
Stochastic Optimization of Sorting Networks via Continuous Relaxations
Sorting input objects is an important step in many machine learning pipe...
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Improved Variational Bayesian Phylogenetic Inference with Normalizing Flows
Variational Bayesian phylogenetic inference (VBPI) provides a promising ...
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Learning Permutations with Sinkhorn Policy Gradient
Many problems at the intersection of combinatorics and computer science ...
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General Bayesian Inference over the Stiefel Manifold via the Givens Transform
We introduce the Givens Transform, a novel transform between the space o...
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AutoShuffleNet: Learning Permutation Matrices via an Exact Lipschitz Continuous Penalty in Deep Convolutional Neural Networks
ShuffleNet is a stateoftheart light weight convolutional neural netwo...
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A Blind Permutation Similarity Algorithm
This paper introduces a polynomial blind algorithm that determines when ...
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Sorting Permutations with Fixed Pinnacle Set
We give a positive answer to a question raised by Davis et al. ( Discret...
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Reparameterizing the Birkhoff Polytope for Variational Permutation Inference
Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation, but fully Bayesian inference poses a severe challenge in this highdimensional, discrete space. To surmount this challenge, we start with the usual step of relaxing a discrete set (here, of permutation matrices) to its convex hull, which here is the Birkhoff polytope: the set of all doublystochastic matrices. We then introduce two novel transformations: first, an invertible and differentiable stickbreaking procedure that maps unconstrained space to the Birkhoff polytope; second, a map that rounds points toward the vertices of the polytope. Both transformations include a temperature parameter that, in the limit, concentrates the densities on permutation matrices. We then exploit these transformations and reparameterization gradients to introduce variational inference over permutation matrices, and we demonstrate its utility in a series of experiments.
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