Related papers: Nonparametric Evaluation of Noisy ICA Solutions

We revise the problem of extracting one independent component from an instantaneous linear mixture of signals. The mixing matrix is parameterized by two vectors, one column of the mixing matrix and one row of the de-mixing matrix. The…

We present a new, fast, algorithm for the separation of astrophysical components superposed in maps of the sky, based on the fast Independent Component Analysis technique (FastICA). It allows to recover both the spatial pattern and the…

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…

In the last two decades, unsupervised latent variable models---blind source separation (BSS) especially---have enjoyed a strong reputation for the interpretable features they produce. Seldom do these models combine the rich diversity of…

Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep…

Independent low-rank matrix analysis (ILRMA) is the state-of-the-art algorithm for blind source separation (BSS) in the determined situation (the number of microphones is greater than or equal to that of source signals). ILRMA achieves a…

We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a…

We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a…

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

The FastICA algorithm is one of the most popular iterative algorithms in the domain of linear independent component analysis. Despite its success, it is observed that FastICA occasionally yields outcomes that do not correspond to any true…

We apply the independent component analysis (ICA) to the real data from a gravitational wave detector for the first time. Specifically we use the iKAGRA data taken in April 2016, and calculate the correlations between the gravitational wave…

Independent component analysis (ICA), as a data driven method, has shown to be a powerful tool for functional magnetic resonance imaging (fMRI) data analysis. One drawback of this multivariate approach is, that it is not compatible to the…

Causal discovery witnessed significant progress over the past decades. In particular, many recent causal discovery methods make use of independent, non-Gaussian noise to achieve identifiability of the causal models. Existence of hidden…

We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical…

We are interested in consistent estimation of the mixing matrix in the ICA model, when the error distribution is close to (but different from) Gaussian. In particular, we consider $n$ independent samples from the ICA model $X = A\epsilon$,…

In independent component analysis it is assumed that the observed random variables are linear combinations of latent, mutually independent random variables called the independent components. Our model further assumes that only 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…

We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…

In this paper, we address a blind source separation (BSS) problem and propose a new extended framework of independent positive semidefinite tensor analysis (IPSDTA). IPSDTA is a state-of-the-art BSS method that enables us to take…