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Blind source separation (BSS), particularly independent component analysis (ICA), has been widely used in various fields of science such as biomedical signal processing to recover latent source signals from the observed mixture. While ICA…

In spite of considerable practical importance, current algorithmic fairness literature lacks technical methods to account for underlying geographic dependency while evaluating or mitigating bias issues for spatial data. We initiate the…

A wide range of systems exhibit high dimensional incomplete data. Accurate estimation of the missing data is often desired, and is crucial for many downstream analyses. Many state-of-the-art recovery methods involve supervised learning…

We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…

Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…

Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain…

We give an efficient algorithm that, given a graph $G$ and a partition $V_1,\ldots,V_m$ of its vertex set, finds either an independent transversal (an independent set $\{v_1,\ldots,v_m\}$ in $G$ such that $v_i\in V_i$ for each $i$), or a…

We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…

Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many…

Independent Component Analysis (ICA) aims to recover independent latent variables from observed mixtures thereof. Causal Representation Learning (CRL) aims instead to infer causally related (thus often statistically dependent) latent…

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…

Independent component analysis (ICA) is a computational method for separating a multivariate signal into subcomponents assuming the mutual statistical independence of the non-Gaussian source signals. The classical Independent Components…

Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of…

Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…

We introduce methods to count and enumerate all maximal independent, all maximum independent sets, and all independent sets in threshold graphs and k-threshold graphs. Within threshold graphs and k-threshold graphs independent sets…

Independent Component Analysis (ICA) is a foundational tool for unsupervised representation learning, yet its high-dimensional theory remains largely limited to single-component recovery. We develop an asymptotically exact mean-field theory…

In the context of difference image analysis (DIA), we present a new method for determining the convolution kernel matching a pair of images of the same field. Unlike the standard DIA technique which involves modelling the kernel as a linear…

With the popularity of multimedia technology, information is always represented or transmitted from multiple views. Most of the existing algorithms are graph-based ones to learn the complex structures within multiview data but overlooked…

We investigate the identifiability of nonlinear Canonical Correlation Analysis (CCA) in a multi-view setup, where each view is generated by an unknown nonlinear map applied to a linear mixture of shared latents and view-private noise.…

Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…