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Jul 8

Matryoshka Representation Learning

Learned representations are a central component in modern ML systems, serving a multitude of downstream tasks. When training such representations, it is often the case that computational and statistical constraints for each downstream task are unknown. In this context rigid, fixed capacity representations can be either over or under-accommodating to the task at hand. This leads us to ask: can we design a flexible representation that can adapt to multiple downstream tasks with varying computational resources? Our main contribution is Matryoshka Representation Learning (MRL) which encodes information at different granularities and allows a single embedding to adapt to the computational constraints of downstream tasks. MRL minimally modifies existing representation learning pipelines and imposes no additional cost during inference and deployment. MRL learns coarse-to-fine representations that are at least as accurate and rich as independently trained low-dimensional representations. The flexibility within the learned Matryoshka Representations offer: (a) up to 14x smaller embedding size for ImageNet-1K classification at the same level of accuracy; (b) up to 14x real-world speed-ups for large-scale retrieval on ImageNet-1K and 4K; and (c) up to 2% accuracy improvements for long-tail few-shot classification, all while being as robust as the original representations. Finally, we show that MRL extends seamlessly to web-scale datasets (ImageNet, JFT) across various modalities -- vision (ViT, ResNet), vision + language (ALIGN) and language (BERT). MRL code and pretrained models are open-sourced at https://github.com/RAIVNLab/MRL.

Object Pose Estimation with Statistical Guarantees: Conformal Keypoint Detection and Geometric Uncertainty Propagation

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal keypoint detection applies the statistical machinery of inductive conformal prediction to convert heuristic keypoint detections into circular or elliptical prediction sets that cover the groundtruth keypoints with a user-specified marginal probability (e.g., 90%). Geometric uncertainty propagation, on the other, propagates the geometric constraints on the keypoints to the 6D object pose, leading to a Pose UnceRtainty SEt (PURSE) that guarantees coverage of the groundtruth pose with the same probability. The PURSE, however, is a nonconvex set that does not directly lead to estimated poses and uncertainties. Therefore, we develop RANdom SAmple averaGing (RANSAG) to compute an average pose and apply semidefinite relaxation to upper bound the worst-case errors between the average pose and the groundtruth. On the LineMOD Occlusion dataset we demonstrate: (i) the PURSE covers the groundtruth with valid probabilities; (ii) the worst-case error bounds provide correct uncertainty quantification; and (iii) the average pose achieves better or similar accuracy as representative methods based on sparse keypoints.

Standardized Benchmark Dataset for Localized Exposure to a Realistic Source at 10$-$90 GHz

The lack of freely available standardized datasets represents an aggravating factor during the development and testing the performance of novel computational techniques in exposure assessment and dosimetry research. This hinders progress as researchers are required to generate numerical data (field, power and temperature distribution) anew using simulation software for each exposure scenario. Other than being time consuming, this approach is highly susceptible to errors that occur during the configuration of the electromagnetic model. To address this issue, in this paper, the limited available data on the incident power density and resultant maximum temperature rise on the skin surface considering various steady-state exposure scenarios at 10-90 GHz have been statistically modeled. The synthetic data have been sampled from the fitted statistical multivariate distribution with respect to predetermined dosimetric constraints. We thus present a comprehensive and open-source dataset compiled of the high-fidelity numerical data considering various exposures to a realistic source. Furthermore, different surrogate models for predicting maximum temperature rise on the skin surface were fitted based on the synthetic dataset. All surrogate models were tested on the originally available data where satisfactory predictive performance has been demonstrated. A simple technique of combining quadratic polynomial and tensor-product spline surrogates, each operating on its own cluster of data, has achieved the lowest mean absolute error of 0.058 {\deg}C. Therefore, overall experimental results indicate the validity of the proposed synthetic dataset.

HideNseek: Federated Lottery Ticket via Server-side Pruning and Sign Supermask

Federated learning alleviates the privacy risk in distributed learning by transmitting only the local model updates to the central server. However, it faces challenges including statistical heterogeneity of clients' datasets and resource constraints of client devices, which severely impact the training performance and user experience. Prior works have tackled these challenges by combining personalization with model compression schemes including quantization and pruning. However, the pruning is data-dependent and thus must be done on the client side which requires considerable computation cost. Moreover, the pruning normally trains a binary supermask in {0, 1} which significantly limits the model capacity yet with no computation benefit. Consequently, the training requires high computation cost and a long time to converge while the model performance does not pay off. In this work, we propose HideNseek which employs one-shot data-agnostic pruning at initialization to get a subnetwork based on weights' synaptic saliency. Each client then optimizes a sign supermask in {-1, +1} multiplied by the unpruned weights to allow faster convergence with the same compression rates as state-of-the-art. Empirical results from three datasets demonstrate that compared to state-of-the-art, HideNseek improves inferences accuracies by up to 40.6\% while reducing the communication cost and training time by up to 39.7\% and 46.8\% respectively.

