due to acquiring the ground truth does not increase the learning regret in the long-run. Our analysis shows that prior information about the ground truth plays a critical role in improving the system performance in scenarios where active learning is necessary.
Linqi Song and Jie Xu
null
1701.06725
null
null
Collective Vertex Classification Using Recursive Neural Network
cs.LG cs.SI
Collective classification of vertices is a task of assigning categories to each vertex in a graph based on both vertex attributes and link structure. Nevertheless, some existing approaches do not use the features of neighbouring vertices properly, due to the noise introduced by these features. In this paper, we propose a graph-based recursive neural network framework for collective vertex classification. In this framework, we generate hidden representations from both attributes of vertices and representations of neighbouring vertices via recursive neural networks. Under this framework, we explore two types of recursive neural units, naive recursive neural unit and long short-term memory unit. We have conducted experiments on four real-world network datasets. The experimental results show that our frame- work with long short-term memory model achieves better results and outperforms several competitive baseline methods.
Qiongkai Xu, Qing Wang, Chenchen Xu and Lizhen Qu
null
1701.06751
null
null
Discriminative Neural Topic Models
cs.LG
We propose a neural network based approach for learning topics from text and image datasets. The model makes no assumptions about the conditional distribution of the observed features given the latent topics. This allows us to perform topic modelling efficiently using sentences of documents and patches of images as observed features, rather than limiting ourselves to words. Moreover, the proposed approach is online, and hence can be used for streaming data. Furthermore, since the approach utilizes neural networks, it can be implemented on GPU with ease, and hence it is very scalable.
Gaurav Pandey and Ambedkar Dukkipati
null
1701.06796
null
null
A Survey of Quantum Learning Theory
quant-ph cs.CC cs.LG
This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably Approximately Correct (PAC) and agnostic learning from classical or quantum examples.
Srinivasan Arunachalam (CWI) and Ronald de Wolf (CWI and U of Amsterdam)
null
1701.06806
null
null
Deep Network Guided Proof Search
cs.AI cs.LG cs.LO
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go. Automated first-order theorem provers can aid in the formalization and verification of mathematical theorems and play a crucial role in program analysis, theory reasoning, security, interpolation, and system verification. Here we suggest deep learning based guidance in the proof search of the theorem prover E. We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search. We give experimental evidence that with a hybrid, two-phase approach, deep learning based guidance can significantly reduce the average number of proof search steps while increasing the number of theorems proved. Using a few proof guidance strategies that leverage deep neural networks, we have found first-order proofs of 7.36% of the first-order logic translations of the Mizar Mathematical Library theorems that did not previously have ATP generated proofs. This increases the ratio of statements in the corpus with ATP generated proofs from 56% to 59%.
Sarah Loos, Geoffrey Irving, Christian Szegedy, Cezary Kaliszyk
null
1701.06972
null
null
On the Effectiveness of Discretizing Quantitative Attributes in Linear Classifiers
cs.LG
Learning algorithms that learn linear models often have high representation bias on real-world problems. In this paper, we show that this representation bias can be greatly reduced by discretization. Discretization is a common procedure in machine learning that is used to convert a quantitative attribute into a qualitative one. It is often motivated by the limitation of some learners to qualitative data. Discretization loses information, as fewer distinctions between instances are possible using discretized data relative to undiscretized data. In consequence, where discretization is not essential, it might appear desirable to avoid it. However, it has been shown that discretization often substantially reduces the error of the linear generative Bayesian classifier naive Bayes. This motivates a systematic study of the effectiveness of discretizing quantitative attributes for other linear classifiers. In this work, we study the effect of discretization on the performance of linear classifiers optimizing three distinct discriminative objective functions --- logistic regression (optimizing negative log-likelihood), support vector classifiers (optimizing hinge loss) and a zero-hidden layer artificial neural network (optimizing mean-square-error). We show that discretization can greatly increase the accuracy of these linear discriminative learners by reducing their representation bias, especially on big datasets. We substantiate our claims with an empirical study on $42$ benchmark datasets.
Nayyar A. Zaidi, Yang Du, Geoffrey I. Webb
null
1701.07114
null
null
jsCoq: Towards Hybrid Theorem Proving Interfaces
cs.PL cs.HC cs.LG cs.LO
We describe jsCcoq, a new platform and user environment for the Coq interactive proof assistant. The jsCoq system targets the HTML5-ECMAScript 2015 specification, and it is typically run inside a standards-compliant browser, without the need of external servers or services. Targeting educational use, jsCoq allows the user to start interaction with proof scripts right away, thanks to its self-contained nature. Indeed, a full Coq environment is packed along the proof scripts, easing distribution and installation. Starting to use jsCoq is as easy as clicking on a link. The current release ships more than 10 popular Coq libraries, and supports popular books such as Software Foundations or Certified Programming with Dependent Types. The new target platform has opened up new interaction and display possibilities. It has also fostered the development of some new Coq-related technology. In particular, we have implemented a new serialization-based protocol for interaction with the proof assistant, as well as a new package format for library distribution.
