Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA

TL;DR

This paper introduces Structured Nonlinear ICA (SNICA), a broad framework for disentangling features from noisy data, extending identifiability theory to complex temporal and spatial models with noise of unknown distribution.

Contribution

It extends the identifiability theory of deep generative models to more general structured models, including temporal and spatial dependencies, with noise of unknown distribution.

Findings

Proves identifiability for models with complex structures and noise.

Introduces the first nonlinear ICA model for time-series with nonstationarity and autocorrelation.

Enables unsupervised estimation and inference via variational maximum-likelihood.

Abstract

We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. While previous works have shown identifiability for specific classes of time-series models, our theorems extend this to more general temporal structures as well as to models with more complex structures such as spatial dependencies. In particular, we establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution. Finally, as an example of our framework's flexibility, we introduce the first nonlinear ICA model for time-series that combines the following very useful properties: it accounts for both nonstationarity and autocorrelation in a fully unsupervised setting; performs dimensionality reduction; models hidden states; and enables principled estimation and inference by variational maximum-likelihood.