Mamba Integrated with Physics Principles Masters Long-term Chaotic System Forecasting

Long-term forecasting of chaotic systems from short-term observations remains a fundamental and underexplored challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Existing approaches often rely on long-term training data or focus on short-term sequence correlations, struggling to maintain predictive stability and dynamical coherence over extended horizons. We propose PhyxMamba, a novel framework that integrates a Mamba-based state-space model with physics-informed principles to capture the underlying dynamics of chaotic systems. By reconstructing the attractor manifold from brief observations using time-delay embeddings, PhyxMamba extracts global dynamical features essential for accurate forecasting. Our generative training scheme enables Mamba to replicate the physical process, augmented by multi-token prediction and attractor geometry regularization for physical constraints, enhancing prediction accuracy and preserving key statistical invariants. Extensive evaluations on diverse simulated and real-world chaotic systems demonstrate that PhyxMamba delivers superior long-term forecasting and faithfully captures essential dynamical invariants from short-term data. This framework opens new avenues for reliably predicting chaotic systems under observation-scarce conditions, with broad implications across climate science, neuroscience, epidemiology, and beyond. Our code is open-source at https://github.com/tsinghua-fib-lab/PhyxMamba.

Domain constraints improve risk prediction when outcome data is missing

Machine learning models are often trained to predict the outcome resulting from a human decision. For example, if a doctor decides to test a patient for disease, will the patient test positive? A challenge is that historical decision-making determines whether the outcome is observed: we only observe test outcomes for patients doctors historically tested. Untested patients, for whom outcomes are unobserved, may differ from tested patients along observed and unobserved dimensions. We propose a Bayesian model class which captures this setting. The purpose of the model is to accurately estimate risk for both tested and untested patients. Estimating this model is challenging due to the wide range of possibilities for untested patients. To address this, we propose two domain constraints which are plausible in health settings: a prevalence constraint, where the overall disease prevalence is known, and an expertise constraint, where the human decision-maker deviates from purely risk-based decision-making only along a constrained feature set. We show theoretically and on synthetic data that domain constraints improve parameter inference. We apply our model to a case study of cancer risk prediction, showing that the model's inferred risk predicts cancer diagnoses, its inferred testing policy captures known public health policies, and it can identify suboptimalities in test allocation. Though our case study is in healthcare, our analysis reveals a general class of domain constraints which can improve model estimation in many settings.

Preserving Statistical Validity in Adaptive Data Analysis

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

Modular versus Hierarchical: A Structural Signature of Topic Popularity in Mathematical Research

Mathematical researchers, especially those in early-career positions, face critical decisions about topic specialization with limited information about the collaborative environments of different research areas. The aim of this paper is to study how the popularity of a research topic is associated with the structure of that topic's collaboration network, as observed by a suite of measures capturing organizational structure at several scales. We apply these measures to 1,938 algorithmically discovered topics across 121,391 papers sourced from arXiv metadata during the period 2020--2025. Our analysis, which controls for the confounding effects of network size, reveals a structural dichotomy--we find that popular topics organize into modular "schools of thought," while niche topics maintain hierarchical core-periphery structures centered around established experts. This divide is not an artifact of scale, but represents a size-independent structural pattern correlated with popularity. We also document a "constraint reversal": after controlling for size, researchers in popular fields face greater structural constraints on collaboration opportunities, contrary to conventional expectations. Our findings suggest that topic selection is an implicit choice between two fundamentally different collaborative environments, each with distinct implications for a researcher's career. To make these structural patterns transparent to the research community, we developed the Math Research Compass (https://mathresearchcompass.com), an interactive platform providing data on topic popularity and collaboration patterns across mathematical topics.

Fixed-Budget Differentially Private Best Arm Identification

We study best arm identification (BAI) in linear bandits in the fixed-budget regime under differential privacy constraints, when the arm rewards are supported on the unit interval. Given a finite budget T and a privacy parameter varepsilon>0, the goal is to minimise the error probability in finding the arm with the largest mean after T sampling rounds, subject to the constraint that the policy of the decision maker satisfies a certain {\em varepsilon-differential privacy} (varepsilon-DP) constraint. We construct a policy satisfying the varepsilon-DP constraint (called {\sc DP-BAI}) by proposing the principle of {\em maximum absolute determinants}, and derive an upper bound on its error probability. Furthermore, we derive a minimax lower bound on the error probability, and demonstrate that the lower and the upper bounds decay exponentially in T, with exponents in the two bounds matching order-wise in (a) the sub-optimality gaps of the arms, (b) varepsilon, and (c) the problem complexity that is expressible as the sum of two terms, one characterising the complexity of standard fixed-budget BAI (without privacy constraints), and the other accounting for the varepsilon-DP constraint. Additionally, we present some auxiliary results that contribute to the derivation of the lower bound on the error probability. These results, we posit, may be of independent interest and could prove instrumental in proving lower bounds on error probabilities in several other bandit problems. Whereas prior works provide results for BAI in the fixed-budget regime without privacy constraints or in the fixed-confidence regime with privacy constraints, our work fills the gap in the literature by providing the results for BAI in the fixed-budget regime under the varepsilon-DP constraint.

Generating Private Synthetic Data with Genetic Algorithms

We study the problem of efficiently generating differentially private synthetic data that approximate the statistical properties of an underlying sensitive dataset. In recent years, there has been a growing line of work that approaches this problem using first-order optimization techniques. However, such techniques are restricted to optimizing differentiable objectives only, severely limiting the types of analyses that can be conducted. For example, first-order mechanisms have been primarily successful in approximating statistical queries only in the form of marginals for discrete data domains. In some cases, one can circumvent such issues by relaxing the task's objective to maintain differentiability. However, even when possible, these approaches impose a fundamental limitation in which modifications to the minimization problem become additional sources of error. Therefore, we propose Private-GSD, a private genetic algorithm based on zeroth-order optimization heuristics that do not require modifying the original objective. As a result, it avoids the aforementioned limitations of first-order optimization. We empirically evaluate Private-GSD against baseline algorithms on data derived from the American Community Survey across a variety of statistics--otherwise known as statistical queries--both for discrete and real-valued attributes. We show that Private-GSD outperforms the state-of-the-art methods on non-differential queries while matching accuracy in approximating differentiable ones.

