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We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…
Compositional data are common in many fields, both as outcomes and predictor variables. The inventory of models for the case when both the outcome and predictor variables are compositional is limited and the existing models are difficult to…
Recent advances in citation recommendation have improved accuracy by leveraging multi-view representation learning to integrate the various modalities present in scholarly documents. However, effectively combining multiple data views…
Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches…
Multiple sets of measurements on the same objects obtained from different platforms may reflect partially complementary information of the studied system. The integrative analysis of such data sets not only provides us with the opportunity…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Canonical correlation analysis (CCA) describes the associations between two sets of variables by maximizing the correlation between linear combinations of the variables in each data set. However, in high-dimensional settings where the…
Large Language Models (LLMs) like LLaMA, Mistral, and Gemma are increasingly used in decision-critical domains such as healthcare, law, and finance, yet their reliability remains uncertain. They often make overconfident errors, degrade…
In microbiome and genomic studies, the regression of compositional data has been a crucial tool for identifying microbial taxa or genes that are associated with clinical phenotypes. To account for the variation in sequencing depth, the…
The Latent Dirichlet Allocation (LDA) model is a popular method for creating mixed-membership clusters. Despite having been originally developed for text analysis, LDA has been used for a wide range of other applications. We propose a new…
The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…
In compositional data analysis an observation is a vector containing non-negative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of…
Accurately assessing a patient's risk of a given event is essential in making informed treatment decisions. One approach is to stratify patients into two or more distinct risk groups with respect to a specific outcome using both clinical…
High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…
Compositional data analysis is carried out either by neglecting the compositional constraint and applying standard multivariate data analysis, or by transforming the data using the logs of the ratios of the components. In this work we…
Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…
Multi-headed Attention's (MHA) quadratic compute and linearly growing KV-cache make long-context transformers expensive to train and serve. Prior works such as Grouped Query Attention (GQA) and Multi-Latent Attention (MLA) shrink the cache,…
In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This…
Thanks to high-tech measurement systems like sensors, data are often collected with high frequency in modern industrial processes. This phenomenon could potentially produce autocorrelated and cross-correlated measurements. It has been shown…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…