Related papers: Deep Deterministic Nonlinear ICA via Total Correla…
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…
Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian…
Latent variable discovery is a central problem in data analysis with a broad range of applications in applied science. In this work, we consider data given as an invertible mixture of two statistically independent components and assume that…
As one of the newest members in the field of artificial immune systems (AIS), the Dendritic Cell Algorithm (DCA) is based on behavioural models of natural dendritic cells (DCs). Unlike other AIS, the DCA does not rely on training data,…
Complex biological systems have been successfully modeled by biochemical and genetic interaction networks, typically gathered from high-throughput (HTP) data. These networks can be used to infer functional relationships between genes or…
In recent years, Independent Component Analysis (ICA) has successfully been applied to remove noise and artifacts in images obtained from Three-dimensional Polarized Light Imaging (3D-PLI) at the mesoscale (i.e., 64 $\mu$m). Here, we…
We introduce a new approach to apply the boosted difference of convex functions algorithm (BDCA) for solving non-convex and non-differentiable problems involving difference of two convex functions (DC functions). Supposing the first DC…
This paper extends recent work on nonlinear Independent Component Analysis (ICA) by introducing a theoretical framework for nonlinear Independent Subspace Analysis (ISA) in the presence of auxiliary variables. Observed high dimensional…
In this work, we propose efficient algorithms for joint independent subspace analysis (JISA), an extension of independent component analysis that deals with parallel mixtures, where not all the components are independent. We derive an…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
Independent component analysis (ICA) is the problem of efficiently recovering a matrix $A \in \mathbb{R}^{n\times n}$ from i.i.d. observations of $X=AS$ where $S \in \mathbb{R}^n$ is a random vector with mutually independent coordinates.…
This paper addresses the high dimensionality problem in blind source separation (BSS), where the number of sources is greater than two. Two pairwise iterative schemes are proposed to tackle this high dimensionality problem. The two pairwise…
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…
We address the convolutive blind source separation problem for the (over-)determined case where (i) the number of nonstationary target-sources $K$ is less than that of microphones $M$, and (ii) there are up to $M - K$ stationary Gaussian…
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…
Deep neural networks learn structured features from complex, non-Gaussian inputs, but the mechanisms behind this process remain poorly understood. Our work is motivated by the observation that the first-layer filters learnt by deep…
We propose a method for the blind separation of sounds of musical instruments in audio signals. We describe the individual tones via a parametric model, training a dictionary to capture the relative amplitudes of the harmonics. The model…
Identifying the causal relations between interested variables plays a pivotal role in representation learning as it provides deep insights into the dataset. Identifiability, as the central theme of this approach, normally hinges on…
We apply belief propagation to a Bayesian bipartite graph composed of discrete independent hidden variables and discrete visible variables. The network is the Discrete counterpart of Independent Component Analysis (DICA) and it is…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…