A Tutorial on Bayesian Optimization

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

Flexible Model Aggregation for Quantile Regression

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

Predicting Rare Events by Shrinking Towards Proportional Odds

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

An Old-Fashioned Framework for Machine Learning in Turbulence Modeling

The objective is to provide clear and well-motivated guidance to Machine Learning (ML) teams, founded on our experience in empirical turbulence modeling. Guidance is also needed for modeling outside ML. ML is not yet successful in turbulence modeling, and many papers have produced unusable proposals either due to errors in math or physics, or to severe overfitting. We believe that "Turbulence Culture" (TC) takes years to learn and is difficult to convey especially considering the modern lack of time for careful study; important facts which are self-evident after a career in turbulence research and modeling and extensive reading are easy to miss. In addition, many of them are not absolute facts, a consequence of the gaps in our understanding of turbulence and the weak connection of models to first principles. Some of the mathematical facts are rigorous, but the physical aspects often are not. Turbulence models are surprisingly arbitrary. Disagreement between experts confuses the new entrants. In addition, several key properties of the models are ascertained through non-trivial analytical properties of the differential equations, which puts them out of reach of purely data-driven ML-type approaches. The best example is the crucial behavior of the model at the edge of the turbulent region (ETR). The knowledge we wish to put out here may be divided into "Mission" and "Requirements," each combining physics and mathematics. Clear lists of "Hard" and "Soft" constraints are presented. A concrete example of how DNS data could be used, possibly allied with ML, is first carried through and illustrates the large number of decisions needed. Our focus is on creating effective products which will empower CFD, rather than on publications.

Synthesizing mixed-integer linear programming models from natural language descriptions

Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations research and mathematical optimization, which restricts non-experts' accessibility to MILP. To address this challenge, we propose a framework for automatically formulating MILP models from unstructured natural language descriptions of decision problems, which integrates Large Language Models (LLMs) and mathematical modeling techniques. This framework consists of three phases: i) identification of decision variables, ii) classification of objective and constraints, and iii) finally, generation of MILP models. In this study, we present a constraint classification scheme and a set of constraint templates that can guide the LLMs in synthesizing a complete MILP model. After fine-tuning LLMs, our approach can identify and synthesize logic constraints in addition to classic demand and resource constraints. The logic constraints have not been studied in existing work. To evaluate the performance of the proposed framework, we extend the NL4Opt dataset with more problem descriptions and constraint types, and with the new dataset, we compare our framework with one-step model generation methods offered by LLMs. The experimental results reveal that with respect to the accuracies of generating the correct model, objective, and constraints, our method which integrates constraint classification and templates with LLMs significantly outperforms the others. The prototype system that we developed has a great potential to capture more constraints for more complex MILPs. It opens up opportunities for developing training tools for operations research practitioners and has the potential to be a powerful tool for automatic decision problem modeling and solving in practice.

Adaptive Sampling Strategies to Construct Equitable Training Datasets

In domains ranging from computer vision to natural language processing, machine learning models have been shown to exhibit stark disparities, often performing worse for members of traditionally underserved groups. One factor contributing to these performance gaps is a lack of representation in the data the models are trained on. It is often unclear, however, how to operationalize representativeness in specific applications. Here we formalize the problem of creating equitable training datasets, and propose a statistical framework for addressing this problem. We consider a setting where a model builder must decide how to allocate a fixed data collection budget to gather training data from different subgroups. We then frame dataset creation as a constrained optimization problem, in which one maximizes a function of group-specific performance metrics based on (estimated) group-specific learning rates and costs per sample. This flexible approach incorporates preferences of model-builders and other stakeholders, as well as the statistical properties of the learning task. When data collection decisions are made sequentially, we show that under certain conditions this optimization problem can be efficiently solved even without prior knowledge of the learning rates. To illustrate our approach, we conduct a simulation study of polygenic risk scores on synthetic genomic data -- an application domain that often suffers from non-representative data collection. We find that our adaptive sampling strategy outperforms several common data collection heuristics, including equal and proportional sampling, demonstrating the value of strategic dataset design for building equitable models.

Using Imperfect Surrogates for Downstream Inference: Design-based Supervised Learning for Social Science Applications of Large Language Models

In computational social science (CSS), researchers analyze documents to explain social and political phenomena. In most scenarios, CSS researchers first obtain labels for documents and then explain labels using interpretable regression analyses in the second step. One increasingly common way to annotate documents cheaply at scale is through large language models (LLMs). However, like other scalable ways of producing annotations, such surrogate labels are often imperfect and biased. We present a new algorithm for using imperfect annotation surrogates for downstream statistical analyses while guaranteeing statistical properties -- like asymptotic unbiasedness and proper uncertainty quantification -- which are fundamental to CSS research. We show that direct use of surrogate labels in downstream statistical analyses leads to substantial bias and invalid confidence intervals, even with high surrogate accuracy of 80-90%. To address this, we build on debiased machine learning to propose the design-based supervised learning (DSL) estimator. DSL employs a doubly-robust procedure to combine surrogate labels with a smaller number of high-quality, gold-standard labels. Our approach guarantees valid inference for downstream statistical analyses, even when surrogates are arbitrarily biased and without requiring stringent assumptions, by controlling the probability of sampling documents for gold-standard labeling. Both our theoretical analysis and experimental results show that DSL provides valid statistical inference while achieving root mean squared errors comparable to existing alternatives that focus only on prediction without inferential guarantees.