Emilio Jes\'us Gallego Arias (MINES ParisTech, PSL Research University, France), Beno\^it Pin (MINES ParisTech, PSL Research University, France), Pierre Jouvelot (MINES ParisTech, PSL Research University, France)
10.4204/EPTCS.239.2
1701.07125
null
null
CP-decomposition with Tensor Power Method for Convolutional Neural Networks Compression
cs.LG
Convolutional Neural Networks (CNNs) has shown a great success in many areas including complex image classification tasks. However, they need a lot of memory and computational cost, which hinders them from running in relatively low-end smart devices such as smart phones. We propose a CNN compression method based on CP-decomposition and Tensor Power Method. We also propose an iterative fine tuning, with which we fine-tune the whole network after decomposing each layer, but before decomposing the next layer. Significant reduction in memory and computation cost is achieved compared to state-of-the-art previous work with no more accuracy loss.
Marcella Astrid and Seung-Ik Lee
null
1701.07148
null
null
Personalized Classifier Ensemble Pruning Framework for Mobile Crowdsourcing
cs.DC cs.HC cs.LG
Ensemble learning has been widely employed by mobile applications, ranging from environmental sensing to activity recognitions. One of the fundamental issue in ensemble learning is the trade-off between classification accuracy and computational costs, which is the goal of ensemble pruning. During crowdsourcing, the centralized aggregator releases ensemble learning models to a large number of mobile participants for task evaluation or as the crowdsourcing learning results, while different participants may seek for different levels of the accuracy-cost trade-off. However, most of existing ensemble pruning approaches consider only one identical level of such trade-off. In this study, we present an efficient ensemble pruning framework for personalized accuracy-cost trade-offs via multi-objective optimization. Specifically, for the commonly used linear-combination style of the trade-off, we provide an objective-mixture optimization to further reduce the number of ensemble candidates. Experimental results show that our framework is highly efficient for personalized ensemble pruning, and achieves much better pruning performance with objective-mixture optimization when compared to state-of-art approaches.
Shaowei Wang, Liusheng Huang, Pengzhan Wang, Hongli Xu, Wei Yang
null
1701.07166
null
null
Malicious URL Detection using Machine Learning: A Survey
cs.LG cs.CR
Malicious URL, a.k.a. malicious website, is a common and serious threat to cybersecurity. Malicious URLs host unsolicited content (spam, phishing, drive-by exploits, etc.) and lure unsuspecting users to become victims of scams (monetary loss, theft of private information, and malware installation), and cause losses of billions of dollars every year. It is imperative to detect and act on such threats in a timely manner. Traditionally, this detection is done mostly through the usage of blacklists. However, blacklists cannot be exhaustive, and lack the ability to detect newly generated malicious URLs. To improve the generality of malicious URL detectors, machine learning techniques have been explored with increasing attention in recent years. This article aims to provide a comprehensive survey and a structural understanding of Malicious URL Detection techniques using machine learning. We present the formal formulation of Malicious URL Detection as a machine learning task, and categorize and review the contributions of literature studies that addresses different dimensions of this problem (feature representation, algorithm design, etc.). Further, this article provides a timely and comprehensive survey for a range of different audiences, not only for machine learning researchers and engineers in academia, but also for professionals and practitioners in cybersecurity industry, to help them understand the state of the art and facilitate their own research and practical applications. We also discuss practical issues in system design, open research challenges, and point out some important directions for future research.
Doyen Sahoo, Chenghao Liu, and Steven C.H. Hoi
null
1701.07179
null
null
Privileged Multi-label Learning
stat.ML cs.LG
This paper presents privileged multi-label learning (PrML) to explore and exploit the relationship between labels in multi-label learning problems. We suggest that for each individual label, it cannot only be implicitly connected with other labels via the low-rank constraint over label predictors, but also its performance on examples can receive the explicit comments from other labels together acting as an \emph{Oracle teacher}. We generate privileged label feature for each example and its individual label, and then integrate it into the framework of low-rank based multi-label learning. The proposed algorithm can therefore comprehensively explore and exploit label relationships by inheriting all the merits of privileged information and low-rank constraints. We show that PrML can be efficiently solved by dual coordinate descent algorithm using iterative optimization strategy with cheap updates. Experiments on benchmark datasets show that through privileged label features, the performance can be significantly improved and PrML is superior to several competing methods in most cases.
Shan You, Chang Xu, Yunhe Wang, Chao Xu, Dacheng Tao
null
1701.07194
null
null
Fast Exact k-Means, k-Medians and Bregman Divergence Clustering in 1D
cs.DS cs.AI cs.LG
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that uses $O(kn)$ space. It turns out that the problem has been considered under a different name more than twenty years ago. We present all the existing work that had been overlooked and compare the various solutions theoretically. Moreover, we show how to reduce the space usage for some of them, as well as generalize them to data structures that can quickly report an optimal $k$-Means clustering for any $k$. Finally we also generalize all the algorithms to work for the absolute distance and to work for any Bregman Divergence. We complement our theoretical contributions by experiments that compare the practical performance of the various algorithms.
