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We study the problem of unsupervised representation learning in slightly misspecified settings, and thus formalize the study of robustness of nonlinear representation learning. We focus on the case where the mixing is close to a local…
In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality…
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…
Recently, nonlinear ICA has surfaced as a popular alternative to the many heuristic models used in deep representation learning and disentanglement. An advantage of nonlinear ICA is that a sophisticated identifiability theory has been…
Independent Component Analysis (ICA) aims to find a coordinate system in which the components of the data are independent. In this paper we construct a new nonlinear ICA model, called WICA, which obtains better and more stable results than…
This paper introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating and testing the existence of mutually independent components for a given dataset, and a…
Independent component analysis (ICA) has been a popular dimension reduction tool in statistical machine learning and signal processing. In this paper, we present a convergence analysis for an online tensorial ICA algorithm, by viewing the…
Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully…
Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been…
Independent component analysis (ICA) has been shown to be useful in many applications. However, most ICA methods are sensitive to data contamination and outliers. In this article we introduce a general minimum U-divergence framework for…
Identifying the causal relations between interested variables plays a pivotal role in representation learning as it provides deep insights into the dataset. Identifiability, as the central theme of this approach, normally hinges on…
Compressive learning forms the exciting intersection between compressed sensing and statistical learning where one exploits forms of sparsity and structure to reduce the memory and/or computational complexity of the learning task. In this…
Independent Component Analysis (ICA) is a dimensionality reduction technique that can boost efficiency of machine learning models that deal with probability density functions, e.g. Bayesian neural networks. Algorithms that implement…
Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data widely used in observational sciences. In its classical form, ICA relies on modeling the data as a linear mixture of non-Gaussian…
Independent component analysis (ICA) is a powerful method for blind source separation based on the assumption that sources are statistically independent. Though ICA has proven useful and has been employed in many applications, complete…
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical…
Independent component analysis (ICA) is a computational method for separating a multivariate signal into subcomponents assuming the mutual statistical independence of the non-Gaussian source signals. The classical Independent Components…
In recent years, there has been growing interest in jointly analyzing a foreground dataset, representing an experimental group, and a background dataset, representing a control group. The goal of such contrastive investigations is to…
Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability…
Independent Component Analysis (ICA) is a statistical method often used to decompose a complex dataset in its independent sub-parts. It is a powerful technique to solve a typical Blind Source Separation problem. A fast calculation of the…