Improve Machine Learning carbon footprint using Nvidia GPU and Mixed Precision training for classification models -- Part I

This is the 1st part of the dissertation for my master degree and compares the power consumption using the default floating point (32bit) and Nvidia mixed precision (16bit and 32bit) while training a classification ML model. A custom PC with specific hardware was built to perform the experiments, and different ML hyper-parameters, such as batch size, neurons, and epochs, were chosen to build Deep Neural Networks (DNN). Additionally, various software was used during the experiments to collect the power consumption data in Watts from the Graphics Processing Unit (GPU), Central Processing Unit (CPU), Random Access Memory (RAM) and manually from a wattmeter connected to the wall. A benchmarking test with default hyper parameter values for the DNN was used as a reference, while the experiments used a combination of different settings. The results were recorded in Excel, and descriptive statistics were chosen to calculate the mean between the groups and compare them using graphs and tables. The outcome was positive when using mixed precision combined with specific hyper-parameters. Compared to the benchmarking, the optimisation for the classification reduced the power consumption between 7 and 11 Watts. Similarly, the carbon footprint is reduced because the calculation uses the same power consumption data. Still, a consideration is required when configuring hyper-parameters because it can negatively affect hardware performance. However, this research required inferential statistics, specifically ANOVA and T-test, to compare the relationship between the means. Furthermore, tests indicated no statistical significance of the relationship between the benchmarking and experiments. However, a more extensive implementation with a cluster of GPUs can increase the sample size significantly, as it is an essential factor and can change the outcome of the statistical analysis.

A Flexible Parametric Modelling Framework for Survival Analysis

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

Selective Machine Learning of the Average Treatment Effect with an Invalid Instrumental Variable

Instrumental variable methods have been widely used to identify causal effects in the presence of unmeasured confounding. A key identification condition known as the exclusion restriction states that the instrument cannot have a direct effect on the outcome which is not mediated by the exposure in view. In the health and social sciences, such an assumption is often not credible. To address this concern, we consider identification conditions of the population average treatment effect with an invalid instrumental variable which does not satisfy the exclusion restriction, and derive the efficient influence function targeting the identifying functional under a nonparametric observed data model. We propose a novel multiply robust locally efficient estimator of the average treatment effect that is consistent in the union of multiple parametric nuisance models, as well as a multiply debiased machine learning estimator for which the nuisance parameters are estimated using generic machine learning methods, that effectively exploit various forms of linear or nonlinear structured sparsity in the nuisance parameter space. When one cannot be confident that any of these machine learners is consistent at sufficiently fast rates to ensure n-consistency for the average treatment effect, we introduce a new criteria for selective machine learning which leverages the multiple robustness property in order to ensure small bias. The proposed methods are illustrated through extensive simulations and a data analysis evaluating the causal effect of 401(k) participation on savings.

Questioning the Survey Responses of Large Language Models

As large language models increase in capability, researchers have started to conduct surveys of all kinds on these models with varying scientific motivations. In this work, we examine what we can learn from a model's survey responses on the basis of the well-established American Community Survey (ACS) by the U.S. Census Bureau. Evaluating more than a dozen different models, varying in size from a few hundred million to ten billion parameters, hundreds of thousands of times each on questions from the ACS, we systematically establish two dominant patterns. First, smaller models have a significant position and labeling bias, for example, towards survey responses labeled with the letter "A". This A-bias diminishes, albeit slowly, as model size increases. Second, when adjusting for this labeling bias through randomized answer ordering, models still do not trend toward US population statistics or those of any cognizable population. Rather, models across the board trend toward uniformly random aggregate statistics over survey responses. This pattern is robust to various different ways of prompting the model, including what is the de-facto standard. Our findings demonstrate that aggregate statistics of a language model's survey responses lack the signals found in human populations. This absence of statistical signal cautions about the use of survey responses from large language models at present time.

Primary and Secondary Factor Consistency as Domain Knowledge to Guide Happiness Computing in Online Assessment

Happiness computing based on large-scale online web data and machine learning methods is an emerging research topic that underpins a range of issues, from personal growth to social stability. Many advanced Machine Learning (ML) models with explanations are used to compute the happiness online assessment while maintaining high accuracy of results. However, domain knowledge constraints, such as the primary and secondary relations of happiness factors, are absent from these models, which limits the association between computing results and the right reasons for why they occurred. This article attempts to provide new insights into the explanation consistency from an empirical study perspective. Then we study how to represent and introduce domain knowledge constraints to make ML models more trustworthy. We achieve this through: (1) proving that multiple prediction models with additive factor attributions will have the desirable property of primary and secondary relations consistency, and (2) showing that factor relations with quantity can be represented as an importance distribution for encoding domain knowledge. Factor explanation difference is penalized by the Kullback-Leibler divergence-based loss among computing models. Experimental results using two online web datasets show that domain knowledge of stable factor relations exists. Using this knowledge not only improves happiness computing accuracy but also reveals more significative happiness factors for assisting decisions well.

