Causal mediation analysis (CMA) is a powerful method to dissect the total effect of a treatment into direct and mediated effects within the potential outcome framework. This is important in many scientific applications to identify the underlying mechanisms of a treatment effect. However, in many scientific applications the mediator is unobserved, but there may exist related measurements. For example, we may want to identify how changes in brain activity or structure mediate an antidepressant's effect on behavior, but we may only have access to electrophysiological or imaging brain measurements. To date, most CMA methods assume that the mediator is one-dimensional and observable, which oversimplifies such real-world scenarios. To overcome this limitation, we introduce a CMA framework that can handle complex and indirectly observed mediators based on the identifiable variational autoencoder (iVAE) architecture. We prove that the true joint distribution over observed and latent variables is identifiable with the proposed method. Additionally, our framework captures a disentangled representation of the indirectly observed mediator and yields accurate estimation of the direct and mediated effects in synthetic and semi-synthetic experiments, providing evidence of its potential utility in real-world applications.

In this work we introduce a new approach for identifiable non-linear ICA models. Recently there has been a renaissance in identifiability results in deep generative models, not least for non-linear ICA. These prior works, however, have assumed access to a sufficiently-informative auxiliary set of observations, denoted $\mathbf{u}$. We show here how identifiability can be obtained in the absence of this side-information, rendering possible fully-unsupervised identifiable non-linear ICA. While previous theoretical results have established the impossibility of identifiable non-linear ICA in the presence of infinitely-flexible universal function approximators, here we rely on the intrinsically-finite modelling capacity of any particular chosen parameterisation of a deep generative model. In particular, we focus on generative models which perform clustering in their latent space -- a model structure which matches previous identifiable models, but with the learnt clustering providing a synthetic form of auxiliary information. We evaluate our proposals using VAEs, on synthetic and image datasets, and find that the learned clusterings function effectively: deep generative models with latent clusterings are empirically identifiable, to the same degree as models which rely on side information.

Our ability to generalize beyond training data to novel, out-of-distribution, image degradations is a hallmark of primate vision. The predictive brain, exemplified by predictive coding networks (PCNs), has become a prominent neuroscience theory of neural computation. Motivated by the recent successes of variational autoencoders (VAEs) in machine learning, we rigorously derive a correspondence between PCNs and VAEs. This motivates us to consider iterative extensions of VAEs (iVAEs) as plausible variational extensions of the PCNs. We further demonstrate that iVAEs generalize to distributional shifts significantly better than both PCNs and VAEs. In addition, we propose a novel measure of recognizability for individual samples which can be tested against human psychophysical data. Overall, we hope this work will spur interest in iVAEs as a promising new direction for modeling in neuroscience.

A large part of the literature on learning disentangled representations focuses on variational autoencoders (VAEs). Recent developments demonstrate that disentanglement cannot be obtained in a fully unsupervised setting without inductive biases on models and data. As such, Khemakhem et al., AISTATS 2020, suggest employing a factorized prior distribution over the latent variables that is conditionally dependent on auxiliary observed variables complementing input observations. While this is a remarkable advancement toward model identifiability, the learned conditional prior only focuses on sufficiency, giving no guarantees on a minimal representation. Motivated by information theoretic principles, we propose a novel VAE-based generative model with theoretical guarantees on disentanglement. Our proposed model learns a sufficient and compact - thus optimal - conditional prior, which serves as regularization for the latent space. Experimental results indicate superior performance with respect to state-of-the-art methods, according to several established metrics proposed in the literature on disentanglement.