Allan Gr{\o}nlund and Kasper Green Larsen and Alexander Mathiasen and Jesper Sindahl Nielsen and Stefan Schneider and Mingzhou Song
null
1701.07204
null
null
Learn&Fuzz: Machine Learning for Input Fuzzing
cs.AI cs.CR cs.LG cs.PL cs.SE
Fuzzing consists of repeatedly testing an application with modified, or fuzzed, inputs with the goal of finding security vulnerabilities in input-parsing code. In this paper, we show how to automate the generation of an input grammar suitable for input fuzzing using sample inputs and neural-network-based statistical machine-learning techniques. We present a detailed case study with a complex input format, namely PDF, and a large complex security-critical parser for this format, namely, the PDF parser embedded in Microsoft's new Edge browser. We discuss (and measure) the tension between conflicting learning and fuzzing goals: learning wants to capture the structure of well-formed inputs, while fuzzing wants to break that structure in order to cover unexpected code paths and find bugs. We also present a new algorithm for this learn&fuzz challenge which uses a learnt input probability distribution to intelligently guide where to fuzz inputs.
Patrice Godefroid, Hila Peleg, Rishabh Singh
null
1701.07232
null
null
Decoding Epileptogenesis in a Reduced State Space
q-bio.NC cs.LG q-bio.QM
We describe here the recent results of a multidisciplinary effort to design a biomarker that can actively and continuously decode the progressive changes in neuronal organization leading to epilepsy, a process known as epileptogenesis. Using an animal model of acquired epilepsy, wechronically record hippocampal evoked potentials elicited by an auditory stimulus. Using a set of reduced coordinates, our algorithm can identify universal smooth low-dimensional configurations of the auditory evoked potentials that correspond to distinct stages of epileptogenesis. We use a hidden Markov model to learn the dynamics of the evoked potential, as it evolves along these smooth low-dimensional subsets. We provide experimental evidence that the biomarker is able to exploit subtle changes in the evoked potential to reliably decode the stage of epileptogenesis and predict whether an animal will eventually recover from the injury, or develop spontaneous seizures.
Fran\c{c}ois G. Meyer, Alexander M. Benison, Zachariah Smith, and Daniel S. Barth
null
1701.07243
null
null
k*-Nearest Neighbors: From Global to Local
stat.ML cs.LG
The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has received much attention throughout the years, nevertheless this problem seems to have remained unsettled. In this paper we offer a simple approach to locally weighted regression/classification, where we make the bias-variance tradeoff explicit. Our formulation enables us to phrase a notion of optimal weights, and to efficiently find these weights as well as the optimal number of neighbors efficiently and adaptively, for each data point whose value we wish to estimate. The applicability of our approach is demonstrated on several datasets, showing superior performance over standard locally weighted methods.
Oren Anava, Kfir Y. Levy
null
1701.07266
null
null
Deep Reinforcement Learning: An Overview
cs.LG
We give an overview of recent exciting achievements of deep reinforcement learning (RL). We discuss six core elements, six important mechanisms, and twelve applications. We start with background of machine learning, deep learning and reinforcement learning. Next we discuss core RL elements, including value function, in particular, Deep Q-Network (DQN), policy, reward, model, planning, and exploration. After that, we discuss important mechanisms for RL, including attention and memory, unsupervised learning, transfer learning, multi-agent RL, hierarchical RL, and learning to learn. Then we discuss various applications of RL, including games, in particular, AlphaGo, robotics, natural language processing, including dialogue systems, machine translation, and text generation, computer vision, neural architecture design, business management, finance, healthcare, Industry 4.0, smart grid, intelligent transportation systems, and computer systems. We mention topics not reviewed yet, and list a collection of RL resources. After presenting a brief summary, we close with discussions. Please see Deep Reinforcement Learning, arXiv:1810.06339, for a significant update.
Yuxi Li
null
1701.07274
null
null
Learning Light Transport the Reinforced Way
cs.LG cs.GR
We show that the equations of reinforcement learning and light transport simulation are related integral equations. Based on this correspondence, a scheme to learn importance while sampling path space is derived. The new approach is demonstrated in a consistent light transport simulation algorithm that uses reinforcement learning to progressively learn where light comes from. As using this information for importance sampling includes information about visibility, too, the number of light transport paths with zero contribution is dramatically reduced, resulting in much less noisy images within a fixed time budget.
Ken Dahm and Alexander Keller
null
1701.07403
null
null
A Convex Similarity Index for Sparse Recovery of Missing Image Samples
cs.LG stat.ML
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used as the similarity criterion between the original and the reconstructed images. The proposed criterion called Convex SIMilarity (CSIM) index is a modified version of the Structural SIMilarity (SSIM) index, which despite its predecessor, is convex and uni-modal. We derive mathematical properties for the proposed index and show how to optimally choose the parameters of the proposed criterion, investigating the Restricted Isometry (RIP) and error-sensitivity properties. We also propose an iterative sparse recovery method based on a constrained $l_1$-norm minimization problem, incorporating CSIM as the fidelity criterion. The resulting convex optimization problem is solved via an algorithm based on Alternating Direction Method of Multipliers (ADMM). Taking advantage of the convexity of the CSIM index, we also prove the convergence of the algorithm to the globally optimal solution of the proposed optimization problem, starting from any arbitrary point. Simulation results confirm the performance of the new similarity index as well as the proposed algorithm for missing sample recovery of image patch signals.