Model Evaluation, Model Selection, and Algorithm Selection in Machine Learning

The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these three subtasks and discusses the main advantages and disadvantages of each technique with references to theoretical and empirical studies. Further, recommendations are given to encourage best yet feasible practices in research and applications of machine learning. Common methods such as the holdout method for model evaluation and selection are covered, which are not recommended when working with small datasets. Different flavors of the bootstrap technique are introduced for estimating the uncertainty of performance estimates, as an alternative to confidence intervals via normal approximation if bootstrapping is computationally feasible. Common cross-validation techniques such as leave-one-out cross-validation and k-fold cross-validation are reviewed, the bias-variance trade-off for choosing k is discussed, and practical tips for the optimal choice of k are given based on empirical evidence. Different statistical tests for algorithm comparisons are presented, and strategies for dealing with multiple comparisons such as omnibus tests and multiple-comparison corrections are discussed. Finally, alternative methods for algorithm selection, such as the combined F-test 5x2 cross-validation and nested cross-validation, are recommended for comparing machine learning algorithms when datasets are small.

On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Martingale Posterior Neural Processes

A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data without any inductive biases, but in practice, we often restrict the class of stochastic processes for the ease of estimation. One such restriction is the use of a finite-dimensional latent variable accounting for the uncertainty in the functions drawn from NPs. Some recent works show that this can be improved with more "data-driven" source of uncertainty such as bootstrapping. In this work, we take a different approach based on the martingale posterior, a recently developed alternative to Bayesian inference. For the martingale posterior, instead of specifying prior-likelihood pairs, a predictive distribution for future data is specified. Under specific conditions on the predictive distribution, it can be shown that the uncertainty in the generated future data actually corresponds to the uncertainty of the implicitly defined Bayesian posteriors. Based on this result, instead of assuming any form of the latent variables, we equip a NP with a predictive distribution implicitly defined with neural networks and use the corresponding martingale posteriors as the source of uncertainty. The resulting model, which we name as Martingale Posterior Neural Process (MPNP), is demonstrated to outperform baselines on various tasks.

Statistical Rejection Sampling Improves Preference Optimization

Improving the alignment of language models with human preferences remains an active research challenge. Previous approaches have primarily utilized Reinforcement Learning from Human Feedback (RLHF) via online RL methods such as Proximal Policy Optimization (PPO). Recently, offline methods such as Sequence Likelihood Calibration (SLiC) and Direct Preference Optimization (DPO) have emerged as attractive alternatives, offering improvements in stability and scalability while maintaining competitive performance. SLiC refines its loss function using sequence pairs sampled from a supervised fine-tuned (SFT) policy, while DPO directly optimizes language models based on preference data, foregoing the need for a separate reward model. However, the maximum likelihood estimator (MLE) of the target optimal policy requires labeled preference pairs sampled from that policy. DPO's lack of a reward model constrains its ability to sample preference pairs from the optimal policy, and SLiC is restricted to sampling preference pairs only from the SFT policy. To address these limitations, we introduce a novel approach called Statistical Rejection Sampling Optimization (RSO) that aims to source preference data from the target optimal policy using rejection sampling, enabling a more accurate estimation of the optimal policy. We also propose a unified framework that enhances the loss functions used in both SLiC and DPO from a preference modeling standpoint. Through extensive experiments across three diverse tasks, we demonstrate that RSO consistently outperforms both SLiC and DPO on evaluations from both Large Language Model (LLM) and human raters.

Improved Analysis of Sparse Linear Regression in Local Differential Privacy Model

In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case where the underlying parameter is 1-sparse, and extending such bounds to the more general k-sparse case has proven to be challenging. Moreover, it is unclear whether efficient non-interactive LDP (NLDP) algorithms exist. To address these issues, we first consider the problem in the epsilon non-interactive LDP model and provide a lower bound of Omega(sqrt{dklog d}{nepsilon}) on the ell_2-norm estimation error for sub-Gaussian data, where n is the sample size and d is the dimension of the space. We propose an innovative NLDP algorithm, the very first of its kind for the problem. As a remarkable outcome, this algorithm also yields a novel and highly efficient estimator as a valuable by-product. Our algorithm achieves an upper bound of O({dsqrt{k}{nepsilon}}) for the estimation error when the data is sub-Gaussian, which can be further improved by a factor of O(d) if the server has additional public but unlabeled data. For the sequentially interactive LDP model, we show a similar lower bound of Omega({sqrt{dk}{nepsilon}}). As for the upper bound, we rectify a previous method and show that it is possible to achieve a bound of O(ksqrt{d}{nepsilon}). Our findings reveal fundamental differences between the non-private case, central DP model, and local DP model in the sparse linear regression problem.

Applicability and Surrogacy of Uncorrelated Airspace Encounter Models at Low Altitudes

The National Airspace System (NAS) is a complex and evolving system that enables safe and efficient aviation. Advanced air mobility concepts and new airspace entrants, such as unmanned aircraft, must integrate into the NAS without degrading overall safety or efficiency. For instance, regulations, standards, and systems are required to mitigate the risk of a midair collision between aircraft. Monte Carlo simulations have been a foundational capability for decades to develop, assess, and certify aircraft conflict avoidance systems. These are often validated through human-in-the-loop experiments and flight testing. For many aviation safety studies, manned aircraft behavior is represented using dynamic Bayesian networks. The original statistical models were developed from 2008-2013 to support safety simulations for altitudes above 500 feet Above Ground Level (AGL). However, these models were not sufficient to assess the safety of smaller UAS operations below 500 feet AGL. In response, newer models with altitude floors below 500 feet AGL have been in development since 2018. Many of the models assume that aircraft behavior is uncorrelated and not dependent on air traffic services or nearby aircraft. Our research objective was to compare the various uncorrelated models of conventional aircraft and identify how the models differ. Particularly if models of rotorcraft were sufficiently different than models of fixed-wing aircraft to require type specific models. The primary contribution is guidance on which uncorrelated models to leverage when evaluating the performance of a collision avoidance system designed for low altitude operations. We also address which models can be surrogates for noncooperative aircraft without transponders.

Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

Awareness in Practice: Tensions in Access to Sensitive Attribute Data for Antidiscrimination

Organizations cannot address demographic disparities that they cannot see. Recent research on machine learning and fairness has emphasized that awareness of sensitive attributes, such as race and sex, is critical to the development of interventions. However, on the ground, the existence of these data cannot be taken for granted. This paper uses the domains of employment, credit, and healthcare in the United States to surface conditions that have shaped the availability of sensitive attribute data. For each domain, we describe how and when private companies collect or infer sensitive attribute data for antidiscrimination purposes. An inconsistent story emerges: Some companies are required by law to collect sensitive attribute data, while others are prohibited from doing so. Still others, in the absence of legal mandates, have determined that collection and imputation of these data are appropriate to address disparities. This story has important implications for fairness research and its future applications. If companies that mediate access to life opportunities are unable or hesitant to collect or infer sensitive attribute data, then proposed techniques to detect and mitigate bias in machine learning models might never be implemented outside the lab. We conclude that today's legal requirements and corporate practices, while highly inconsistent across domains, offer lessons for how to approach the collection and inference of sensitive data in appropriate circumstances. We urge stakeholders, including machine learning practitioners, to actively help chart a path forward that takes both policy goals and technical needs into account.

Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

Partial Correlations in Compositional Data Analysis

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

Constraints on the variation of the fine-structure constant at 3<z<10 with JWST emission-line galaxies

We present constraints on the spacetime variation of the fine-structure constant alpha at redshifts 2.5le z<9.5 using JWST emission-line galaxies. The galaxy sample consists of 621 high-quality spectra with strong and narrow [O III] lambdalambda4959,5007 doublet emission lines from 578 galaxies, including 232 spectra at z>5. The [O III] doublet lines are arguably the best emission lines to probe the variation in alpha. We divide our sample into six subsamples based on redshift and calculate the relative variation Deltaalpha/alpha for the individual subsamples. The calculated Deltaalpha/alpha values are consistent with zero within 1sigma at all redshifts, suggesting no time variation in alpha above a level of (1-2) times10^{-4} (1sigma) in the past 13.2 billion years. When the whole sample is combined, the constraint is improved to be Deltaalpha/alpha = (0.2pm0.7) times10^{-4}. We further test the spatial variation in alpha using four subsamples of galaxies in four different directions on the sky. The measured Deltaalpha/alpha values are consistent with zero at a 1sigma level of sim 2times10^{-4}. While the constraints in this work are not as stringent as those from lower-redshift quasar absorption lines in previous studies, this work uses an independent tracer and provides the first constraints on Deltaalpha/alpha at the highest redshifts. With the growing number of emission-line galaxies from JWST, we expect to achieve stronger constraints in the future.

Solving Data Quality Problems with Desbordante: a Demo

Data profiling is an essential process in modern data-driven industries. One of its critical components is the discovery and validation of complex statistics, including functional dependencies, data constraints, association rules, and others. However, most existing data profiling systems that focus on complex statistics do not provide proper integration with the tools used by contemporary data scientists. This creates a significant barrier to the adoption of these tools in the industry. Moreover, existing systems were not created with industrial-grade workloads in mind. Finally, they do not aim to provide descriptive explanations, i.e. why a given pattern is not found. It is a significant issue as it is essential to understand the underlying reasons for a specific pattern's absence to make informed decisions based on the data. Because of that, these patterns are effectively rest in thin air: their application scope is rather limited, they are rarely used by the broader public. At the same time, as we are going to demonstrate in this presentation, complex statistics can be efficiently used to solve many classic data quality problems. Desbordante is an open-source data profiler that aims to close this gap. It is built with emphasis on industrial application: it is efficient, scalable, resilient to crashes, and provides explanations. Furthermore, it provides seamless Python integration by offloading various costly operations to the C++ core, not only mining. In this demonstration, we show several scenarios that allow end users to solve different data quality problems. Namely, we showcase typo detection, data deduplication, and data anomaly detection scenarios.

Pair Programming with Large Language Models for Sampling and Estimation of Copulas

Without writing a single line of code by a human, an example Monte Carlo simulation based application for stochastic dependence modeling with copulas is developed using a state-of-the-art large language model (LLM) fine-tuned for conversations. This includes interaction with ChatGPT in natural language and using mathematical formalism, which, under careful supervision by a human-expert, led to producing a working code in MATLAB, Python and R for sampling from a given copula model, evaluation of the model's density, performing maximum likelihood estimation, optimizing the code for parallel computing for CPUs as well as for GPUs, and visualization of the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human-expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a solution that is correct. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques.

