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Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…

Memory hierarchy is used to compete the processors speed. Cache memory is the fast memory which is used to conduit the speed difference of memory and processor. The access patterns of Level 1 cache (L1) and Level 2 cache (L2) are different,…

Providing various machine learning (ML) applications in the real world, concerns about discrimination hidden in ML models are growing, particularly in high-stakes domains. Existing techniques for assessing the discrimination level of ML…

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…

Likelihood-free methods are an essential tool for performing inference for implicit models which can be simulated from, but for which the corresponding likelihood is intractable. However, common likelihood-free methods do not scale well to…

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

Neural memory enables fast adaptation to new tasks with just a few training samples. Existing memory models store features only from the single last layer, which does not generalize well in presence of a domain shift between training and…

The programming paradigm Map-Reduce and its main open-source implementation, Hadoop, have had an enormous impact on large scale data processing. Our goal in this expository writeup is two-fold: first, we want to present some complexity…

Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…

Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

Fueled by their remarkable ability to tackle diverse tasks across multiple domains, large language models (LLMs) have grown at an unprecedented rate, with some recent models containing trillions of parameters. This growth is accompanied by…

We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…

In this paper, we propose a new neural network architecture based on the H2 matrix. Even though networks with H2-inspired architecture already exist, and our approach is designed to reduce memory costs and improve performance by taking into…

Few-shot classification and meta-learning methods typically struggle to generalize across diverse domains, as most approaches focus on a single dataset, failing to transfer knowledge across various seen and unseen domains. Existing…

Applications of machine learning (ML) to high-stakes policy settings -- such as education, criminal justice, healthcare, and social service delivery -- have grown rapidly in recent years, sparking important conversations about how to ensure…

This article focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas…

Due to the high computational demands executing a rigorous comparison between hyperparameter optimization (HPO) methods is often cumbersome. The goal of this paper is to facilitate a better empirical evaluation of HPO methods by providing…

We present an adaptation of two recent low-rank approximation technique proposed for first-order model reduction systems to the second-order systems. The resulting reduced order models are guaranteed to keep the second order structure which…