Related papers: Variable elimination in binary CSPs
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
For parameterized mixed-binary optimization problems, we construct local decision rules that prescribe near-optimal courses of action across a set of parameter values. The decision rules stem from solving risk-adaptive training problems…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
In a valued constraint satisfaction problem (VCSP), the goal is to find an assignment of labels to variables that minimizes a given sum of functions. Each function in the sum depends on a subset of variables, takes values which are rational…
Intelligent test requires efficient and effective analysis of high-dimensional data in a large scale. Traditionally, the analysis is often conducted by human experts, but it is not scalable in the era of big data. To tackle this challenge,…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…
Biases in existing datasets used to train algorithmic decision rules can raise ethical and economic concerns due to the resulting disparate treatment of different groups. We propose an algorithm for sequentially debiasing such datasets…
Discovering interpretable patterns for classification of sequential data is of key importance for a variety of fields, ranging from genomics to fraud detection or more generally interpretable decision-making. In this paper, we propose a…
We consider the task of training machine learning models with data-dependent constraints. Such constraints often arise as empirical versions of expected value constraints that enforce fairness or stability goals. We reformulate…
Domain reduction is an essential tool for solving the constraint satisfaction problem (CSP). In the binary CSP, neighbourhood substitution consists in eliminating a value if there exists another value which can be substituted for it in each…
This paper deals with variable selection in the regression and binary classification frameworks. It proposes an automatic and exhaustive procedure which relies on the use of the CART algorithm and on model selection via penalization. This…
We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
A discrete temporal constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over $(\Bbb Z,<)$. Our main result says that every distance CSP is…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
A constraint satisfaction problem (CSP) is a problem of computing a homomorphism ${\bf R} \rightarrow {\bf \Gamma}$ between two relational structures. Analyzing its complexity has been a very fruitful research direction, especially for…
We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of…
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…
In variable selection, a selection rule that prescribes the permissible sets of selected variables (called a "selection dictionary") is desirable due to the inherent structural constraints among the candidate variables. Such selection rules…