text: 330,142,1237327422044979200,2656744506,Kaspar Märtens 💙💛,"Excited to share our #AISTATS2020 paper with @cwcyau, where we propose the BasisVAE: a VAE framework for clustering features (allowing for scale and/or translation invariance).  Paper: <LINK> PyTorch implementation: <LINK> <LINK> Our goal is to have a joint model for 1) dimensionality reduction (inferring latent z) and 2) clustering features. Specifically, based on the mappings z -&gt; data, we want to find features that have a similar shape (scale invariance) and those that are shifted (translation inv). <LINK> We propose to achieve this within the VAE framework. Specifically, we modify the decoder network by embedding a probabilistic clustering prior within the last layer of the decoder. This lets us learn a one-hot basis function representation as part of the decoder network. <LINK> Training illustrated on a toy example: (A) scale-invariant BasisVAE on the left, and (B) scale-and-translation-invariant on the right. <LINK> Due to the scalability of VAEs, we can use this on large-scale data sets, e.g. single-cell gene expression. On a mouse spermatogenesis data set (Ernst et al 2019) we show how BasisVAE lets us jointly learn a one-dimensional representation and cluster genes with similar shapes. <LINK>",https://arxiv.org/abs/2003.03462,"Variational Autoencoders (VAEs) provide a flexible and scalable framework for non-linear dimensionality reduction. However, in application domains such as genomics where data sets are typically tabular and high-dimensional, a black-box approach to dimensionality reduction does not provide sufficient insights. Common data analysis workflows additionally use clustering techniques to identify groups of similar features. This usually leads to a two-stage process, however, it would be desirable to construct a joint modelling framework for simultaneous dimensionality reduction and clustering of features. In this paper, we propose to achieve this through the BasisVAE: a combination of the VAE and a probabilistic clustering prior, which lets us learn a one-hot basis function representation as part of the decoder network. Furthermore, for scenarios where not all features are aligned, we develop an extension to handle translation-invariant basis functions. We show how a collapsed variational inference scheme leads to scalable and efficient inference for BasisVAE, demonstrated on various toy examples as well as on single-cell gene expression data. ","BasisVAE: Translation-invariant feature-level clustering with