Global optimization for low-dimensional switching linear regression and bounded-error estimation

Global optimization for low-dimensional switching linear regression and bounded-error estimation

The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local optimization heuristics without global optimality guarantees or with guarantees valid only under restrictive conditions, the proposed approach always yields a solution...

Optimization with few violated constraints for linear bounded error parameter estimation

In the context of linear constrained optimization, we study in this paper the problem of finding an optimal solution satisfying all but of the given constraints. A solution is obtained by means of an algorithm of the complexitymin ( ) ( ) , where is the dimension of the problem. We then use these results to solve the problem of robust identification in the presence of outliers in the setting of...

An Opertional Method for The Numerical Solution of Two Dimensional Linear Fredholm Integral Equations With an Error Estimation

Minimax Subsampling for Estimation and Prediction in Low-Dimensional Linear Regression

Subsampling strategies are derived to sample a small portion of design (data) points in a low-dimensional linear regression model y = Xβ+ε with near-optimal statistical rates. Our results apply to both problems of estimation of the underlying linear model β and predicting the real-valued response y of a new data point x. The derived subsampling strategies are minimax optimal under the fixed des...

A Global Homogeneity Test for High-Dimensional Linear Regression

This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from estimation uncertainties. Adopting a neighborhood approach, we consider a twosample linear regression model with random design and propose a procedure to test whether...