Related papers: Max-Product Belief Propagation for Linear Programm…
Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this manuscript we describe how a loop series expansion…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
This applied research article explores the application of Mixed-Integer Linear Programming (MILP) to address line-balancing challenges in the garment industry, focusing on optimizing production processes under multiple constraints. By…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…
This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean…
Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a…
Computation of observables in discrete stochastic, possibly conditioned, dynamics over large sparse networks is at the basis of a myriad of applications. The Matrix-Product Belief Propagation method allows a semi-analytical estimation of…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
In the drug discovery process, where experiments can be costly and time-consuming, computational models that predict drug-target interactions are valuable tools to accelerate the development of new therapeutic agents. Estimating the…
We argue the case for Gaussian Belief Propagation (GBP) as a strong algorithmic framework for the distributed, generic and incremental probabilistic estimation we need in Spatial AI as we aim at high performance smart robots and devices…
Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…
In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products. We say that an optimization problem $\Pi$ is direct product feasible if it is possible to efficiently…
We illustrate the utility of the recently developed loop calculus for improving the Belief Propagation (BP) algorithm. If the algorithm that minimizes the Bethe free energy fails we modify the free energy by accounting for a critical loop…
Mixed-effects regression models represent a useful subclass of regression models for grouped data; the introduction of random effects allows for the correlation between observations within each group to be conveniently captured when…
The Survey Propagation (SP) algorithm for solving $k$-SAT problems has been shown recently as an instance of the Belief Propagation (BP) algorithm. In this paper, we show that for general constraint-satisfaction problems, SP may not be…
In this paper, we propose a novel hierarchical representation via message propagation (HRMP) method for robust model fitting, which simultaneously takes advantages of both the consensus analysis and the preference analysis to estimate the…
For a network formed by nodes and undirected links between pairs of nodes, the network optimal attack problem aims at deleting a minimum number of target nodes to break the network down into many small components. This problem is…
A major benefit of graphical models is that most knowledge is captured in the model structure. Many models, however, produce inference problems with a lot of symmetries not reflected in the graphical structure and hence not exploitable by…