English
Related papers

Related papers: New bounds and efficient algorithm for sparse diff…

200 papers

We consider the problem of multivariate regression in a setting where the relevant predictors could be shared among different responses. We propose an algorithm which decomposes the coefficient matrix into the product of a long matrix and a…

Machine Learning · Statistics 2016-03-02 Milad Kharratzadeh , Mark Coates

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system…

Symbolic Computation · Computer Science 2014-07-11 Johannes Bluemlein , Abilio De Freitas , Carsten Schneider

We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…

Numerical Analysis · Mathematics 2012-07-27 David Lawlor , Yang Wang , Andrew Christlieb

In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of…

Symbolic Computation · Computer Science 2015-03-17 Wei Zhu , Xiao-Shan Gao

A relaxation method based on border basis reduction which improves the efficiency of Lasserre's approach is proposed to compute the optimum of a polynomial function on a basic closed semi algebraic set. A new stopping criterion is given to…

Algebraic Geometry · Mathematics 2015-08-25 Marta Abril Bucero , Bernard Mourrain

A new sparse SOS decomposition algorithm is proposed based on a new sparsity pattern, called cross sparsity patterns. The new sparsity pattern focuses on the sparsity of terms and thus is different from the well-known correlative sparsity…

Optimization and Control · Mathematics 2019-01-23 Jie Wang , Haokun Li , Bican Xia

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…

Machine Learning · Computer Science 2021-05-05 Gert-Jan Both , Gijs Vermarien , Remy Kusters

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

Computation · Statistics 2022-11-02 Qian LI , Binyan Jiang , Defeng Sun

The finite difference equation system introduced by Christiane Poupard in the study of tangent trees is reinterpreted in the alternating permutation environment. It makes it possible to make a joint study of both tangent and secant trees…

Combinatorics · Mathematics 2013-04-10 Dominique Foata , Guo-Niu Han

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

Machine Learning · Statistics 2012-06-08 Ali Jalali , Sujay Sanghavi

We consider resultant-based methods for elimination of indeterminates of Ore polynomial systems in Ore algebra. We start with defining the concept of resultant for bivariate Ore polynomials then compute it by the Dieudonne determinant of…

Symbolic Computation · Computer Science 2022-10-10 Raqeeb Rasheed

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…

Methodology · Statistics 2022-05-25 Fatma Sevinç Kurnaz , Peter Filzmoser

We propose a novel, efficient approach for distributed sparse learning in high-dimensions, where observations are randomly partitioned across machines. Computationally, at each round our method only requires the master machine to solve a…

Machine Learning · Statistics 2016-05-26 Jialei Wang , Mladen Kolar , Nathan Srebro , Tong Zhang

We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is…

Machine Learning · Statistics 2010-10-06 Ryota Tomioka , Masashi Sugiyama

This work studies the problem of learning appropriate low dimensional image representations. We propose a generic algorithmic framework, which leverages two classic representation learning paradigms, i.e., sparse representation and the…

Computer Vision and Pattern Recognition · Computer Science 2018-10-09 Xian Wei , Hao Shen , Martin Kleinsteuber

We propose a new, computationally efficient, sparsity adaptive changepoint estimator for detecting changes in unknown subsets of a high-dimensional data sequence. Assuming the data sequence is Gaussian, we prove that the new method…

Methodology · Statistics 2023-11-27 Per August Jarval Moen , Ingrid Kristine Glad , Martin Tveten

Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade,…

Data Structures and Algorithms · Computer Science 2014-10-22 Amihood Amir , Oren Kapah , Ely Porat , Amir Rothschild

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

Methodology · Statistics 2019-09-09 Alexandre Belloni , Abhishek Kaul , Mathieu Rosenbaum

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

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…

Computation · Statistics 2025-02-03 Pia Pfeiffer , Andreas Alfons , Peter Filzmoser