Related papers: PhD Dissertation: Generalized Independent Componen…

Noise subtraction is a crucial process in gravitational wave (GW) data analysis to improve the sensitivity of interferometric detectors. While linear noise coupling has been extensively studied and successfully mitigated using methods such…

We investigate the algebra and geometry of the independence conditions on discrete random variables in which we fix some random variables and study the complete independence of some subcollections. We interpret such independence conditions…

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…

Online blind source separation is essential for both speech communication and human-machine interaction. Among existing approaches, overdetermined independent vector analysis (OverIVA) delivers strong performance by exploiting the…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

Causal discovery witnessed significant progress over the past decades. In particular, many recent causal discovery methods make use of independent, non-Gaussian noise to achieve identifiability of the causal models. Existence of hidden…

Independent vector analysis (IVA) is an attractive solution to address the problem of joint blind source separation (JBSS), that is, the simultaneous extraction of latent sources from several datasets implicitly sharing some information.…

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…

Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or…

Discovering the complete set of causal relations among a group of variables is a challenging unsupervised learning problem. Often, this challenge is compounded by the fact that there are latent or hidden confounders. When only observational…

We propose the Sobolev Independence Criterion (SIC), an interpretable dependency measure between a high dimensional random variable X and a response variable Y . SIC decomposes to the sum of feature importance scores and hence can be used…

In recent years, Independent Component Analysis (ICA) has successfully been applied to remove noise and artifacts in images obtained from Three-dimensional Polarized Light Imaging (3D-PLI) at the mesoscale (i.e., 64 $\mu$m). Here, we…

Commercial cellular networks, like the systems based on DS-CDMA, face many types of interferences such as multi-user interference inside each sector in a cell to interoperate interference. Independent Component Analysis (ICA) has been used…

Spatial Independent Component Analysis (ICA) decomposes the time by space functional MRI (fMRI) matrix into a set of 1-D basis time courses and their associated 3-D spatial maps that are optimized for mutual independence. When applied to…

We propose a new algorithm for blind source separation (BSS) using independent vector analysis (IVA). This is an improvement over the popular auxiliary function based IVA (AuxIVA) with iterative projection (IP) or iterative source steering…

We present a unified framework for studying the identifiability of representations learned from simultaneously observed views, such as different data modalities. We allow a partially observed setting in which each view constitutes a…

We present a new high performance Convex Cauchy Schwarz Divergence (CCS DIV) measure for Independent Component Analysis (ICA) and Blind Source Separation (BSS). The CCS DIV measure is developed by integrating convex functions into the…

With the emergence of wireless sensor networks (WSNs), many traditional signal processing tasks are required to be computed in a distributed fashion, without transmissions of the raw data to a centralized processing unit, due to the limited…