Efficient estimation of multiple expectations with the same sample by adaptive importance sampling and control variates

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates for estimating more efficiently multiple expectations with the same sample. We first show that there exists a family of optimal estimators combining both importance sampling and control variates, which however cannot be used in practice because they require the knowledge of the values of the expectations to estimate. Motivated by the form of these optimal estimators and some interesting properties, we therefore propose an adaptive algorithm. The general idea is to adaptively update the parameters of the estimators for approaching the optimal ones. We suggest then a quantitative stopping criterion that exploits the trade-off between approaching these optimal parameters and having a sufficient budget left. This left budget is then used to draw a new independent sample from the final sampling distribution, allowing to get unbiased estimators of the expectations. We show how to apply our procedure to sensitivity analysis, by estimating Sobol' indices and quantifying the impact of the input distributions. Finally, realistic test cases show the practical interest of the proposed algorithm, and its significant improvement over estimating the expectations separately.

Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.

A Nearly-Optimal Bound for Fast Regression with ell_infty Guarantee

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

Impact of a Batter in ODI Cricket Implementing Regression Models from Match Commentary

Cricket, "a Gentleman's Game", is a prominent sport rising worldwide. Due to the rising competitiveness of the sport, players and team management have become more professional with their approach. Prior studies predicted individual performance or chose the best team but did not highlight the batter's potential. On the other hand, our research aims to evaluate a player's impact while considering his control in various circumstances. This paper seeks to understand the conundrum behind this impactful performance by determining how much control a player has over the circumstances and generating the "Effective Runs",a new measure we propose. We first gathered the fundamental cricket data from open-source datasets; however, variables like pitch, weather, and control were not readily available for all matches. As a result, we compiled our corpus data by analyzing the commentary of the match summaries. This gave us an insight into the particular game's weather and pitch conditions. Furthermore, ball-by-ball inspection from the commentary led us to determine the control of the shots played by the batter. We collected data for the entire One Day International career, up to February 2022, of 3 prominent cricket players: Rohit G Sharma, David A Warner, and Kane S Williamson. Lastly, to prepare the dataset, we encoded, scaled, and split the dataset to train and test Machine Learning Algorithms. We used Multiple Linear Regression (MLR), Polynomial Regression, Support Vector Regression (SVR), Decision Tree Regression, and Random Forest Regression on each player's data individually to train them and predict the Impact the player will have on the game. Multiple Linear Regression and Random Forest give the best predictions accuracy of 90.16 percent and 87.12 percent, respectively.

Unboxing Occupational Bias: Grounded Debiasing LLMs with U.S. Labor Data

Large Language Models (LLMs) are prone to inheriting and amplifying societal biases embedded within their training data, potentially reinforcing harmful stereotypes related to gender, occupation, and other sensitive categories. This issue becomes particularly problematic as biased LLMs can have far-reaching consequences, leading to unfair practices and exacerbating social inequalities across various domains, such as recruitment, online content moderation, or even the criminal justice system. Although prior research has focused on detecting bias in LLMs using specialized datasets designed to highlight intrinsic biases, there has been a notable lack of investigation into how these findings correlate with authoritative datasets, such as those from the U.S. National Bureau of Labor Statistics (NBLS). To address this gap, we conduct empirical research that evaluates LLMs in a ``bias-out-of-the-box" setting, analyzing how the generated outputs compare with the distributions found in NBLS data. Furthermore, we propose a straightforward yet effective debiasing mechanism that directly incorporates NBLS instances to mitigate bias within LLMs. Our study spans seven different LLMs, including instructable, base, and mixture-of-expert models, and reveals significant levels of bias that are often overlooked by existing bias detection techniques. Importantly, our debiasing method, which does not rely on external datasets, demonstrates a substantial reduction in bias scores, highlighting the efficacy of our approach in creating fairer and more reliable LLMs.

Predictive Multiplicity in Probabilistic Classification

Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely.

Inference Scaling scriptsizeFLaws: The Limits of LLM Resampling with Imperfect Verifiers

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

PAC Generalization via Invariant Representations

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

On the Provable Advantage of Unsupervised Pretraining

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

Knowledge Augmented Machine Learning with Applications in Autonomous Driving: A Survey

The availability of representative datasets is an essential prerequisite for many successful artificial intelligence and machine learning models. However, in real life applications these models often encounter scenarios that are inadequately represented in the data used for training. There are various reasons for the absence of sufficient data, ranging from time and cost constraints to ethical considerations. As a consequence, the reliable usage of these models, especially in safety-critical applications, is still a tremendous challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches. Knowledge augmented machine learning approaches offer the possibility of compensating for deficiencies, errors, or ambiguities in the data, thus increasing the generalization capability of the applied models. Even more, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-driven models with existing knowledge. The identified approaches are structured according to the categories knowledge integration, extraction and conformity. In particular, we address the application of the presented methods in the field of autonomous driving.

Procedural Generation of Grain Orientations using the Wave Function Collapse Algorithm

Statistics of grain sizes and orientations in metals correlate to the material's mechanical properties. Reproducing representative volume elements for further analysis of deformation and failure in metals, like 316L stainless steel, is particularly important due to their wide use in manufacturing goods today. Two approaches, initially created for video games, were considered for the procedural generation of representative grain microstructures. The first is the Wave Function Collapse (WFC) algorithm, and the second is constraint propagation and probabilistic inference through Markov Junior, a free and open-source software. This study aimed to investigate these two algorithms' effectiveness in using reference electron backscatter diffraction (EBSD) maps and recreating a statistically similar one that could be used in further research. It utilized two stainless steel EBSD maps as references to test both algorithms. First, the WFC algorithm was too constricting and, thus, incapable of producing images that resembled EBSDs. The second, MarkovJunior, was much more effective in creating a Voronoi tessellation that could be used to create an EBSD map in Python. When comparing the results between the reference and the generated EBSD, we discovered that the orientation and volume fractions were extremely similar. With the study, it was concluded that MarkovJunior is an effective machine learning tool that can reproduce representative grain microstructures.