Amirhossein Javaheri, Hadi Zayyani and Farokh Marvasti
null
1701.07422
null
null
Robust mixture of experts modeling using the $t$ distribution
stat.ME cs.LG stat.ML
Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification, and clustering. For regression and cluster analyses of continuous data, MoE usually use normal experts following the Gaussian distribution. However, for a set of data containing a group or groups of observations with heavy tails or atypical observations, the use of normal experts is unsuitable and can unduly affect the fit of the MoE model. We introduce a robust MoE modeling using the $t$ distribution. The proposed $t$ MoE (TMoE) deals with these issues regarding heavy-tailed and noisy data. We develop a dedicated expectation-maximization (EM) algorithm to estimate the parameters of the proposed model by monotonically maximizing the observed data log-likelihood. We describe how the presented model can be used in prediction and in model-based clustering of regression data. The proposed model is validated on numerical experiments carried out on simulated data, which show the effectiveness and the robustness of the proposed model in terms of modeling non-linear regression functions as well as in model-based clustering. Then, it is applied to the real-world data of tone perception for musical data analysis, and the one of temperature anomalies for the analysis of climate change data. The obtained results show the usefulness of the TMoE model for practical applications.
Faicel Chamroukhi
10.1016/j.neunet.2016.03.002
1701.07429
null
null
Exploiting Convolutional Neural Network for Risk Prediction with Medical Feature Embedding
cs.LG stat.ML
The widespread availability of electronic health records (EHRs) promises to usher in the era of personalized medicine. However, the problem of extracting useful clinical representations from longitudinal EHR data remains challenging. In this paper, we explore deep neural network models with learned medical feature embedding to deal with the problems of high dimensionality and temporality. Specifically, we use a multi-layer convolutional neural network (CNN) to parameterize the model and is thus able to capture complex non-linear longitudinal evolution of EHRs. Our model can effectively capture local/short temporal dependency in EHRs, which is beneficial for risk prediction. To account for high dimensionality, we use the embedding medical features in the CNN model which hold the natural medical concepts. Our initial experiments produce promising results and demonstrate the effectiveness of both the medical feature embedding and the proposed convolutional neural network in risk prediction on cohorts of congestive heart failure and diabetes patients compared with several strong baselines.
Zhengping Che, Yu Cheng, Zhaonan Sun, Yan Liu
null
1701.07474
null
null
A Model-based Projection Technique for Segmenting Customers
stat.ME cs.LG stat.AP stat.ML
We consider the problem of segmenting a large population of customers into non-overlapping groups with similar preferences, using diverse preference observations such as purchases, ratings, clicks, etc. over subsets of items. We focus on the setting where the universe of items is large (ranging from thousands to millions) and unstructured (lacking well-defined attributes) and each customer provides observations for only a few items. These data characteristics limit the applicability of existing techniques in marketing and machine learning. To overcome these limitations, we propose a model-based projection technique, which transforms the diverse set of observations into a more comparable scale and deals with missing data by projecting the transformed data onto a low-dimensional space. We then cluster the projected data to obtain the customer segments. Theoretically, we derive precise necessary and sufficient conditions that guarantee asymptotic recovery of the true customer segments. Empirically, we demonstrate the speed and performance of our method in two real-world case studies: (a) 84% improvement in the accuracy of new movie recommendations on the MovieLens data set and (b) 6% improvement in the performance of similar item recommendations algorithm on an offline dataset at eBay. We show that our method outperforms standard latent-class and demographic-based techniques.
Srikanth Jagabathula, Lakshminarayanan Subramanian, Ashwin Venkataraman
null
1701.07483
null
null
FPGA Architecture for Deep Learning and its application to Planetary Robotics
cs.LG astro-ph.IM cs.RO
Autonomous control systems onboard planetary rovers and spacecraft benefit from having cognitive capabilities like learning so that they can adapt to unexpected situations in-situ. Q-learning is a form of reinforcement learning and it has been efficient in solving certain class of learning problems. However, embedded systems onboard planetary rovers and spacecraft rarely implement learning algorithms due to the constraints faced in the field, like processing power, chip size, convergence rate and costs due to the need for radiation hardening. These challenges present a compelling need for a portable, low-power, area efficient hardware accelerator to make learning algorithms practical onboard space hardware. This paper presents a FPGA implementation of Q-learning with Artificial Neural Networks (ANN). This method matches the massive parallelism inherent in neural network software with the fine-grain parallelism of an FPGA hardware thereby dramatically reducing processing time. Mars Science Laboratory currently uses Xilinx-Space-grade Virtex FPGA devices for image processing, pyrotechnic operation control and obstacle avoidance. We simulate and program our architecture on a Xilinx Virtex 7 FPGA. The architectural implementation for a single neuron Q-learning and a more complex Multilayer Perception (MLP) Q-learning accelerator has been demonstrated. The results show up to a 43-fold speed up by Virtex 7 FPGAs compared to a conventional Intel i5 2.3 GHz CPU. Finally, we simulate the proposed architecture using the Symphony simulator and compiler from Xilinx, and evaluate the performance and power consumption.
