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The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…

Machine Learning · Statistics 2020-01-16 Vincent Adam , Stefanos Eleftheriadis , Nicolas Durrande , Artem Artemev , James Hensman

Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…

Machine Learning · Computer Science 2025-01-08 Sebastian Ament , Elizabeth Santorella , David Eriksson , Ben Letham , Maximilian Balandat , Eytan Bakshy

We consider the structured-output prediction problem through probabilistic approaches and generalize the "perturb-and-MAP" framework to more challenging weighted Hamming losses, which are crucial in applications. While in principle our…

Machine Learning · Statistics 2018-11-22 Tatiana Shpakova , Francis Bach , Anton Osokin

Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…

Algebraic Topology · Mathematics 2023-01-19 Yuan Luo , Bradley J. Nelson

We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…

Machine Learning · Computer Science 2013-11-12 Yanshuai Cao , Marcus A. Brubaker , David J. Fleet , Aaron Hertzmann

The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the…

Machine Learning · Computer Science 2016-10-06 Bamdev Mishra , Rodolphe Sepulchre

This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…

Information Theory · Computer Science 2024-10-10 Yinjian Wang

This article provides an original understanding of the behavior of a class of graph-oriented semi-supervised learning algorithms in the limit of large and numerous data. It is demonstrated that the intuition at the root of these methods…

Machine Learning · Computer Science 2017-11-10 Xiaoyi Mai , Romain Couillet

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…

Machine Learning · Statistics 2015-09-08 David A. Knowles

We propose a learning-based approach for the sparse Gaussian Elimination. There are many hard combinatorial optimization problems in modern sparse solver. These NP-hard problems could be handled in the framework of Markov Decision Process,…

Numerical Analysis · Mathematics 2021-10-01 Yingshi Chen

The research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non-increasing order of processing times. In this paper, we find…

Numerical Analysis · Mathematics 2012-02-15 Lei Wang , Heng Liang , Fengshan Bai , Yan Huo

Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…

Optimization and Control · Mathematics 2024-06-21 Monse Guedes-Ayala , Pierre-Louis Poirion , Lars Schewe , Akiko Takeda

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…

Optimization and Control · Mathematics 2011-08-30 Alexandre d'Aspremont

This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…

Optimization and Control · Mathematics 2026-01-21 Ahmad Mousavi , Morteza Kimiaei , Saman Babaie-Kafaki , Vyacheslav Kungurtsev

The Gaussian process (GP) regression can be severely biased when the data are contaminated by outliers. This paper presents a new robust GP regression algorithm that iteratively trims the most extreme data points. While the new algorithm…

Machine Learning · Computer Science 2021-06-15 Zhao-Zhou Li , Lu Li , Zhengyi Shao

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

Machine Learning · Computer Science 2021-04-07 Bingxin Zhou , Junbin Gao , Minh-Ngoc Tran , Richard Gerlach

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…

Machine Learning · Statistics 2010-02-11 Julien Mairal , Francis Bach , Jean Ponce , Guillermo Sapiro

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…

Machine Learning · Statistics 2017-12-14 Thanh V. Nguyen , Raymond K. W. Wong , Chinmay Hegde

Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…

Applications · Statistics 2019-01-08 Raoul R. Wadhwa , Andrew Dhawan , Drew F. K. Williamson , Jacob G. Scott

We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…

Statistics Theory · Mathematics 2025-07-29 Christian Borgs , Jennifer Chayes , Devavrat Shah , Christina Lee Yu