相关论文: Random multi-index matching problems
Machine learning interatomic potentials (MLIPs) are routinely used to model diverse atomistic phenomena, yet parameterizing them to accurately capture solid-state phase transformations remains difficult. We present error metrics and…
We translate the problem of calculating the entropy of a set of binary configurations/signals into a sequence of supervised classification tasks. Subsequently, one can use virtually any machine learning classification algorithm for…
The Dirichlet process mixture (DPM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as…
This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…
Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding and more. Current…
A major challenge for matching-based depth estimation is to prevent mismatches in occlusion and smooth regions. An effective matching window satisfying three characteristics: texture richness, disparity consistency and anti-occlusion should…
We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant…
There are many extensions of the Standard Model with a dark matter (DM) candidate obtained via the freeze-out mechanism. It can happen that after all experimental and theoretical constraints are taken into account, all parameter points have…
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
The one-step replica symmetry breaking cavity method is proposed as a new tool to investigate large deviations in random graph ensembles. The procedure hinges on a general connection between negative complexities and probabilities of rare…
Multimodal data is a precious asset enabling a variety of downstream tasks in machine learning. However, real-world data collected across different modalities is often not paired, which is a significant challenge to learn a joint…
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…
Complementarity problems often permit distinct solutions, a fact of major significance in optimization, game theory and other fields. In this paper, we develop a numerical technique for computing multiple isolated solutions of…
Maximum Inner Product Search (MIPS) is an important task in many machine learning applications such as the prediction phase of a low-rank matrix factorization model for a recommender system. There have been some works on how to perform MIPS…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has…
Weakly- and Feebly-Interacting Massive Particles (WIMPs and FIMPs) are among the best-motivated dark matter (DM) candidates. In this paper, we investigate the production of DM through the WIMP and FIMP mechanisms during inflationary…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
We provide a geometric formulation of the problem of identification of the matching surplus function and we show how the estimation problem can be solved by the introduction of a generalized entropy function over the set of matchings.