Related papers: Regression for sets of polynomial equations
We introduce a method to improve the tractability of the well-known Sample Average Approximation (SAA) without compromising important theoretical properties, such as convergence in probability and the consistency of an independent and…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the…
In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a…
We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…
To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more…
The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical…
This survey study discusses main aspects to optimal estimation methodologies for panel data regression models. In particular, we present current methodological developments for modeling stationary panel data as well as robust methods for…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…
This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre type Moment-SOS relaxations are used to solve the sample average optimization.…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…
The goal of regression analysis is to predict the value of a numeric outcome variable y given a vector of joint values of other (predictor) variables x. Usually a particular x-vector does not specify a repeatable value for y, but rather a…
Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…
In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…