Pranay Gankidi and Jekan Thangavelautham
null
1701.07543
null
null
Dynamic Regret of Strongly Adaptive Methods
cs.LG
To cope with changing environments, recent developments in online learning have introduced the concepts of adaptive regret and dynamic regret independently. In this paper, we illustrate an intrinsic connection between these two concepts by showing that the dynamic regret can be expressed in terms of the adaptive regret and the functional variation. This observation implies that strongly adaptive algorithms can be directly leveraged to minimize the dynamic regret. As a result, we present a series of strongly adaptive algorithms that have small dynamic regrets for convex functions, exponentially concave functions, and strongly convex functions, respectively. To the best of our knowledge, this is the first time that exponential concavity is utilized to upper bound the dynamic regret. Moreover, all of those adaptive algorithms do not need any prior knowledge of the functional variation, which is a significant advantage over previous specialized methods for minimizing dynamic regret.
Lijun Zhang, Tianbao Yang, Rong Jin, Zhi-Hua Zhou
null
1701.0757
null
null
Fast and Accurate Time Series Classification with WEASEL
cs.DS cs.LG stat.ML
Time series (TS) occur in many scientific and commercial applications, ranging from earth surveillance to industry automation to the smart grids. An important type of TS analysis is classification, which can, for instance, improve energy load forecasting in smart grids by detecting the types of electronic devices based on their energy consumption profiles recorded by automatic sensors. Such sensor-driven applications are very often characterized by (a) very long TS and (b) very large TS datasets needing classification. However, current methods to time series classification (TSC) cannot cope with such data volumes at acceptable accuracy; they are either scalable but offer only inferior classification quality, or they achieve state-of-the-art classification quality but cannot scale to large data volumes. In this paper, we present WEASEL (Word ExtrAction for time SEries cLassification), a novel TSC method which is both scalable and accurate. Like other state-of-the-art TSC methods, WEASEL transforms time series into feature vectors, using a sliding-window approach, which are then analyzed through a machine learning classifier. The novelty of WEASEL lies in its specific method for deriving features, resulting in a much smaller yet much more discriminative feature set. On the popular UCR benchmark of 85 TS datasets, WEASEL is more accurate than the best current non-ensemble algorithms at orders-of-magnitude lower classification and training times, and it is almost as accurate as ensemble classifiers, whose computational complexity makes them inapplicable even for mid-size datasets. The outstanding robustness of WEASEL is also confirmed by experiments on two real smart grid datasets, where it out-of-the-box achieves almost the same accuracy as highly tuned, domain-specific methods.
Patrick Sch\"afer and Ulf Leser
10.1145/3132847.3132980
1701.07681
null
null
Theoretical Foundations of Forward Feature Selection Methods based on Mutual Information
stat.ML cs.LG
Feature selection problems arise in a variety of applications, such as microarray analysis, clinical prediction, text categorization, image classification and face recognition, multi-label learning, and classification of internet traffic. Among the various classes of methods, forward feature selection methods based on mutual information have become very popular and are widely used in practice. However, comparative evaluations of these methods have been limited by being based on specific datasets and classifiers. In this paper, we develop a theoretical framework that allows evaluating the methods based on their theoretical properties. Our framework is grounded on the properties of the target objective function that the methods try to approximate, and on a novel categorization of features, according to their contribution to the explanation of the class; we derive upper and lower bounds for the target objective function and relate these bounds with the feature types. Then, we characterize the types of approximations taken by the methods, and analyze how these approximations cope with the good properties of the target objective function. Additionally, we develop a distributional setting designed to illustrate the various deficiencies of the methods, and provide several examples of wrong feature selections. Based on our work, we identify clearly the methods that should be avoided, and the methods that currently have the best performance.
Francisco Macedo and M. Ros\'ario Oliveira and Ant\'onio Pacheco and Rui Valadas
null
1701.07761
null
null
Riemannian-geometry-based modeling and clustering of network-wide non-stationary time series: The brain-network case
cs.LG stat.ML
This paper advocates Riemannian multi-manifold modeling in the context of network-wide non-stationary time-series analysis. Time-series data, collected sequentially over time and across a network, yield features which are viewed as points in or close to a union of multiple submanifolds of a Riemannian manifold, and distinguishing disparate time series amounts to clustering multiple Riemannian submanifolds. To support the claim that exploiting the latent Riemannian geometry behind many statistical features of time series is beneficial to learning from network data, this paper focuses on brain networks and puts forth two feature-generation schemes for network-wide dynamic time series. The first is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positive-definite matrices. Capitilizing on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their geometrical properties, revealed within Riemannian feature spaces. Extensive numerical tests demonstrate that the proposed framework outperforms classical and state-of-the-art techniques in clustering brain-network states/structures hidden beneath synthetic fMRI time series and brain-activity signals generated from real brain-network structural connectivity matrices.
