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Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems…

Machine Learning · Computer Science 2020-08-19 Dylan Peifer , Michael Stillman , Daniel Halpern-Leistner

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

Machine Learning · Computer Science 2022-01-11 Calvin Murdock , George Cazenavette , Simon Lucey

Existing subset selection methods for efficient learning predominantly employ discrete combinatorial and model-specific approaches which lack generalizability. For an unseen architecture, one cannot use the subset chosen for a different…

Machine Learning · Computer Science 2024-09-20 Eeshaan Jain , Tushar Nandy , Gaurav Aggarwal , Ashish Tendulkar , Rishabh Iyer , Abir De

The optimization algorithm and its hyperparameters can significantly affect the training speed and resulting model accuracy in machine learning applications. The wish list for an ideal optimizer includes fast and smooth convergence to low…

Machine Learning · Computer Science 2024-02-20 Marco Eckhoff , Markus Reiher

We consider a basic problem at the interface of two fundamental fields: submodular optimization and online learning. In the online unconstrained submodular maximization (online USM) problem, there is a universe $[n]=\{1,2,...,n\}$ and a…

Machine Learning · Computer Science 2018-06-12 Tim Roughgarden , Joshua R. Wang

Unsupervised anomaly detection (AD) is critical for a wide range of practical applications, from network security to health and medical tools. Due to the diversity of problems, no single algorithm has been found to be superior for all AD…

Machine Learning · Computer Science 2023-05-18 Małgorzata Gutowska , Suzanne Little , Andrew McCarren

We study the close interplay between error and compression in the non-parametric multiclass classification setting in terms of prototype learning rules. We focus in particular on a recently proposed compression-based learning rule termed…

Machine Learning · Computer Science 2022-12-27 Omer Kerem , Roi Weiss

We introduce a new library named abess that implements a unified framework of best-subset selection for solving diverse machine learning problems, e.g., linear regression, classification, and principal component analysis. Particularly, the…

Machine Learning · Statistics 2024-04-02 Jin Zhu , Xueqin Wang , Liyuan Hu , Junhao Huang , Kangkang Jiang , Yanhang Zhang , Shiyun Lin , Junxian Zhu

Data valuation and subset selection have emerged as valuable tools for application-specific selection of important training data. However, the efficiency-accuracy tradeoffs of state-of-the-art methods hinder their widespread application to…

Machine Learning · Computer Science 2022-03-15 Soumi Das , Manasvi Sagarkar , Suparna Bhattacharya , Sourangshu Bhattacharya

Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…

Optimization and Control · Mathematics 2024-01-31 Anurag Dutta , K. Lakshmanan , John Harshith , A. Ramamoorthy

Machine learning algorithms play an important role in a variety of important decision-making processes, including targeted advertisement displays, home loan approvals, and criminal behavior predictions. Given the far-reaching impact of…

Machine Learning · Computer Science 2023-04-14 Shaojie Tang , Jing Yuan

The performance of modern machine learning methods highly depends on their hyperparameter configurations. One simple way of selecting a configuration is to use default settings, often proposed along with the publication and implementation…

Machine Learning · Statistics 2021-05-03 Florian Pfisterer , Jan N. van Rijn , Philipp Probst , Andreas Müller , Bernd Bischl

This work describes the principled design of a theoretical framework leading to fast and accurate algorithmic information measures on finite multisets of finite strings by means of compression. One distinctive feature of our approach is to…

Information Theory · Computer Science 2025-02-25 François Cayre

Personalized treatment decisions have become an integral part of modern medicine. Thereby, the aim is to make treatment decisions based on individual patient characteristics. Numerous methods have been developed for learning such policies…

Machine Learning · Statistics 2023-06-27 Daniel Tschernutter , Tobias Hatt , Stefan Feuerriegel

Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example,…

Machine Learning · Computer Science 2025-02-07 Jakob Bach

The arrival of AI techniques in computations, with the potential for hallucinations and non-robustness, has made trustworthiness of algorithms a focal point. However, trustworthiness of the many classical approaches are not well understood.…

Optimization and Control · Mathematics 2023-12-19 Alexander Bastounis , Felipe Cucker , Anders C. Hansen

Deciding what to sense is a crucial task, made harder by dependencies and by a nonadditive utility function. We develop approximation algorithms for selecting an optimal set of measurements, under a dependency structure modeled by a…

Artificial Intelligence · Computer Science 2012-06-18 Yan Radovilsky , Solomon Eyal Shimony

There are a number of approximation algorithms for NP-hard versions of low rank approximation, such as finding a rank-$k$ matrix $B$ minimizing the sum of absolute values of differences to a given $n$-by-$n$ matrix $A$,…

Data Structures and Algorithms · Computer Science 2020-04-20 Zhao Song , David P. Woodruff , Peilin Zhong

A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settings, the nature of this anisotropy may be…

Numerical Analysis · Mathematics 2026-04-10 Ben Adcock , Avi Gupta

Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter…

Optimization and Control · Mathematics 2023-02-24 Mark Turner , Thorsten Koch , Felipe Serrano , Michael Winkler