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We propose a novel unsupervised framework for \emph{Invariant Risk Minimization} (IRM), extending the concept of invariance to settings where labels are unavailable. Traditional IRM methods rely on labeled data to learn representations that…
Contrastive learning is a recent promising approach in unsupervised representation learning where a feature representation of data is learned by solving a pseudo classification problem from unlabelled data. However, it is not…
We extend frequency-domain blind source separation based on independent vector analysis to the case where there are more microphones than sources. The signal is modelled as non-Gaussian sources in a Gaussian background. The proposed…
Self-supervised learning aims to learn a embedding space where semantically similar samples are close. Contrastive learning methods pull views of samples together and push different samples away, which utilizes semantic invariance of…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
Marine controlled source electromagnetic (CSEM) sensing method used for the detection of hydrocarbons based reservoirs in seabed logging application does not perform well due to the presence of the airwaves (or sea-surface). These airwaves…
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…
In this paper the conditions for identifiability, separability and uniqueness of linear complex valued independent component analysis (ICA) models are established. These results extend the well-known conditions for solving real-valued ICA…
We consider linear models where $d$ potential causes $X_1,...,X_d$ are correlated with one target quantity $Y$ and propose a method to infer whether the association is causal or whether it is an artifact caused by overfitting or hidden…
Pattern-mixture models provide a transparent approach for handling missing data, where the full-data distribution is factorized in a way that explicitly shows the parts that can be estimated from observed data alone, and the parts that…
We give under weak assumptions a complete combinatorial characterization of identifiability for linear mixtures of finite alphabet sources, with unknown mixing weights and unknown source signals, but known alphabet. This is based on a…
Discovering the complete set of causal relations among a group of variables is a challenging unsupervised learning problem. Often, this challenge is compounded by the fact that there are latent or hidden confounders. When only observational…
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…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…
In spatial blind source separation the observed multivariate random fields are assumed to be mixtures of latent spatially dependent random fields. The objective is to recover latent random fields by estimating the unmixing transformation.…
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…
Independent component analysis (ICA), as an approach to the blind source-separation (BSS) problem, has become the de-facto standard in many medical imaging settings. Despite successes and a large ongoing research effort, the limitation of…
Canonical Correlation Analysis (CCA) is a classic technique for multi-view data analysis. To overcome the deficiency of linear correlation in practical multi-view learning tasks, various CCA variants were proposed to capture nonlinear…
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…