74 citations · 429 across the 31 of their papers we have counts for
31 papers
Spanning trees in the Assignment Problem: two theorems and two conjectures
Sergio Caracciolo, Gabriele Sicuro, Andrea Sportiello
The \emph{Minimum Matching Problem} consists of finding an independent edge set of minimum weight in a given edge-weighted graph . When is bipartite, this red…
Sparse corruption in low-rank matrix inference: the PCA benchmark
Urte Adomaityte, Gabriele Sicuro, Pierpaolo Vivo
Principal Component Analysis (PCA) is a standard tool for extracting a low-rank signal from noisy observations. It is known that applying PCA to a rank-one signal corrupted by a de…
High-dimensional robust regression under heavy-tailed data: Asymptotics and Universality
Urte Adomaityte, Leonardo Defilippis, Bruno Loureiro +1
We investigate the high-dimensional properties of robust regression estimators in the presence of heavy-tailed contamination of both the covariates and response functions. In parti…
Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approach
Urte Adomaityte, Gabriele Sicuro, Pierpaolo Vivo
We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions…
Planted matching problems on random hypergraphs
Urte Adomaityte, Anshul Toshniwal, Gabriele Sicuro +1
We consider the problem of inferring a matching hidden in a weighted random -hypergraph. We assume that the hyperedges' weights are random and distributed according to two diffe…
Fluctuations, Bias, Variance & Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension
Bruno Loureiro, Cédric Gerbelot, Maria Refinetti +2
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered b…
Aligning random graphs with a sub-tree similarity message-passing algorithm
Giovanni Piccioli, Guilhem Semerjian, Gabriele Sicuro +1
The problem of aligning Erdös-Rényi random graphs is a noisy, average-case version of the graph isomorphism problem, in which a pair of correlated random graphs is observed through…
Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions
Bruno Loureiro, Gabriele Sicuro, Cédric Gerbelot +3
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise t…
Criticality and conformality in the random dimer model
Sergio Caracciolo, Riccardo Fabbricatore, Marco Gherardi +3
In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized…
The planted -factor problem
Gabriele Sicuro, Lenka Zdeborová
We consider the problem of recovering an unknown -factor, hidden in a weighted random graph. For this is the planted matching problem, while the case is closely rela…
Random assignment problems on manifolds
Dario Benedetto, Emanuele Caglioti, Sergio Caracciolo +3
We consider the assignment problem between two sets of random points on a smooth, two-dimensional manifold of unit area. It is known that the average cost scales as $E_Ω(N)…
Recovery thresholds in the sparse planted matching problem
Guilhem Semerjian, Gabriele Sicuro, Lenka Zdeborová
We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of tw…
Random-link matching problems on random regular graphs
Giorgio Parisi, Gianmarco Perrupato, Gabriele Sicuro
We study the random-link matching problem on random regular graphs, alongside with two relaxed versions of the problem, namely the fractional matching and the so-called "loopy" fra…
Fluctuations in the random-link matching problem
Enrico M. Malatesta, Giorgio Parisi, Gabriele Sicuro
Using the replica approach and the cavity method, we study the fluctuations of the optimal cost in the random-link matching problem. By means of replica arguments, we derive the ex…
Mean-field model for the density of states of jammed soft spheres
Fernanda P. C. Benetti, Giorgio Parisi, Francesca Pietracaprina +1
We propose a class of mean-field models for the isostatic transition of systems of soft spheres, in which the contact network is modeled as a random graph and each contact is assoc…
Anomalous scaling of the optimal cost in the one-dimensional random assignment problem
Sergio Caracciolo, Matteo D'Achille, Gabriele Sicuro
We consider the random Euclidean assignment problem on the line between two sets of random points, independently generated with the same probability density function .…
The Random Fractional Matching Problem
Carlo Lucibello, Enrico M. Malatesta, Giorgio Parisi +1
We consider two formulations of the random-link fractional matching problem, a relaxed version of the more standard random-link (integer) matching problem. In one formulation, we a…
Random Euclidean matching problems in one dimension
Sergio Caracciolo, Matteo D'Achille, Gabriele Sicuro
We discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions. We consider the probl…
-Generalized representation of the -dimensional Dirac delta and -Fourier transform
Gabriele Sicuro, Constantino Tsallis
We discuss a generalized representation of the Dirac delta function in dimensions in terms of -exponential functions. We apply this new representation to the study of the so…
Finite-size corrections in the random assignment problem
Sergio Caracciolo, Matteo P. D'Achille, Enrico M. Malatesta +1
We analytically derive, in the context of the replica formalism, the first finite size corrections to the average optimal cost in the random assignment problem for a quite generic…
One-loop diagrams in the Random Euclidean Matching Problem
Carlo Lucibello, Giorgio Parisi, Gabriele Sicuro
The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euc…
Nonlinear inhomogeneous Fokker-Planck equations: entropy and free-energy time evolution
Gabriele Sicuro, Peter Rapčan, Constantino Tsallis
We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck eq…
On the connection between linear combination of entropies and linear combination of extremizing distributions
Gabriele Sicuro, Debarshee Bagchi, Constantino Tsallis
We analyze the distribution that extremizes a linear combination of the Boltzmann--Gibbs entropy and the nonadditive -entropy. We show that this distribution can be expressed in…
Groups, Information Theory and Einstein's Likelihood Principle
Gabriele Sicuro, Piergiulio Tempesta
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the…