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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…

Latent component identification from unknown nonlinear mixtures is a foundational challenge in machine learning, with applications in tasks such as disentangled representation learning and causal inference. Prior work in nonlinear…

Markov chain Monte Carlo (MCMC) samplers are numerical methods for drawing samples from a given target probability distribution. We discuss one particular MCMC sampler, the MALA-within-Gibbs sampler, from the theoretical and practical…

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…

We consider independent component analysis of binary data. While fundamental in practice, this case has been much less developed than ICA for continuous data. We start by assuming a linear mixing model in a continuous-valued latent space,…

This study uses a Variational Autoencoder method to enhance the efficiency and applicability of Markov Chain Monte Carlo (McMC) methods by generating broader-spectrum prior proposals. Traditional approaches, such as the Karhunen-Lo\`eve…

We consider a distributed source coding problem of $L$ correlated Gaussian observations $Y_i, i=1,2,...,L$. We assume that the random vector $Y^{L}={}^{\rm t} (Y_1,Y_2,$ $...,Y_L)$ is an observation of the Gaussian random vector…

Sparse inverse covariance estimation (i.e., edge de-tection) is an important research problem in recent years, wherethe goal is to discover the direct connections between a set ofnodes in a networked system based upon the observed…

We address the determined audio source separation problem in the time-frequency domain. In independent deeply learned matrix analysis (IDLMA), it is assumed that the inter-frequency correlation of each source spectrum is zero, which is…

In this paper the conditions for identifiability, separability and uniqueness of linear complex valued independent component analysis (ICA) models are established. These results extend the well-known conditions for solving real-valued ICA…

The rapid adoption of synthetic data for training Large Language Models (LLMs) has introduced the technical challenge of "model collapse"-a degenerative process where recursive training on model-generated content leads to a contraction of…

We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees. In particular, suppose we are given samples of the form $y = Ax + \eta$ where $A$ is an unknown $n \times n$ matrix and $x$ is a…

Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain…

Fair machine learning seeks to identify and mitigate biases in predictions against unfavorable populations characterized by demographic attributes, such as race and gender. Recently, a few works have extended fairness to graph data, such as…

Graph-structured combinatorial problems in complex networks are prevalent in many domains, and are computationally demanding due to their complexity and non-linear nature. Traditional evolutionary algorithms (EAs), while robust, often face…

We consider Bayesian inference for image deblurring with total variation (TV) prior. Since the posterior is analytically intractable, we resort to Markov chain Monte Carlo (MCMC) methods. However, since most MCMC methods significantly…

Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact…

In this paper, we address a multichannel audio source separation task and propose a new efficient method called independent deeply learned matrix analysis (IDLMA). IDLMA estimates the demixing matrix in a blind manner and updates the…

We study a Compressed Sensing (CS) problem known as Multiple Measurement Vectors (MMV) problem, which arises in joint estimation of multiple signal realizations when the signal samples have a common (joint) sparse support over a fixed known…

Deep latent variable models (DLVMs) are designed to learn meaningful representations in an unsupervised manner, such that the hidden explanatory factors are interpretable by independent latent variables (aka disentanglement). The…