Konstantinos Slavakis and Shiva Salsabilian and David S. Wack and Sarah F. Muldoon and Henry E. Baidoo-Williams and Jean M. Vettel and Matthew Cieslak and Scott T. Grafton
null
1701.07767
null
null
Linear convergence of SDCA in statistical estimation
stat.ML cs.LG
In this paper, we consider stochastic dual coordinate (SDCA) {\em without} strongly convex assumption or convex assumption. We show that SDCA converges linearly under mild conditions termed restricted strong convexity. This covers a wide array of popular statistical models including Lasso, group Lasso, and logistic regression with $\ell_1$ regularization, corrected Lasso and linear regression with SCAD regularizer. This significantly improves previous convergence results on SDCA for problems that are not strongly convex. As a by product, we derive a dual free form of SDCA that can handle general regularization term, which is of interest by itself.
Chao Qu, Huan Xu
null
1701.07808
null
null
DroidStar: Callback Typestates for Android Classes
cs.LO cs.LG cs.PL
Event-driven programming frameworks, such as Android, are based on components with asynchronous interfaces. The protocols for interacting with these components can often be described by finite-state machines we dub *callback typestates*. Callback typestates are akin to classical typestates, with the difference that their outputs (callbacks) are produced asynchronously. While useful, these specifications are not commonly available, because writing them is difficult and error-prone. Our goal is to make the task of producing callback typestates significantly easier. We present a callback typestate assistant tool, DroidStar, that requires only limited user interaction to produce a callback typestate. Our approach is based on an active learning algorithm, L*. We improved the scalability of equivalence queries (a key component of L*), thus making active learning tractable on the Android system. We use DroidStar to learn callback typestates for Android classes both for cases where one is already provided by the documentation, and for cases where the documentation is unclear. The results show that DroidStar learns callback typestates accurately and efficiently. Moreover, in several cases, the synthesized callback typestates uncovered surprising and undocumented behaviors.
Arjun Radhakrishna, Nicholas V. Lewchenko, Shawn Meier, Sergio Mover, Krishna Chaitanya Sripada, Damien Zufferey, Bor-Yuh Evan Chang, and Pavol \v{C}ern\'y
null
1701.07842
null
null
An Empirical Analysis of Feature Engineering for Predictive Modeling
cs.LG
Machine learning models, such as neural networks, decision trees, random forests, and gradient boosting machines, accept a feature vector, and provide a prediction. These models learn in a supervised fashion where we provide feature vectors mapped to the expected output. It is common practice to engineer new features from the provided feature set. Such engineered features will either augment or replace portions of the existing feature vector. These engineered features are essentially calculated fields based on the values of the other features. Engineering such features is primarily a manual, time-consuming task. Additionally, each type of model will respond differently to different kinds of engineered features. This paper reports empirical research to demonstrate what kinds of engineered features are best suited to various machine learning model types. We provide this recommendation by generating several datasets that we designed to benefit from a particular type of engineered feature. The experiment demonstrates to what degree the machine learning model can synthesize the needed feature on its own. If a model can synthesize a planned feature, it is not necessary to provide that feature. The research demonstrated that the studied models do indeed perform differently with various types of engineered features.
Jeff Heaton
10.1109/SECON.2016.7506650
1701.07852
null
null
Wasserstein GAN
stat.ML cs.LG
We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to other distances between distributions.
Martin Arjovsky, Soumith Chintala, L\'eon Bottou
null
1701.07875
null
null
Information Theoretic Limits for Linear Prediction with Graph-Structured Sparsity
cs.LG cs.IT math.IT stat.ML
We analyze the necessary number of samples for sparse vector recovery in a noisy linear prediction setup. This model includes problems such as linear regression and classification. We focus on structured graph models. In particular, we prove that sufficient number of samples for the weighted graph model proposed by Hegde and others is also necessary. We use the Fano's inequality on well constructed ensembles as our main tool in establishing information theoretic lower bounds.
Adarsh Barik, Jean Honorio, Mohit Tawarmalani
null
1701.07895
null
null
The Price of Differential Privacy For Online Learning
cs.LG stat.ML
We design differentially private algorithms for the problem of online linear optimization in the full information and bandit settings with optimal $\tilde{O}(\sqrt{T})$ regret bounds. In the full-information setting, our results demonstrate that $\epsilon$-differential privacy may be ensured for free -- in particular, the regret bounds scale as $O(\sqrt{T})+\tilde{O}\left(\frac{1}{\epsilon}\right)$. For bandit linear optimization, and as a special case, for non-stochastic multi-armed bandits, the proposed algorithm achieves a regret of $\tilde{O}\left(\frac{1}{\epsilon}\sqrt{T}\right)$, while the previously known best regret bound was $\tilde{O}\left(\frac{1}{\epsilon}T^{\frac{2}{3}}\right)$.
