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We propose a new unbiased threshold for network analysis named the Cluster-Span Threshold (CST). This is based on the clustering coefficient, C, following logic that a balance of `clustering' to `spanning' triples results in a useful…
We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…
High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called…
We show that the uniform Constraint Satisfaction Problem (CSP) parameterized by the size of the solution is in W[1] (the problem is W[1]-hard and it is easy to place it in W[3]). Given a single "free" element of the domain, denoted by $0$,…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
Modified gravitational forces in models that seek to explain cosmic acceleration without dark energy typically predict deviations in the abundance of massive dark matter halos. We conduct the first, simulation calibrated, cluster abundance…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets,…
We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…
We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…
We show that estimating the complexity (mean and distribution) of the instances of a fixed size Constraint Satisfaction Problem (CSP) can be very hard. We deal with the main two aspects of the problem: defining a measure of complexity and…
We consider a high-dimensional random constrained optimization problem in which a set of binary variables is subjected to a linear system of equations. The cost function is a simple linear cost, measuring the Hamming distance with respect…
We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at…
Given a CNF formula F on n variables, the problem of model counting or #SAT is to compute the number of satisfying assignments of F . Model counting is a fundamental but hard problem in computer science with varied applications. Recent…
A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve…
In this paper, we study the pooled data problem of identifying the labels associated with a large collection of items, based on a sequence of pooled tests revealing the counts of each label within the pool. In the noiseless setting, we…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
This paper first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it…
Clustering of variables is as a way to arrange variables into homogeneous clusters, i.e., groups of variables which are strongly related to each other and thus bring the same information. These approaches can then be useful for dimension…