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The goal of this paper is to extend independent subspace analysis (ISA) to the case of (i) nonparametric, not strictly stationary source dynamics and (ii) unknown source component dimensions. We make use of functional autoregressive (fAR)…

Methodology · Statistics 2012-01-04 Zoltan Szabo

In this paper we derive a new framework for independent component analysis (ICA), called measure-transformed ICA (MTICA), that is based on applying a structured transform to the probability distribution of the observation vector, i.e.,…

Methodology · Statistics 2013-12-10 Koby Todros , Alfred O. Hero

In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality…

Statistics Theory · Mathematics 2023-04-03 Arnab Auddy , Ming Yuan

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…

Statistics Theory · Mathematics 2024-02-16 Marina Garrote-López , Monroe Stephenson

Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data widely used in observational sciences. In its classical form, ICA relies on modeling the data as a linear mixture of non-Gaussian…

Machine Learning · Statistics 2017-11-30 Pierre Ablin , Jean-François Cardoso , Alexandre Gramfort

Independent component analysis (ICA) is linked up with the problem of estimating a non linear functional of a density, for which optimal estimators are well known. The precision of ICA is analyzed from the viewpoint of functional spaces in…

Statistics Theory · Mathematics 2007-06-13 Pascal Barbedor

Independent Component Analysis (ICA) is an algorithm originally developed for finding separate sources in a mixed signal, such as a recording of multiple people in the same room speaking at the same time. Unlike Principal Component Analysis…

Computation and Language · Computer Science 2024-09-05 Tomáš Musil , David Mareček

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…

Machine Learning · Computer Science 2023-11-03 Yujia Zheng , Kun Zhang

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…

For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world…

Machine Learning · Statistics 2020-12-15 Takuya Isomura , Taro Toyoizumi

Background: Independent Component Analysis (ICA) is a widespread tool for exploration and denoising of electroencephalography (EEG) or magnetoencephalography (MEG) signals. In its most common formulation, ICA assumes that the signal matrix…

Signal Processing · Electrical Eng. & Systems 2020-08-25 Pierre Ablin , Jean-François Cardoso , Alexandre Gramfort

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…

Machine Learning · Statistics 2016-11-15 Vicente Zarzoso , Pierre Comon

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…

Machine Learning · Statistics 2022-12-14 Seonjoo Lee , Haipeng Shen , Young K. Truong

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…

Independent component analysis (ICA) has been a popular dimension reduction tool in statistical machine learning and signal processing. In this paper, we present a convergence analysis for an online tensorial ICA algorithm, by viewing the…

Machine Learning · Computer Science 2021-07-30 Chris Junchi Li , Michael I. Jordan

Although approaches to Independent Component Analysis (ICA) based on characteristic function seem theoretically elegant, they may suffer from implementational challenges because of numerical integration steps or selection of tuning…

Methodology · Statistics 2025-11-07 Vincent Starck

A seminal result in the ICA literature states that for $AY = \varepsilon$, if the components of $\varepsilon$ are independent and at most one is Gaussian, then $A$ is identified up to sign and permutation of its rows (Comon, 1994). In this…

Statistics Theory · Mathematics 2024-03-21 Geert Mesters , Piotr Zwiernik

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…

Machine Learning · Statistics 2026-05-12 Eser Ilke Genc , Samet Demir , Zafer Dogan

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the…

Applications · Statistics 2012-03-19 Stéphanie Allassonniére , Laurent Younes

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…

Machine Learning · Computer Science 2012-11-13 Sanjeev Arora , Rong Ge , Ankur Moitra , Sushant Sachdeva