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In this paper, we introduce a new approach to multiclass classification problem. We decompose the problem into a series of regression tasks, that are solved with CART trees. The proposed method works significantly faster than…

Machine Learning · Computer Science 2019-09-12 Igor E. Kuralenok , Yurii Rebryk , Ruslan Solovev , Anton Ermilov

Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…

Machine Learning · Statistics 2024-10-10 Vassilis Apidopoulos , Tomaso Poggio , Lorenzo Rosasco , Silvia Villa

The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…

Machine Learning · Statistics 2014-06-10 Siong Thye Goh , Cynthia Rudin

We propose an algorithm of generating hard instances for the Satisfying Assignment Search Problem (in short, SAT). The algorithm transforms instances of the integer factorization problem into SAT instances efficiently by using the Chinese…

Computational Complexity · Computer Science 2007-05-23 Satoshi Horie , Osamu Watanabe

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…

Artificial Intelligence · Computer Science 2012-03-19 Vibhav Gogate , Pedro Domingos

A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced…

Data Structures and Algorithms · Computer Science 2022-04-25 N. A. Carella

Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…

Methodology · Statistics 2018-01-17 Wilson Y. Chen , Matt P. Wand

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

Symbolic Computation · Computer Science 2019-01-31 Jean-Guillaume Dumas , Joris Van Der Hoeven , Clément Pernet , Daniel Roche

We describe a dynamic programming algorithm for computing the marginal distribution of discrete probabilistic programs. This algorithm takes a functional interpreter for an arbitrary probabilistic programming language and turns it into an…

Artificial Intelligence · Computer Science 2012-09-12 Andreas Stuhlmüller , Noah D. Goodman

Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…

Numerical Analysis · Mathematics 2019-05-28 Steffen Börm

The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…

Machine Learning · Computer Science 2023-12-19 Srikumar Ramalingam , Pranjal Awasthi , Sanjiv Kumar

Machine Learning classification models learn the relation between input as features and output as a class in order to predict the class for the new given input. Quantum Mechanics (QM) has already shown its effectiveness in many fields and…

Ensemble learning combines multiple classifiers in the hope of obtaining better predictive performance. Empirical studies have shown that ensemble pruning, that is, choosing an appropriate subset of the available classifiers, can lead to…

Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…

Machine Learning · Computer Science 2022-10-04 Peter Belcák , David Hofer , Roger Wattenhofer

Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…

Number Theory · Mathematics 2021-10-27 Matthew B. Crawford

The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…

Machine Learning · Statistics 2020-03-19 Kun Chen , Ruipeng Dong , Wanwan Xu , Zemin Zheng

We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…

Data Structures and Algorithms · Computer Science 2024-07-26 Tim Randolph , Karol Węgrzycki

The main objective of this paper is to solve the optimization problem that is associated with the classification of DNA samples in PCR plates for Sanger sequencing. To achieve this goal, we design an integer linear programming model. Given…

Data Structures and Algorithms · Computer Science 2024-01-23 Luisa Carpente , Ana Cerdeira-Pena , Silvia Lorenzo-Freire , Ángeles S. Places

Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…

Data Structures and Algorithms · Computer Science 2014-11-20 Khaled Elbassioni , Trung Thanh Nguyen

Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…

Computational Complexity · Computer Science 2026-04-21 Mircea-Adrian Digulescu