Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series
This work solves the problem of requiring manual data segmentation for unsupervised feature learning in time series analysis, making it more practical for researchers and practitioners in machine learning.
The paper tackles the problem of unsupervised learning from nonstationary time series by addressing the need for manual segmentation in nonlinear ICA, which is computationally expensive and inaccurate. It introduces a Hidden Markov Nonlinear ICA model that uses a latent state instead of observed segment indices, proving identifiability and enabling maximum likelihood estimation with the EM algorithm, resulting in a more efficient and fully unsupervised framework.
Recent advances in nonlinear Independent Component Analysis (ICA) provide a principled framework for unsupervised feature learning and disentanglement. The central idea in such works is that the latent components are assumed to be independent conditional on some observed auxiliary variables, such as the time-segment index. This requires manual segmentation of data into non-stationary segments which is computationally expensive, inaccurate and often impossible. These models are thus not fully unsupervised. We remedy these limitations by combining nonlinear ICA with a Hidden Markov Model, resulting in a model where a latent state acts in place of the observed segment-index. We prove identifiability of the proposed model for a general mixing nonlinearity, such as a neural network. We also show how maximum likelihood estimation of the model can be done using the expectation-maximization algorithm. Thus, we achieve a new nonlinear ICA framework which is unsupervised, more efficient, as well as able to model underlying temporal dynamics.