Naman Agarwal and Karan Singh
null
1701.07953
null
null
Reinforced stochastic gradient descent for deep neural network learning
cs.LG cs.NE
Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the high-dimensional parameter space. Therefore, it is highly desirable to design an efficient algorithm to escape from these saddle points and reach a parameter region of better generalization capabilities. Here, we propose a simple extension of SGD, namely reinforced SGD, which simply adds previous first-order gradients in a stochastic manner with a probability that increases with learning time. As verified in a simple synthetic dataset, this method significantly accelerates learning compared with the original SGD. Surprisingly, it dramatically reduces over-fitting effects, even compared with state-of-the-art adaptive learning algorithm---Adam. For a benchmark handwritten digits dataset, the learning performance is comparable to Adam, yet with an extra advantage of requiring one-fold less computer memory. The reinforced SGD is also compared with SGD with fixed or adaptive momentum parameter and Nesterov's momentum, which shows that the proposed framework is able to reach a similar generalization accuracy with less computational costs. Overall, our method introduces stochastic memory into gradients, which plays an important role in understanding how gradient-based training algorithms can work and its relationship with generalization abilities of deep networks.
Haiping Huang and Taro Toyoizumi
null
1701.07974
null
null
Modelling Competitive Sports: Bradley-Terry-\'{E}l\H{o} Models for Supervised and On-Line Learning of Paired Competition Outcomes
stat.ML cs.LG stat.AP stat.ME
Prediction and modelling of competitive sports outcomes has received much recent attention, especially from the Bayesian statistics and machine learning communities. In the real world setting of outcome prediction, the seminal \'{E}l\H{o} update still remains, after more than 50 years, a valuable baseline which is difficult to improve upon, though in its original form it is a heuristic and not a proper statistical "model". Mathematically, the \'{E}l\H{o} rating system is very closely related to the Bradley-Terry models, which are usually used in an explanatory fashion rather than in a predictive supervised or on-line learning setting. Exploiting this close link between these two model classes and some newly observed similarities, we propose a new supervised learning framework with close similarities to logistic regression, low-rank matrix completion and neural networks. Building on it, we formulate a class of structured log-odds models, unifying the desirable properties found in the above: supervised probabilistic prediction of scores and wins/draws/losses, batch/epoch and on-line learning, as well as the possibility to incorporate features in the prediction, without having to sacrifice simplicity, parsimony of the Bradley-Terry models, or computational efficiency of \'{E}l\H{o}'s original approach. We validate the structured log-odds modelling approach in synthetic experiments and English Premier League outcomes, where the added expressivity yields the best predictions reported in the state-of-art, close to the quality of contemporary betting odds.
Franz J. Kir\'aly and Zhaozhi Qian
null
1701.08055
null
null
Model-Free Control of Thermostatically Controlled Loads Connected to a District Heating Network
cs.SY cs.LG
Optimal control of thermostatically controlled loads connected to a district heating network is considered a sequential decision- making problem under uncertainty. The practicality of a direct model-based approach is compromised by two challenges, namely scalability due to the large dimensionality of the problem and the system identification required to identify an accurate model. To help in mitigating these problems, this paper leverages on recent developments in reinforcement learning in combination with a market-based multi-agent system to obtain a scalable solution that obtains a significant performance improvement in a practical learning time. The control approach is applied on a scenario comprising 100 thermostatically controlled loads connected to a radial district heating network supplied by a central combined heat and power plant. Both for an energy arbitrage and a peak shaving objective, the control approach requires 60 days to obtain a performance within 65% of a theoretical lower bound on the cost.
Bert J. Claessens, Dirk Vanhoudt, Johan Desmedt, Frederik Ruelens
null
1701.08074
null
null
Faster Discovery of Faster System Configurations with Spectral Learning
cs.SE cs.LG
Despite the huge spread and economical importance of configurable software systems, there is unsatisfactory support in utilizing the full potential of these systems with respect to finding performance-optimal configurations. Prior work on predicting the performance of software configurations suffered from either (a) requiring far too many sample configurations or (b) large variances in their predictions. Both these problems can be avoided using the WHAT spectral learner. WHAT's innovation is the use of the spectrum (eigenvalues) of the distance matrix between the configurations of a configurable software system, to perform dimensionality reduction. Within that reduced configuration space, many closely associated configurations can be studied by executing only a few sample configurations. For the subject systems studied here, a few dozen samples yield accurate and stable predictors - less than 10% prediction error, with a standard deviation of less than 2%. When compared to the state of the art, WHAT (a) requires 2 to 10 times fewer samples to achieve similar prediction accuracies, and (b) its predictions are more stable (i.e., have lower standard deviation). Furthermore, we demonstrate that predictive models generated by WHAT can be used by optimizers to discover system configurations that closely approach the optimal performance.
