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Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse,…

In a broad range of computer vision applications, the purpose of Low-rank matrix approximation (LRMA) models is to recover the underlying low-rank matrix from its degraded observation. The latest LRMA methods - Robust Principal Component…

Recovering the support of sparse vectors in underdetermined linear regression models, \textit{aka}, compressive sensing is important in many signal processing applications. High SNR consistency (HSC), i.e., the ability of a support recovery…

Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

N:M structured pruning is essential for large language models (LLMs) because it can remove less important network weights and reduce the memory and computation requirements. Existing pruning methods mainly focus on designing metrics to…

We introduce a reformulation of regularized low-rank recovery models to take advantage of GPU, multiple CPU, and hybridized architectures. Low-rank recovery often involves nuclear-norm minimization through iterative thresholding of singular…

The ventral, dorsal, and lateral streams in high-level human visual cortex are implicated in distinct functional processes. Yet, deep neural networks (DNNs) trained on a single task model the entire visual system surprisingly well, hinting…

Differentiable reinforcement learning (RL) frameworks like DiffRO offer a powerful approach for controllable text-to-speech (TTS), but are vulnerable to reward hacking, particularly for nuanced tasks like emotion control. The policy model…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…

This paper proposes a new method and algorithm for predicting multivariate responses in a regression setting. Research into classification of High Dimension Low Sample Size (HDLSS) data, in particular microarray data, has made considerable…

Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…

Multi-cellular programs (MCPs) are coordinated patterns of gene expression across interacting cell types that collectively drive complex biological processes such as tissue development and immune responses. While MCPs are typically…

Learned sparse retrieval (LSR) is a family of neural methods that encode queries and documents into sparse lexical vectors that can be indexed and retrieved efficiently with an inverted index. We explore the application of LSR to the…

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…

Recent studies have utilized sparse classifications to predict categorical variables from high-dimensional brain activity signals to expose human's intentions and mental states, selecting the relevant features automatically in the model…

Functional Magnetic Resonance Images acquired during resting-state provide information about the functional organization of the brain through measuring correlations between brain areas. Independent components analysis is the reference…