MAP Inference via Block-Coordinate Frank-Wolfe Algorithm

Swoboda, Paul; Kolmogorov, Vladimir

doi:10.1109/cvpr.2019.01140

Cited by 9 publications

(7 citation statements)

References 32 publications

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“…Frank-Wolfe Bundle Method [SK19]: Lagrange decomposition into minimal number of tree subproblems solved with a bundle method using the Frank-Wolfe algorithm.…”

Section: Subgradient On Dual Decomposition [Kpt07]mentioning

confidence: 99%

Structured Prediction Problem Archive

Swoboda¹,

Horňáková²,

Roetzer³

et al. 2022

Preprint

Self Cite

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Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a diverse set of problem classes. We provide archival links to datasets, description of the considered problems and problem formats, and a short summary of problem characteristics including size, number of instances etc. For reference we also give a non-exhaustive selection of algorithms proposed in the literature for their solution. We hope that this central repository will make benchmarking and comparison to established works easier. We welcome submission of interesting new datasets and algorithms for inclusion in our archive 1 .

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“…Frank-Wolfe Bundle Method [SK19]: Lagrange decomposition into minimal number of tree subproblems solved with a bundle method using the Frank-Wolfe algorithm.…”

Section: Subgradient On Dual Decomposition [Kpt07]mentioning

confidence: 99%

Structured Prediction Problem Archive

Swoboda¹,

Horňáková²,

Roetzer³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…then we can perform a single cheaper update of only M (i) instead of on an entire of M. In this line of algorithms, the block-coordinate Frank-Wolfe (BCFW) algorithm has been proposed, for example, in the structural SVM problem [27] and in the MAP inference [36]. This algorithm is applicable to the constrained convex problem of the form min…”

Section: Block-coordinate Frank-wolfe Algorithmmentioning

confidence: 99%

Fast block-coordinate Frank-Wolfe algorithm for semi-relaxed optimal transport

Fukunaga¹,

Kasai²

2021

Preprint

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Optimal transport (OT), which provides a distance between two probability distributions by considering their spatial locations, has been applied to widely diverse applications. Computing an OT problem requires solution of linear programming with tight mass-conservation constraints. This requirement hinders its application to large-scale problems. To alleviate this issue, the recently proposed relaxed-OT approach uses a faster algorithm by relaxing such constraints. Its effectiveness for practical applications has been demonstrated. Nevertheless, it still exhibits slow convergence. To this end, addressing a convex semi-relaxed OT, we propose a fast blockcoordinate Frank-Wolfe (BCFW) algorithm, which gives sparse solutions. Specifically, we provide their upper bounds of the worst convergence iterations, and equivalence between the linearization duality gap and the Lagrangian duality gap. Three fast variants of the proposed BCFW are also proposed. Numerical evaluations in color transfer problem demonstrate that the proposed algorithms outperform state-of-the-art algorithms across different settings.

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“…There is a large body of literature on the special case of problem (1) corresponding to Lagrangian relaxation of discrete optimization problems, see e.g. [31,26,13,22,14,24,28,16,19,25,18,30,29,32]. Some of these method apply only to MAP inference problems in pairwise (or low-order) graphical models, because they need to compute marginals in tree-structured subproblems [13,14,25] or because they explicitly exploit the fact that the relaxation can be described by polynomial many constraints [28,19,30,29].…”

Section: Related Workmentioning

confidence: 99%

One-sided Frank-Wolfe algorithms for saddle problems

Kolmogorov¹,

Pock²

2021

Preprint

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We study a class of convex-concave saddle-point problems of the form min x max y Kx, y + f P (x) − h * (y) where K is a linear operator, f P is the sum of a convex function f with a Lipschitz-continuous gradient and the indicator function of a bounded convex polytope P, and h * is a convex (possibly nonsmooth) function. Such problem arises, for example, as a Lagrangian relaxation of various discrete optimization problems. Our main assumptions are the existence of an efficient linear minimization oracle (lmo) for f P and an efficient proximal map (prox) for h * which motivate the solution via a blend of proximal primal-dual algorithms and Frank-Wolfe algorithms. In case h * is the indicator function of a linear constraint and function f is quadratic, we show a O(1/n 2 ) convergence rate on the dual objective, requiring O(n log n) calls of lmo. In the most general case, we show a O(1/n) convergence rate of the primal-dual gap again requiring O(n log n) calls of lmo. To the best of our knowledge, this improves on the known convergence rates for the considered class of saddle-point problems.

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MAP Inference via Block-Coordinate Frank-Wolfe Algorithm

Cited by 9 publications

References 32 publications

Structured Prediction Problem Archive

Structured Prediction Problem Archive

Fast block-coordinate Frank-Wolfe algorithm for semi-relaxed optimal transport

One-sided Frank-Wolfe algorithms for saddle problems

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