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Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…
In this paper, we try to further demonstrate that the models of random CSP instances proposed by [Xu and Li, 2000; 2003] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features.…
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal…
The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…
A ternary Permutation-CSP is specified by a subset $\Pi$ of the symmetric group $\mathcal S_3$. An instance of such a problem consists of a set of variables $V$ and a multiset of constraints, which are ordered triples of distinct variables…
The problem of CSP sparsification asks: for a given CSP instance, what is the sparsest possible reweighting such that for every possible assignment to the instance, the number of satisfied constraints is preserved up to a factor of $1 \pm…
The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
In this paper, we examine the fundamental performance limitations in the control of stochastic dynamical systems; more specifically, we derive generic $\mathcal{L}_p$ bounds that hold for any causal (stabilizing) controllers and any…
We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
We develop an analytical framework for Boolean Promise Constraint Satisfaction Problems (PCSPs) that studies polymorphisms through the notion of influence from Fourier analysis of Boolean functions. Extending the work of Brakensiek,…
We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…
We present a graph theoretical approach to the configurational statistics of random tree-like objects, such as randomly branching polymers. In particular, for ideal trees we show that Pr\"ufer labelling provides: (i) direct access to the…
Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we…
Labeling a classification dataset implies to define classes and associated coarse labels, that may approximate a smoother and more complicated ground truth. For example, natural images may contain multiple objects, only one of which is…
We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these…
We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…
This paper addresses the challenge of identifying a minimal subset of discrete, independent variables that best predicts a binary class. We propose an efficient iterative method that sequentially selects variables based on which one…