Causal representation learning (CRL) aims to identify the underlying latent variables from high-dimensional observations, even when variables are dependent with each other. We study this problem for latent variables that follow a potentially degenerate Gaussian mixture distribution and that are only observed through the transformation via a piecewise affine mixing function. We provide a series of progressively stronger identifiability results for this challenging setting in which the probability density functions are ill-defined because of the potential degeneracy. For identifiability up to permutation and scaling, we leverage a sparsity regularization on the learned representation. Based on our theoretical results, we propose a two-stage method to estimate the latent variables by enforcing sparsity and Gaussianity in the learned representations. Experiments on synthetic and image data highlight our method's effectiveness in recovering the ground-truth latent variables.

Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate science.

T o this end, we propose a simple yet powerful paradigm for seamlessly unifying different human pose and shape-related tasks and datasets. Our formulation is centered on the ability - both at training and test time - to query any arbitrary point of the human volume, and obtain its estimated location in 3D. We achieve this by learning a continuous neural field of body point localizer functions, each of which is a differently parameterized 3D heatmap-based convolutional point localizer (detector).

It is common to assess a model's merit for scientific discovery, and thus novel insights, by how well it aligns with already available domain

However, the design of methods for learning credal set predictors remains a challenging problem. In this paper, we make use of conformal prediction for this purpose.