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Independent component analysis (ICA) has become a popular multivariate analysis and signal processing technique with diverse applications. This paper is targeted at discussing theoretical large sample properties of ICA unmixing matrix…
Independent Component Analysis (ICA) is a popular model for blind signal separation. The ICA model assumes that a number of independent source signals are linearly mixed to form the observed signals. We propose a new algorithm, PEGI (for…
Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to…
The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data.…
We deal with a model where a set of observations is obtained by a linear superposition of unknown components called sources. The problem consists in recovering the sources without knowing the linear transform. We extend the well-known…
We study optimization methods for solving the maximum likelihood formulation of independent component analysis (ICA). We consider both the the problem constrained to white signals and the unconstrained problem. The Hessian of the objective…
Spatial Independent Components Analysis (ICA) is increasingly used in the context of functional Magnetic Resonance Imaging (fMRI) to study cognition and brain pathologies. Salient features present in some of the extracted Independent…
Independent Mechanism Analysis (IMA) seeks to address non-identifiability in nonlinear Independent Component Analysis (ICA) by assuming that the Jacobian of the mixing function has orthogonal columns. As typical in ICA, previous work…
We introduce a new information maximization (infomax) approach for the blind source separation problem. The proposed framework provides an information-theoretic perspective for determinant maximization-based structured matrix factorization…
The Independent Component Analysis (ICA) algorithm is implemented as a neural network for separating signals of different origin in astrophysical sky maps. Due to its self-organizing capability, it works without prior assumptions on the…
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,…
Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the…
A framework named Copula Component Analysis (CCA) for blind source separation is proposed as a generalization of Independent Component Analysis (ICA). It differs from ICA which assumes independence of sources that the underlying components…
We present a novel algorithm for overcomplete independent components analysis (ICA), where the number of latent sources k exceeds the dimension p of observed variables. Previous algorithms either suffer from high computational complexity or…
Independent Component Analysis (ICA) is an important step in EEG processing for a wide-ranging set of applications. However, ICA requires well-designed studies and data collection practices to yield optimal results. Past studies have…
Independent Component Analysis (ICA) plays a central role in modern machine learning as a flexible framework for feature extraction. We introduce a horseshoe-type prior with a latent Polya-Gamma scale mixture representation, yielding…
Independent component analysis (ICA) is now a widely used solution for the analysis of multi-subject functional magnetic resonance imaging (fMRI) data. Independent vector analysis (IVA) generalizes ICA to multiple datasets, i.e., to…
Independent Component Analysis (ICA) offers interpretable semantic components of embeddings. While ICA theory assumes that embeddings can be linearly decomposed into independent components, real-world data often do not satisfy this…
Nonlinear independent component analysis (ICA) aims to uncover the true latent sources from their observable nonlinear mixtures. Despite its significance, the identifiability of nonlinear ICA is known to be impossible without additional…
Independent Component Analysis (ICA) aims to recover independent latent variables from observed mixtures thereof. Causal Representation Learning (CRL) aims instead to infer causally related (thus often statistically dependent) latent…