Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead to unwanted shrinkage. This paper explores instead penalizing the squared distance to constraint sets. Distance penalties are more flexible than algebraic and...

Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. The local optimality approach is to study the regions in parameter space where a given design is optimal. In many situations these regions are semialgebraic. We investigate regions of optimality using computer tools such as yalmip, qepcad, and Mathematica.

We give a simple analysis of the PCP with low amortized query complexity of Samorodnitsky and Trevisan [16]. The analysis also applies to the linearity testing over finite fields, giving a better estimate of the acceptance probability in terms of the distance of the tested function to the closest linear function.

Standard factorial designs may sometimes be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments which uses a criterion that allows for uncertainty in the link function, the linear predictor or the model parameters, together with...

Two-group classification is a key task in decision making and data mining applications. We introduce two new mixed integer programming formulations that make use of multiple separating hyperplanes. They represent a generalization of previous piecewise-linear models that embed rules having the form of hyperplanes, which are used to successively separate the two groups. In fact, the classifiers o...

The inverse spanning tree problem is to make a given spanning tree be a minimum spanning tree on a connected graph via a minimum perturbation on its edge weights. In this paper, a chance-constrained programming model is proposed to handle the inverse spanning tree problem where the edge weights are assumed to be uncertain variables. It is shown that such an uncertain minimum spanning tree can b...

The present paper investigates the word order alternation of English transitive phrasal verbs such as, e.g., to pick up the book versus to pick the book up. It builds on traditional monofactorial analyses, but argues that previously used methods of analysis are grossly inadequate to describe, explain and predict the word order choice by native speakers. A hypothesis integrating virtually all re...