arXiv subjects

Elena Tuzhilina

Publications and source records attributed to Elena Tuzhilina.

7 recordsLinked to original sources

arXiv2026

Efficient Canonical Correlation Analysis with Sparsity

In high-dimensional settings, Canonical Correlation Analysis (CCA) often fails, and existing sparse methods force an untenable choice between computational speed and statistical rigor. This work introduces a fast and provably consistent sparse CCA algorithm (ECCAR) that resolves this trade-off. We formulate CCA as a high-dimensional reduced-rank regression problem, which allows us to derive consistent estimators with high-probability error bounds without relying on computationally expensive techniques like Fantope projections. The resulting algorithm is scalable, projection-free, and significantly faster than its competitors. We validate our method through extensive simulations and demonstrate its power to uncover reliable and interpretable associations in three complex biological datasets, as well as in an ML interpretability task. Our work makes sparse CCA a practical and trustworthy tool for large-scale multimodal data analysis. A companion R package has been made available.

stat.ME↗

arXiv2026

Canonical Correlation Analysis as Reduced Rank Regression in High Dimensions

Canonical correlation analysis is a widespread technique for discovering linear relationships between two sets of variables. In high dimensions, however, standard estimates of the canonical directions cease to be consistent without assuming further structure. In this setting, a possible solution consists in leveraging the presumed sparsity of the solution: only a subset of the covariates span the canonical directions. While the last decade has seen a proliferation of sparse canonical correlation analysis methods, practical challenges regarding the scalability and adaptability of these methods still persist. To circumvent these issues, this paper suggests an alternative strategy that uses reduced rank regression to estimate the canonical directions when one of the datasets is high-dimensional while the other remains low-dimensional. By casting the problem of estimating the canonical direction as a regression problem, our estimator is able to leverage the rich statistics literature on high-dimensional regression and is easily adaptable to accommodate a wider range of structural priors. Our proposed solution maintains computational efficiency and accuracy, even in the presence of very high-dimensional data. We demonstrate the advantages of our approach through a series of simulated experiments, achieving a substantial increase in accuracy compared to existing methods. Additionally, we highlight its practical utility by applying it to three real-world datasets, where we show that our method is able to uncover scientifically meaningful associations between variables.

stat.ME↗

arXiv2026

Weighted Low-Rank Matrix Approximation: Acceleration and Applications

Weighted low-rank matrix approximation (WLRMA) generalizes classical low-rank approximation and matrix completion by allowing arbitrary elementwise weights. Such formulations arise naturally in a broad class of statistical models, including generalized linear low-rank models, where WLRMA serves as the computational primitive for parameter estimation. Despite its broad applicability, efficient optimization methods for general WLRMA remain relatively underdeveloped. In this paper, we formulate both the rank-constrained and nuclear-norm WLRMA problems within a unified first-order optimization framework by showing that the corresponding iterative algorithms are projected and proximal gradient methods. Building on this perspective, we develop accelerated algorithms based on Nesterov momentum and Anderson acceleration, together with a regularized Anderson scheme that improves numerical stability for non-convex problems. We further propose scalable implementations for large sparse data matrices and introduce a practical effective-rank criterion that provides a meaningful correspondence between rank-constrained and nuclear-norm solutions. We further show that fitting generalized linear low-rank models can be reduced to a sequence of weighted low-rank matrix approximation problems, allowing the proposed algorithms to be used as computational building blocks for their estimation. Simulation studies demonstrate substantial computational gains achieved by the proposed accelerated algorithms. Applications to the MovieLens dataset further illustrate the proposed framework for matrix completion, heteroscedastic Gaussian low-rank modeling, and logistic low-rank modeling.

stat.ML↗

arXiv2026

A Probabilistic Model for Zero-Inflated Count Tensors with Structured Latent Representations

We propose a unified probabilistic framework for modeling high-dimensional count tensors with excess zeros. Such data arise naturally in a variety of applications, including single-cell Hi-C experiments, where observations are represented as a third-order tensor indexed by genomic locus pairs and cells. We develop a zero-inflated Poisson tensor model that captures the underlying latent structure through a low-rank tensor decomposition. For single-cell Hi-C data, the proposed framework further accommodates heterogeneous cell populations through latent cluster structure and exploits the ordered nature of genomic loci via smooth latent representations. We develop a likelihood-based estimation procedure together with a Bayes-optimal classifier for distinguishing structural zeros from technical zeros, enabling principled false-zero detection, imputation, and uncertainty quantification. Theoretically, we establish identifiability of the proposed model and consistency of the proposed estimators. Simulation studies and analyses of single-cell Hi-C data demonstrate improved performance in false-zero detection, latent structure recovery, and clustering.

stat.ME↗

arXiv2026

Sparse covariate-driven factorization of high-dimensional brain connectivity with application to site effect correction

Large-scale neuroimaging studies often collect data from multiple scanners across different sites, where variations in scanners, scanning procedures, and other conditions across sites can introduce artificial site effects. These effects may bias brain connectivity measures, such as functional connectivity (FC), which quantify functional network organization derived from functional magnetic resonance imaging (fMRI). How to leverage high-dimensional network structures to effectively mitigate site effects has yet to be addressed. In this paper, we propose SLACC (Sparse LAtent Covariate-driven Connectome) factorization, a multivariate method that explicitly parameterizes covariate effects in latent subject scores corresponding to sparse rank-1 latent patterns derived from brain connectivity. The proposed method identifies localized site-driven variability within and across brain networks, enabling targeted correction. We develop a penalized Expectation-Maximization (EM) algorithm for parameter estimation, incorporating the Bayesian Information Criterion (BIC) to guide optimization. Extensive simulations validate SLACC's robustness in recovering the true parameters and underlying connectivity patterns. Applied to the Autism Brain Imaging Data Exchange (ABIDE) dataset, SLACC demonstrates its ability to reduce site effects.

stat.ME↗

arXiv2022

Smooth multi-period forecasting with application to prediction of COVID-19 cases

Forecasting methodologies have always attracted a lot of attention and have become an especially hot topic since the beginning of the COVID-19 pandemic. In this paper we consider the problem of multi-period forecasting that aims to predict several horizons at once. We propose a novel approach that forces the prediction to be "smooth" across horizons and apply it to two tasks: point estimation via regression and interval prediction via quantile regression. This methodology was developed for real-time distributed COVID-19 forecasting. We illustrate the proposed technique with the CovidCast dataset as well as a small simulation example.

stat.ME↗

arXiv2021

Canonical Correlation Analysis in high dimensions with structured regularization

Canonical correlation analysis (CCA) is a technique for measuring the association between two multivariate data matrices. A regularized modification of canonical correlation analysis (RCCA) which imposes an $\ell_2$ penalty on the CCA coefficients is widely used in applications with high-dimensional data. One limitation of such regularization is that it ignores any data structure, treating all the features equally, which can be ill-suited for some applications. In this paper we introduce several approaches to regularizing CCA that take the underlying data structure into account. In particular, the proposed group regularized canonical correlation analysis (GRCCA) is useful when the variables are correlated in groups. We illustrate some computational strategies to avoid excessive computations with regularized CCA in high dimensions. We demonstrate the application of these methods in our motivating application from neuroscience, as well as in a small simulation example.

stat.ME↗