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Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…

Statistics Theory · Mathematics 2019-05-28 Huijie Feng , Yang Ning , Jiwei Zhao

The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…

Systems and Control · Electrical Eng. & Systems 2022-04-19 Mohammad Khosravi , Roy S. Smith

We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions…

Computer Vision and Pattern Recognition · Computer Science 2016-05-31 Gianni Franchi , Jesus Angulo , Dino Sejdinovic

For nonexpansive fixed-point problems, Halpern's method with optimal parameters, its so-called H-dual algorithm, and in fact, an infinite family of algorithms containing them, all exhibit the exactly minimax optimal convergence rates. In…

Optimization and Control · Mathematics 2025-11-20 TaeHo Yoon , Ernest K. Ryu , Benjamin Grimmer

The aim of this paper is to design a band-limited optimal input with power constraints for identifying a linear multi-input multi-output system. It is assumed that the nominal system parameters are specified. The key idea is to use the…

Systems and Control · Computer Science 2017-06-14 Shravan Mohan , Mithun Im , Bharath Bhikkaji

We introduce a functional gradient descent trajectory optimization algorithm for robot motion planning in Reproducing Kernel Hilbert Spaces (RKHSs). Functional gradient algorithms are a popular choice for motion planning in complex…

Robotics · Computer Science 2016-01-15 Zita Marinho , Anca Dragan , Arun Byravan , Byron Boots , Siddhartha Srinivasa , Geoffrey Gordon

Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spectral algorithm to…

Machine Learning · Statistics 2016-03-01 Igor Melnyk , Arindam Banerjee

In this paper, we discuss the problem of system identification when frequency domain side information is available on the system. Initially, we consider the case where the prior knowledge is provided as being the $\Hcal_{\infty}$-norm of…

Optimization and Control · Mathematics 2022-11-08 Mohammad Khosravi , Roy S. Smith

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem.…

Statistics Theory · Mathematics 2024-10-28 Souvik Dhara , Julia Gaudio , Elchanan Mossel , Colin Sandon

The kernel herding algorithm is used to construct quadrature rules in a reproducing kernel Hilbert space (RKHS). While the computational efficiency of the algorithm and stability of the output quadrature formulas are advantages of this…

Numerical Analysis · Mathematics 2022-07-18 Kazuma Tsuji , Ken'ichiro Tanaka

Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert…

Machine Learning · Computer Science 2024-11-01 Youyuan Long , Tolga Ok , Pedro Zattoni Scroccaro , Peyman Mohajerin Esfahani

The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and…

Systems and Control · Electrical Eng. & Systems 2020-09-08 Sai Tej Paruchuri , Jia Guo , Andrew Kurdila

Spectral risk objectives - also called $L$-risks - allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop stochastic…

Machine Learning · Statistics 2022-12-13 Ronak Mehta , Vincent Roulet , Krishna Pillutla , Lang Liu , Zaid Harchaoui

The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general bounded infinite matrices has only recently been solved. We…

Spectral Theory · Mathematics 2022-09-20 Matthew J. Colbrook , Anders C. Hansen

Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…

Optimization and Control · Mathematics 2014-11-06 Robert Nishihara , Stefanie Jegelka , Michael I. Jordan

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of…

Computer Vision and Pattern Recognition · Computer Science 2017-11-27 Tales Imbiriba , José Carlos Moreira Bermudez , Cédric Richard

Two widely used randomized algorithms are the sketch-and-solve method for least-squares regression and the randomized SVD for low-rank approximation. These algorithms apply a random embedding to compress a target matrix, and they perform…

Numerical Analysis · Mathematics 2026-05-20 Ethan N. Epperly , Robert J. Webber

Neural operators have emerged as powerful surrogates for modeling complex physical problems. However, they suffer from spectral bias making them oblivious to high-frequency modes, which are present in multiscale physical systems. Therefore,…

Machine Learning · Computer Science 2025-03-19 Siavash Khodakarami , Vivek Oommen , Aniruddha Bora , George Em Karniadakis

We study the convergence rates of the EM algorithm for learning two-component mixed linear regression under all regimes of signal-to-noise ratio (SNR). We resolve a long-standing question that many recent results have attempted to tackle:…

Machine Learning · Statistics 2021-02-08 Jeongyeol Kwon , Nhat Ho , Constantine Caramanis

This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…

Numerical Analysis · Mathematics 2024-06-21 Nicat Aliyev , Emre Mengi