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Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean-square error. The derived models are useful for understanding the algorithm behavior under different environments and can be…

Methodology · Statistics 2023-12-04 Marcos H. Maruo , José Carlos M. Bermudez

We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…

Machine Learning · Statistics 2015-01-28 Zhaoran Wang , Han Liu , Tong Zhang

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

Optimization and Control · Mathematics 2016-08-16 Yu Du , Xiaodong Lin , Andrzej Ruszczynski

We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those…

Machine Learning · Statistics 2013-10-21 Martin Riedel , Marika Kästner , Fabrice Rossi , Thomas Villmann

One of the most often used methods of summing divergent series in physics is the Borel-type summation with control parameters improving convergence, which are defined by some optimization conditions. The well known annoying problem in this…

Mathematical Physics · Physics 2025-02-04 V. I. Yukalov , S. Gluzman

To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…

Numerical Analysis · Mathematics 2019-07-09 Yusuke Imoto

System stabilization via policy gradient (PG) methods has drawn increasing attention in both control and machine learning communities. In this paper, we study their convergence and sample complexity for stabilizing linear time-invariant…

Optimization and Control · Mathematics 2023-09-15 Feiran Zhao , Xingyun Fu , Keyou You

Convex regression (CR) is an approach for fitting a convex function to a finite number of observations. It arises in various applications from diverse fields such as statistics, operations research, economics, and electrical engineering.…

Optimization and Control · Mathematics 2016-08-09 Necdet Serhat Aybat , Zi Wang

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good…

Numerical Analysis · Mathematics 2016-08-05 David Brander , Jens Gravesen , Toke Bjerge Nørbjerg

In this paper, a feature extraction approach for the deformable linear object is presented, which uses a Bezier curve to represent the original geometric shape. The proposed extraction strategy is combined with a parameterization technique,…

Robotics · Computer Science 2023-12-29 Fangqing Chen

We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of…

Computer Vision and Pattern Recognition · Computer Science 2016-06-07 Artem Babenko , Relja Arandjelović , Victor Lempitsky

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality…

Machine Learning · Computer Science 2015-04-22 Hong Tao , Chenping Hou , Feiping Nie , Yuanyuan Jiao , Dongyun Yi

Simplifying the geometry of a CAD model using defeaturing techniques enables more efficient discretisation and subsequent simulation for engineering analysis problems. Understanding the effect this simplification has on the solution helps…

Numerical Analysis · Mathematics 2019-10-15 Navid Rahimi , Pierre Kerfriden , Frank C Langbein , Ralph R Martin

This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…

Numerical Analysis · Mathematics 2020-07-08 Walter Cedric Simo Tao Lee

We consider approximating a measure by a parameterized curve subject to length penalization. That is for a given finite positive compactly supported measure $\mu$, for $p \geq 1$ and $\lambda>0$ we consider the functional \[ E(\gamma) =…

Analysis of PDEs · Mathematics 2014-11-12 Xin Yang Lu , Dejan Slepčev

This paper describes a new method for reducing the error in a classifier. It uses an error correction update that includes the very simple rule of either adding or subtracting the error adjustment, based on whether the variable value is…

Artificial Intelligence · Computer Science 2018-03-02 Kieran Greer

In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

Machine Learning · Computer Science 2016-10-18 Lijun Zhang , Tianbao Yang , Rong Jin , Zhi-Hua Zhou

Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…

Computer Vision and Pattern Recognition · Computer Science 2015-03-18 Dai-Qiang Chen , Li-Zhi Cheng

In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, $L_{q}$ regularization with $q\in(0,1)$) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency.…

Numerical Analysis · Computer Science 2015-06-17 Jinshan Zeng , Shaobo Lin , Yao Wang , Zongben Xu

In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regularization operators designed to enforce edge recovery. An…

Numerical Analysis · Mathematics 2023-06-29 Matthias Bolten , Scott P. MacLachlan , Misha E. Kilmer