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We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…

Machine Learning · Statistics 2024-01-17 Abhisek Chakraborty , Anirban Bhattacharya , Debdeep Pati

This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…

Numerical Analysis · Mathematics 2024-05-08 Markus Holzleitner , Sergei Pereverzyev

The matrix-based Renyi's \alpha-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the…

Information Theory · Computer Science 2019-08-01 Shujian Yu , Luis Gonzalo Sanchez Giraldo , Robert Jenssen , Jose C. Principe

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

Statistics Theory · Mathematics 2024-01-05 Y. Baraud , H. Halconruy , G. Maillard

Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…

Statistics Theory · Mathematics 2025-05-07 Alejandro Cholaquidis , Ricardo Fraiman , Leonardo Moreno , Gonzalo Perera

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…

Machine Learning · Statistics 2016-04-21 Khai X. Chiong , Matthew Shum

A significant challenge in molecular dynamics (MD) simulations is ensuring that sampled configurations converge to the equilibrium or nonequilibrium stationary distribution of interest. Lack of convergence constrains the estimation of free…

Computational Physics · Physics 2026-04-03 Sagar Kania , Robert J. Webber , Gideon Simpson , David Aristoff , Daniel M. Zuckerman

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

Machine Learning · Statistics 2020-02-26 Ivan Ustyuzhaninov , Ieva Kazlauskaite , Carl Henrik Ek , Neill D. F. Campbell

We analyze the ordinal structure of long-range dependent time series. To this end, we use so called ordinal patterns which describe the relative position of consecutive data points. We provide two estimators for the probabilities of ordinal…

Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied…

Machine Learning · Statistics 2018-05-17 Matt Bonakdarpour , Sabyasachi Chatterjee , Rina Foygel Barber , John Lafferty

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

Optimization and Control · Mathematics 2008-06-19 D. Leventhal , A. S. Lewis

A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…

Methodology · Statistics 2015-02-05 L. A. Garcia-Escudero , A. Gordaliza , F. Greselin , S. Ingrassia , A. Mayo-Iscar

Distributed data aggregation is an important task, allowing the decentralized determination of meaningful global properties, that can then be used to direct the execution of other applications. The resulting values result from the…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-10-05 Paulo Jesus , Carlos Baquero , Paulo Sérgio Almeida

We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our arguments build on certain weighted inequalities based on…

Functional Analysis · Mathematics 2024-07-09 Prasun Roychowdhury , Durvudkhan Suragan

The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a…

Optimization and Control · Mathematics 2020-01-22 Sara Maad Sasane

Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…

Machine Learning · Computer Science 2022-03-22 Nhat Ho , Koulik Khamaru , Raaz Dwivedi , Martin J. Wainwright , Michael I. Jordan , Bin Yu

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

Statistics Theory · Mathematics 2020-12-01 Koohyun Kwon , Soonwoo Kwon

Feature weighting algorithms try to solve a problem of great importance nowadays in machine learning: The search of a relevance measure for the features of a given domain. This relevance is primarily used for feature selection as feature…

Machine Learning · Computer Science 2015-09-17 Gabriel Prat Masramon , Lluís A. Belanche Muñoz

Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…

Functional Analysis · Mathematics 2026-01-30 Diego J. Cornejo

The logistic loss function is often advocated in machine learning and statistics as a smooth and strictly convex surrogate for the 0-1 loss. In this paper we investigate the question of whether these smoothness and convexity properties make…

Machine Learning · Computer Science 2014-05-16 Elad Hazan , Tomer Koren , Kfir Y. Levy