Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA
This work addresses the challenge of principled disentanglement in deep generative models for researchers in machine learning and AI, offering a foundational extension to identifiability theory with broad applicability.
The paper tackles the problem of disentangling identifiable features from noisy data by introducing Structured Nonlinear ICA (SNICA), a general identifiable framework that extends identifiability theory to broad classes of structured models, including temporal and spatial dependencies, even with unknown noise distributions, and demonstrates its flexibility with a nonlinear ICA model for time-series that handles nonstationarity, autocorrelation, dimensionality reduction, hidden states, and variational maximum-likelihood estimation.
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.