Dictionary learning

Optimal transport supports clustering, dictionary learning and domain adaptation, but high-dimensional data often force projections that discard information. Charles Bouveyron develops an alternative for Gaussian distributions with parsimonious covariance structure and low intrinsic dimension. A low-dimensional decomposition of empirical covariance matrices gives an efficient, robust closed form for the 2-Wasserstein distance without projecting the data. An explicit Monge map uses exact covariance square roots and inverse square roots. Numerical comparisons demonstrate analytical and computati

…in many tasks, ranging from dictionary learning to machine learning. Statistical physics can provide on the one hand theoretical limits on the possibility of factorizing matrices in the limit of infinite size, and also practical algorithms. While this program has been successful in the case of finite rank matrices, the regime of extensive rank (scaling linearly with the dimension of the matrix) turns out to be much harder. This talk will describe a new approach to matrix facto

Recent work has indicated that functional connections between C. elegans neurons can be clustered by their role in behavior, i.e. forward vs. reverse crawling vs. turning (Linderman et al. 2019). Furthermore they show how data-driven dynamical systems, e.g., the recurrent switching linear dynamical systems (rSLDS), can be learned in an unsupervised way from whole-brain recordings (Kato et al. 2015). However, these approaches ascribe a discrete overall state to the system at each time point, potentially missing different dimensions of variability in the data. For example, such models cannot fle

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how neural activity relates to perception and behavior. Models of neural dynamics often focus on either low-dimensional projections of neural activity, or on learning dynamical systems that explicitly relate to the neural state over time. We discuss how these two approaches are interrelated by considering dynamical systems as representative of flows on a low-dimensional manifold. Building on this concept, we propose a new decomposed dynamical system model that represents com