Exact MAP-Inference by Confining Combinatorial Search With LP Relaxation

Haller, Stefan; Swoboda, Paul; Savchynskyy, Bogdan

doi:10.1609/aaai.v32i1.12202

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…Although there are plenty of existing approximation algorithms [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], several problems (described below) require finding an optimal solution. Existing exact algorithms [24][25][26][27][28][29][30][31][32][33][34], on the other hand, either make specific assumptions about the energy function or do not provide polynomial run-time guarantees for the worst case. Assuming the worst-case scenario, the junction (or clique)-tree algorithm [1,35], therefore, remains the most efficient and general solution for exact MAP inference.…”

Section: Introductionmentioning

confidence: 99%

Polynomial-Time Constrained Message Passing for Exact MAP Inference on Discrete Models with Global Dependencies

2023

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Considering the worst-case scenario, the junction-tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a corresponding MRF to be bounded, strongly limiting the range of admissible applications. In fact, many practical problems in the area of structured prediction require modeling global dependencies by either directly introducing global factors or enforcing global constraints on the prediction variables. However, this always results in a fully-connected graph, making exact inferences by means of this algorithm intractable. Previous works focusing on the problem of loss-augmented inference have demonstrated how efficient inference can be performed on models with specific global factors representing non-decomposable loss functions within the training regime of SSVMs. Making the observation that the same fundamental idea can be applied to solve a broader class of computational problems, in this paper, we adjust the framework for an efficient exact inference proposed in to allow much finer interactions between the energy of the core model and the sufficient statistics of the global terms. As a result, we greatly increase the range of admissible applications and strongly improve upon the theoretical guarantees of computational efficiency. We illustrate the applicability of our method in several use cases, including one that is not covered by the previous problem formulation. Furthermore, we propose a new graph transformation technique via node cloning, which ensures a polynomial run-time for solving our target problem. In particular, the overall computational complexity of our constrained message-passing algorithm depends only on form-independent quantities such as the treewidth of a corresponding graph (without global connections) and image size of the sufficient statistics of the global terms.

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Section: Introductionmentioning

confidence: 99%

Polynomial-Time Constrained Message Passing for Exact MAP Inference on Discrete Models with Global Dependencies

2023

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“…Exact methods to solve GMs/CFNs mostly rely on Branch-and-Bound (B&B) algorithms [37,20]. These methods have proved useful in many GM applications, such as resource allocation [10], image analysis [23], or computational biology [4,1]. For those, it has been shown to outperform other approaches, including Integer Linear Programming (ILP), MaxSAT and Constraint Programming (CP) [26].…”

Section: Introductionmentioning

confidence: 99%

Multiple-choice Knapsack Constraint in Graphical Models

Montalbano¹,

Givry²,

Katsirelos

2022

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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Graphical models, such as cost function networks (CFNs), can compactly express large decomposable functions, which leads to efficient inference algorithms. Most methods for computing lower bounds in Branch-and-Bound minimization compute feasible dual solutions of a specific linear relaxation. These methods are more effective than solving the linear relaxation exactly, with better worst-case time complexity and better performance in practice. However, these algorithms are specialized to the structure of the linear relaxation of a CFN and cannot, for example, deal with constraints that cannot be expressed in extension, such as linear constraints of large arity. In this work, we show how to extend soft local consistencies, a set of approximate inference techniques for CFNs, so that they handle linear constraints, as well as combinations of linear constraints with at-mostone constraints. We embedded the resulting algorithm in toulbar2, an exact Branch-and-Bound solver for CFNs which has demonstrated superior results in several graphical model competitions and is state-of-theart for solving large computational protein design (CPD) problems. We significantly improved performance of the solver in CPD with diversity guarantees. It also compared favorably with integer linear programming solvers on knapsack problems with conflict graphs.

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