Related papers: Quantifying identifiability in independent compone…
Estimating the number of components is a fundamental challenge in unsupervised learning, particularly when dealing with high-dimensional data with many components or severely imbalanced component sizes. This paper addresses this challenge…
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…
Previous analytical studies of on-line Independent Component Analysis (ICA) learning rules have focussed on asymptotic stability and efficiency. In practice the transient stages of learning will often be more significant in determining the…
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…
We propose an ICA contrast based on the density estimation of the observed signal and its marginals by means of wavelets. The risk of the associated moment estimator is linked with approximation properties in Besov spaces. It is shown to…
Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…
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. In this paper we present Multiple-weighted Independent Component Analysis…
A core task in multi-modal learning is to integrate information from multiple feature spaces (e.g., text and audio), offering modality-invariant essential representations of data. Recent research showed that, classical tools such as {\it…
In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data (Spirtes et al. 2000; Pearl 2000). Such methods make various assumptions on the data generating process to facilitate its…
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…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
We consider the identifiability theory of probabilistic models and establish sufficient conditions under which the representations learned by a very broad family of conditional energy-based models are unique in function space, up to a…
Label noise in multiclass classification is a major obstacle to the deployment of learning systems. However, unlike the widely used class-conditional noise (CCN) assumption that the noisy label is independent of the input feature given the…
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…
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…
We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…
We consider a Gaussian contamination (i.e., mixture) model where the contamination manifests itself as a change in variance. We study this model in various asymptotic regimes, in parallel with the work of Ingster (1997) and Donoho and Jin…
Independent component analysis (ICA) is a powerful method for blind source separation based on the assumption that sources are statistically independent. Though ICA has proven useful and has been employed in many applications, complete…
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…
The contaminated Gaussian distribution represents a simple heavy-tailed elliptical generalization of the Gaussian distribution; unlike the often-considered t-distribution, it also allows for automatic detection of mild outlying or "bad"…