A01Deep stacked independent component analysis and its application to brain science

　Representation learning or feature learning seeks to automatically acquire meaningful representations or features from multivariate data.　Development of its principles and algorithms is one of the central research issues in machine learning, and it may further shed important light on the nature of sensory representation and processing in the brain. Independent component analysis (ICA) is a fundamental method for unsupervised representation learning, i.e., without relying on any auxiliary information such as supervision and reward signals, and has been widely used in brain science. Although many studies have extended the standard linear (single-layer) ICA toward unsupervised multi-layer representation learning, specifically by stacking ICA layers with additional nonlinearities or so-called pooling layers, most previous attempts necessarily resorted to approximate or heuristic methods, having only a limited applicability. Here, we propose a new principled framework for such a multi-layer ICA and its extensions from the viewpoint of probabilistic generative modeling. We will investigate its theoretical basis, compare it with other deep generative models based on multi-layer neural networks, and explore its novel applications to brain science related to e.g. functional brain imaging or natural image statistics.