OTSurv: A Novel Multiple Instance Learning Framework for Survival Prediction with Heterogeneity-aware Optimal Transport

Survival prediction using whole slide images (WSIs) can be formulated as a multiple instance learning (MIL) problem. However, existing MIL methods often fail to explicitly capture pathological heterogeneity within WSIs, both globally -- through long-tailed morphological distributions, and locally through -- tile-level prediction uncertainty. Optimal transport (OT) provides a principled way of modeling such heterogeneity by incorporating marginal distribution constraints. Building on this insight, we propose OTSurv, a novel MIL framework from an optimal transport perspective. Specifically, OTSurv formulates survival predictions as a heterogeneity-aware OT problem with two constraints: (1) global long-tail constraint that models prior morphological distributions to avert both mode collapse and excessive uniformity by regulating transport mass allocation, and (2) local uncertainty-aware constraint that prioritizes high-confidence patches while suppressing noise by progressively raising the total transport mass. We then recast the initial OT problem, augmented by these constraints, into an unbalanced OT formulation that can be solved with an efficient, hardware-friendly matrix scaling algorithm. Empirically, OTSurv sets new state-of-the-art results across six popular benchmarks, achieving an absolute 3.6% improvement in average C-index. In addition, OTSurv achieves statistical significance in log-rank tests and offers high interpretability, making it a powerful tool for survival prediction in digital pathology. Our codes are available at https://github.com/Y-Research-SBU/OTSurv.

Fantastic Generalization Measures are Nowhere to be Found

We study the notion of a generalization bound being uniformly tight, meaning that the difference between the bound and the population loss is small for all learning algorithms and all population distributions. Numerous generalization bounds have been proposed in the literature as potential explanations for the ability of neural networks to generalize in the overparameterized setting. However, in their paper ``Fantastic Generalization Measures and Where to Find Them,'' Jiang et al. (2020) examine more than a dozen generalization bounds, and show empirically that none of them are uniformly tight. This raises the question of whether uniformly-tight generalization bounds are at all possible in the overparameterized setting. We consider two types of generalization bounds: (1) bounds that may depend on the training set and the learned hypothesis (e.g., margin bounds). We prove mathematically that no such bound can be uniformly tight in the overparameterized setting; (2) bounds that may in addition also depend on the learning algorithm (e.g., stability bounds). For these bounds, we show a trade-off between the algorithm's performance and the bound's tightness. Namely, if the algorithm achieves good accuracy on certain distributions, then no generalization bound can be uniformly tight for it in the overparameterized setting. We explain how these formal results can, in our view, inform research on generalization bounds for neural networks, while stressing that other interpretations of these results are also possible.

On the Existence of Simpler Machine Learning Models

It is almost always easier to find an accurate-but-complex model than an accurate-yet-simple model. Finding optimal, sparse, accurate models of various forms (linear models with integer coefficients, decision sets, rule lists, decision trees) is generally NP-hard. We often do not know whether the search for a simpler model will be worthwhile, and thus we do not go to the trouble of searching for one. In this work, we ask an important practical question: can accurate-yet-simple models be proven to exist, or shown likely to exist, before explicitly searching for them? We hypothesize that there is an important reason that simple-yet-accurate models often do exist. This hypothesis is that the size of the Rashomon set is often large, where the Rashomon set is the set of almost-equally-accurate models from a function class. If the Rashomon set is large, it contains numerous accurate models, and perhaps at least one of them is the simple model we desire. In this work, we formally present the Rashomon ratio as a new gauge of simplicity for a learning problem, depending on a function class and a data set. The Rashomon ratio is the ratio of the volume of the set of accurate models to the volume of the hypothesis space, and it is different from standard complexity measures from statistical learning theory. Insight from studying the Rashomon ratio provides an easy way to check whether a simpler model might exist for a problem before finding it, namely whether several different machine learning methods achieve similar performance on the data. In that sense, the Rashomon ratio is a powerful tool for understanding why and when an accurate-yet-simple model might exist. If, as we hypothesize in this work, many real-world data sets admit large Rashomon sets, the implications are vast: it means that simple or interpretable models may often be used for high-stakes decisions without losing accuracy.

Weighted least-squares approximation with determinantal point processes and generalized volume sampling

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

Extending Mixture of Experts Model to Investigate Heterogeneity of Trajectories: When, Where and How to Add Which Covariates

Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-cluster and between-cluster heterogeneity simultaneously, known as a mixture-of-experts (MoE) model. This study aims to extend the MoE framework to investigate heterogeneity in nonlinear trajectories: to identify latent classes, covariates as predictors to clusters, and covariates that explain within-cluster differences in change patterns over time. Our simulation studies demonstrate that the proposed model generally estimates the parameters unbiasedly, precisely and exhibits appropriate empirical coverage for a nominal 95% confidence interval. This study also proposes implementing structural equation model forests to shrink the covariate space of the proposed mixture model. We illustrate how to select covariates and construct the proposed model with longitudinal mathematics achievement data. Additionally, we demonstrate that the proposed mixture model can be further extended in the structural equation modeling framework by allowing the covariates that have direct effects to be time-varying.