Related papers: Low-rank tensor methods for model order reduction

The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…

Low Rank Approximation (LRA) of a matrix is a hot research subject, fundamental for Matrix and Tensor Computations and Big Data Mining and Analysis. Computations with low rank matrices can be performed at sublinear cost -- by using much…

Low-Rank Adaptation (LoRA) is widely used to efficiently adapt Transformers by adding trainable low-rank matrices to attention projections. While effective, these matrices are considered independent for each attention projection (Query,…

In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors…

For a given symmetric tensor, we aim at finding a new one whose symmetric rank is small and that is close to the given one. There exist linear relations among the entries of low rank symmetric tensors. Such linear relations can be expressed…

One of the principal barriers in developing accurate and tractable predictive models in turbulent flows with a large number of species is to track every species by solving a separate transport equation, which can be computationally…

Effective modeling of heterogeneous subpopulations presents a significant challenge due to variations in individual characteristics and behaviors. This paper proposes a novel approach to address this issue through multi-task learning (MTL)…

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…

This paper investigates nonlinear panel regression models with interactive fixed effects and introduces a general framework for parameter estimation under potentially non-convex objective functions. We propose a computationally feasible…

Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…

Diffusion models have become the de facto standard for modern visual generation, including well-established frameworks such as latent diffusion and flow matching. Recently, modeling high-order dynamics has emerged as a promising frontier in…

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…

Real life data often includes information from different channels. For example, in computer vision, we can describe an image using different image features, such as pixel intensity, color, HOG, GIST feature, SIFT features, etc.. These…

The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We…

Ranking is a key aspect of many applications, such as information retrieval, question answering, ad placement and recommender systems. Learning to rank has the goal of estimating a ranking model automatically from training data. In…

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…

We consider reduced-rank modeling of the white noise covariance matrix in a large dimensional vector autoregressive (VAR) model. We first propose the reduced-rank covariance estimator under the setting where independent observations are…

We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…

We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the…