Vivek Nair, Tim Menzies, Norbert Siegmund, Sven Apel
10.1007/s1051
1701.08106
null
null
Multiclass MinMax Rank Aggregation
cs.LG cs.AI q-bio.QM stat.ML
We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall {\tau} and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on the Mallows model and genomic data.
Pan Li and Olgica Milenkovic
null
1701.08305
null
null
Deep Recurrent Neural Network for Protein Function Prediction from Sequence
q-bio.QM cs.LG q-bio.BM stat.ML
As high-throughput biological sequencing becomes faster and cheaper, the need to extract useful information from sequencing becomes ever more paramount, often limited by low-throughput experimental characterizations. For proteins, accurate prediction of their functions directly from their primary amino-acid sequences has been a long standing challenge. Here, machine learning using artificial recurrent neural networks (RNN) was applied towards classification of protein function directly from primary sequence without sequence alignment, heuristic scoring or feature engineering. The RNN models containing long-short-term-memory (LSTM) units trained on public, annotated datasets from UniProt achieved high performance for in-class prediction of four important protein functions tested, particularly compared to other machine learning algorithms using sequence-derived protein features. RNN models were used also for out-of-class predictions of phylogenetically distinct protein families with similar functions, including proteins of the CRISPR-associated nuclease, ferritin-like iron storage and cytochrome P450 families. Applying the trained RNN models on the partially unannotated UniRef100 database predicted not only candidates validated by existing annotations but also currently unannotated sequences. Some RNN predictions for the ferritin-like iron sequestering function were experimentally validated, even though their sequences differ significantly from known, characterized proteins and from each other and cannot be easily predicted using popular bioinformatics methods. As sequencing and experimental characterization data increases rapidly, the machine-learning approach based on RNN could be useful for discovery and prediction of homologues for a wide range of protein functions.
Xueliang Liu
null
1701.08318
null
null
Feature base fusion for splicing forgery detection based on neuro fuzzy
cs.CV cs.AI cs.LG
Most of researches on image forensics have been mainly focused on detection of artifacts introduced by a single processing tool. They lead in the development of many specialized algorithms looking for one or more particular footprints under specific settings. Naturally, the performance of such algorithms are not perfect, and accordingly the provided output might be noisy, inaccurate and only partially correct. Furthermore, a forged image in practical scenarios is often the result of utilizing several tools available by image-processing software systems. Therefore, reliable tamper detection requires developing more poweful tools to deal with various tempering scenarios. Fusion of forgery detection tools based on Fuzzy Inference System has been used before for addressing this problem. Adjusting the membership functions and defining proper fuzzy rules for attaining to better results are time-consuming processes. This can be accounted as main disadvantage of fuzzy inference systems. In this paper, a Neuro-Fuzzy inference system for fusion of forgery detection tools is developed. The neural network characteristic of these systems provides appropriate tool for automatically adjusting the membership functions. Moreover, initial fuzzy inference system is generated based on fuzzy clustering techniques. The proposed framework is implemented and validated on a benchmark image splicing data set in which three forgery detection tools are fused based on adaptive Neuro-Fuzzy inference system. The outcome of the proposed method reveals that applying Neuro Fuzzy inference systems could be a better approach for fusion of forgery detection tools.
Habib Ghaffari Hadigheh and Ghazali bin sulong
null
1701.08374
null
null
When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum
cs.LG cs.CV
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smallest non-zero eigenvalue and plays a key role for graph clustering. Graph signal processing focusses on the analysis of signals that are attributed to the graph nodes. The eigendecomposition of the graph Laplacian allows to define the graph Fourier transform and extend conventional signal-processing operations to graphs. Here, we introduce the design of Slepian graph signals, by maximizing energy concentration in a predefined subgraph for a graph spectral bandlimit. We establish a novel link with classical Laplacian embedding and graph clustering, which provides a meaning to localized graph frequencies.
Dimitri Van De Ville, Robin Demesmaeker, Maria Giulia Preti
10.1109/LSP.2017.2704359
1701.08401
null
null
On the Local Structure of Stable Clustering Instances
cs.DS cs.CG cs.LG
We study the classic $k$-median and $k$-means clustering objectives in the beyond-worst-case scenario. We consider three well-studied notions of structured data that aim at characterizing real-world inputs: Distribution Stability (introduced by Awasthi, Blum, and Sheffet, FOCS 2010), Spectral Separability (introduced by Kumar and Kannan, FOCS 2010), Perturbation Resilience (introduced by Bilu and Linial, ICS 2010). We prove structural results showing that inputs satisfying at least one of the conditions are inherently "local". Namely, for any such input, any local optimum is close both in term of structure and in term of objective value to the global optima. As a corollary we obtain that the widely-used Local Search algorithm has strong performance guarantees for both the tasks of recovering the underlying optimal clustering and obtaining a clustering of small cost. This is a significant step toward understanding the success of local search heuristics in clustering applications.
Vincent Cohen-Addad, Chris Schwiegelshohn
null
1701.08423
null
null