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We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
Statistical physics is used to investigate independent component analysis with polynomial contrast functions. While the replica method fails, an adapted cavity approach yields valid results. The learning curves, obtained in a suitable…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
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…
Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude…
We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Independent Component Analysis (ICA) recently has attracted attention in the statistical literature as an alternative to elliptical models. Whereas k-dimensional elliptical densities depend on one single unspecified radial density, however,…
The analysis of the wavelength-dependent albedo of exoplanets represents a direct way to provide insight of their atmospheric composition and to constrain theoretical planetary atmosphere modelling. Wavelength-dependent albedo can be…
Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…
Image Quality Assessment (IQA) algorithms evaluate the perceptual quality of an image using evaluation scores that assess the similarity or difference between two images. We propose a new low-level feature based IQA technique, which applies…
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 make use of a large set of fast simulations of an intensity mapping experiment with characteristics similar to those expected of the Square Kilometre Array (SKA) in order to study the viability and limits of blind foreground subtraction…
This study utilizes Independent Component Analysis (ICA) to unveil a consistent semantic structure within embeddings of words or images. Our approach extracts independent semantic components from the embeddings of a pre-trained model by…
This paper investigates a general robust one-shot aggregation framework for distributed and federated Independent Component Analysis (ICA) problem. We propose a geometric median-based aggregation algorithm that leverages $k$-means…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number…
Subjective classification of galaxies can mislead us in the quest of the origin regarding formation and evolution of galaxies since this is necessarily limited to a few features. The human mind is not able to apprehend the complex…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…
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 $X = A\epsilon$,…