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In a standard regression problem, we have a set of explanatory variables whose effect on some response vector is modeled. For wide binary data, such as genetic marker data, we often have two limitations. First, we have more parameters than…
We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with…
Standard approaches for variable selection in linear models are not tailored to deal properly with high-dimensional and incomplete data. Currently, methods dedicated to high-dimensional data handle missing values by ad-hoc strategies, like…
In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we…
We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating…
Constrained combinatorial optimization problems (CCOPs) are challenging to solve due to the exponential growth of the solution space. When tackled with Ising machines, constraints are typically enforced by the penalty function method, whose…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
We give safe screening rules to eliminate variables from regression with $\ell_0$ regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening…
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…
We are concerned with three types of uncertainties: probabilistic, possibilitistic and interval. By using possibility and necessity measures as an Interval Valued Probability Measure (IVPM), we present IVPM's interval expected values whose…
We present the Multi-vAlue Rule Set (MARS) model for interpretable classification with feature efficient presentations. MARS introduces a more generalized form of association rules that allows multiple values in a condition. Rules of this…
The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…
We study systems of String Equations where block variables need to be assigned strings so that their concatenation gives a specified target string. We investigate this problem under a multivariate complexity framework, searching for…
We study the addition of shape constraints (SC) and their consideration during the parameter identification step of symbolic regression (SR). SC serve as a means to introduce prior knowledge about the shape of the otherwise unknown model…
Value iteration is a popular algorithm for finding near optimal policies for POMDPs. It is inefficient due to the need to account for the entire belief space, which necessitates the solution of large numbers of linear programs. In this…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective…
Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
In social choice theory, Sen's value restriction and Pattanaik's not-strict value restriction are both attractive conditions for testing social preference transitivity and/or non-empty social choice set existence. This article introduces a…