Related papers: Simultaneous Estimation of Non-Gaussian Components…
Non-Gaussian component analysis (NGCA) is a problem in multidimensional data analysis which, since its formulation in 2006, has attracted considerable attention in statistics and machine learning. In this problem, we have a random variable…
In this work, we explore Partitioned Independent Component Analysis (PICA), an extension of the well-established Independent Component Analysis (ICA) framework. Traditionally, ICA focuses on extracting a vector of independent source signals…
It is well known that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…
We propose automated augmented conjugate inference, a new inference method for non-conjugate Gaussian processes (GP) models. Our method automatically constructs an auxiliary variable augmentation that renders the GP model conditionally…
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…
We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets 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…
Causal discovery based on Independent Component Analysis (ICA) has achieved remarkable success through the LiNGAM framework, which exploits non-Gaussianity and independence of noise variables to identify causal order. However, classical…
This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…
We develop a new modeling framework for Inter-Subject Analysis (ISA). The goal of ISA is to explore the dependency structure between different subjects with the intra-subject dependency as nuisance. It has important applications in…
Methods for analysis of principal components in discrete data have existed for some time under various names such as grade of membership modelling, probabilistic latent semantic analysis, and genotype inference with admixture. In this paper…
The statistical matching problem is a data integration problem with structured missing data. The general form involves the analysis of multiple datasets that only have a strict subset of variables jointly observed across all datasets. The…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation…
Independent component analysis (ICA) is a statistical method for transforming an observable multi-dimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes…
Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…
We propose a new fast generalized functional principal components analysis (fast-GFPCA) algorithm for dimension reduction of non-Gaussian functional data. The method consists of: (1) binning the data within the functional domain; (2)…
We consider the identifiability theory of probabilistic models and establish sufficient conditions under which the representations learned by a very broad family of conditional energy-based models are unique in function space, up to a…
Nonlinear independent component analysis (nICA) aims at recovering statistically independent latent components that are mixed by unknown nonlinear functions. Central to nICA is the identifiability of the latent components, which had been…