Related papers: Optimal designs for regression with spherical data

A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…

Distributionally robust optimization (DRO) has become a powerful framework for estimation under uncertainty, offering strong out-of-sample performance and principled regularization. In this paper, we propose a DRO-based method for linear…

This paper describes a new algorithm to solve the decision making problem in Influence Diagrams based on algorithms for credal networks. Decision nodes are associated to imprecise probability distributions and a reformulation is introduced…

A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…

We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…

Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction…

This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of…

We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches…

A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality…

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

This paper investigates the problem of optimal predictor design for distributed parameter systems using neural networks and shape optimization. Sensors with various shapes are placed on the domain of the distributed parameter system. Data…

We develop a non-parametric, data-driven, tractable approach for solving multistage stochastic optimization problems in which decisions do not affect the uncertainty. The proposed framework represents the decision variables as elements of a…

Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model…

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…

This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…

This paper introduces a new way to calculate distance-based statistics, particularly when the data are multivariate. The main idea is to pre-calculate the optimal projection directions given the variable dimension, and to project…

For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations…

Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly,…

In a physical design problem, the designer chooses values of some physical parameters, within limits, to optimize the resulting field. We focus on the specific case in which each physical design parameter is the ratio of two field…

Sliced inverse regression is one of the most popular sufficient dimension reduction methods. Originally, it was designed for independent and identically distributed data and recently extend to the case of serially and spatially dependent…