Related papers: Binary Independent Component Analysis: A Non-stati…
A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency…
Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this…
We consider modeling, inference, and computation for analyzing multivariate binary data. We propose a new model that consists of a low dimensional latent variable component and a sparse graphical component. Our study is motivated by…
Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the…
Group studies involving large cohorts of subjects are important to draw general conclusions about brain functional organization. However, the aggregation of data coming from multiple subjects is challenging, since it requires accounting for…
Blind source separation (BSS), particularly independent component analysis (ICA), has been widely used in various fields of science such as biomedical signal processing to recover latent source signals from the observed mixture. While ICA…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
We propose two approaches for selecting variables in latent class analysis (i.e.,mixture model assuming within component independence), which is the common model-based clustering method for mixed data. The first approach consists in…
Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…
Independent component analysis (ICA) has often been used as a tool to model natural image statistics by separating multivariate signals in the image into components that are assumed to be independent. However, these estimated components…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
Independent Component Analysis (ICA) is a foundational tool for unsupervised representation learning, yet its high-dimensional theory remains largely limited to single-component recovery. We develop an asymptotically exact mean-field theory…
Finding statistically significant interactions between binary variables is computationally and statistically challenging in high-dimensional settings, due to the combinatorial explosion in the number of hypotheses. Terada et al. recently…
We describe a method for unmixing mixtures of freely independent random variables in a manner analogous to the independent component analysis (ICA) based method for unmixing independent random variables from their additive mixtures. Random…
A fundamental research question is how much a variation in a covariate influences a binary response variable in a logistic regression model, both directly or through mediators. We derive the exact formula linking the parameters of marginal…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…
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…