相关论文: Deterministic Annealing and Nonlinear Assignment

The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse…

The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…

In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…

We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the…

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…

Approximating marginals of a graphical model is one of the fundamental problems in the theory of networks. In a recent paper a method was shown to construct a variational free energy such that the linear response estimates, and maximum…

Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…

Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow…

Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…

Let M be an n X n symmetric cost matrix. Assume that D is a derangement of edges in M, i.e., a set of point-disjoint cycles containing all of the n points of M.The modified Floyd-Warshall algorithm applied to ((D')^-1)A^- (where A is an…

The Potts model is a generalization of the Ising model with $Q>2$ components. In the fully connected ferromagnetic Potts model, a first-order phase transition is induced by varying thermal fluctuations. Therefore, the computational time…

Integrating combinatorial optimization layers into neural networks has recently attracted significant research interest. However, many existing approaches lack theoretical guarantees or fail to perform adequately when relying on inexact…

The support set is a key to providing conditional prior for fast adaption of the model in few-shot tasks. But the strict form of support set makes its construction actually difficult in practical application. Motivated by ANIL, we rethink…

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…

The global inducing point variational approximation for BNNs is based on using a set of inducing inputs to construct a series of conditional distributions that accurately approximate the conditionals of the true posterior distribution. Our…

Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in…

The stochastic shortest path problem (SSP) is a highly expressive model for probabilistic planning. The computational hardness of SSPs has sparked interest in determinization-based planners that can quickly solve large problems. However,…

We study two-layer neural networks in the mean field limit, where the number of neurons tends to infinity. In this regime, the optimization over the neuron parameters becomes the optimization over the probability measures, and by adding an…

We present a systematic and reliable methodology, termed hierarchical mean-field theory (HMFT), to study and predict the behavior of strongly coupled many-particle systems. HMFT is a simple approximation, based upon group theoretical…