Relaxations for inference in restricted Boltzmann machines

We propose a relaxation-based approximate inference algorithm that samples near-MAP configurations of a binary pairwise Markov random field. We experiment on MAP inference tasks in several restricted Boltzmann machines. We also use our underlying sampler to estimate the log-partition function of restricted Boltzmann machines and compare against other sampling-based methods.Comment: ICLR 2014 workshop track submissio

Naturalizing a Programming Language via Interactive Learning

Our goal is to create a convenient natural language interface for performing well-specified but complex actions such as analyzing data, manipulating text, and querying databases. However, existing natural language interfaces for such tasks are quite primitive compared to the power one wields with a programming language. To bridge this gap, we start with a core programming language and allow users to "naturalize" the core language incrementally by defining alternative, more natural syntax and increasingly complex concepts in terms of compositions of simpler ones. In a voxel world, we show that a community of users can simultaneously teach a common system a diverse language and use it to build hundreds of complex voxel structures. Over the course of three days, these users went from using only the core language to using the naturalized language in 85.9\% of the last 10K utterances.Comment: 10 pages, ACL201

A Novel Method for the Absolute Pose Problem with Pairwise Constraints

Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed dimensionality d and the number of measurements N, a robust estimation problem cannot be solved faster than O(N^d). Furthermore, it is almost impossible to remove d from the exponent of the runtime of a globally optimal algorithm. However, absolute pose estimation is a geometric parameter estimation problem, and thus has special constraints. In this paper, we consider pairwise constraints and propose a globally optimal algorithm for solving the absolute pose estimation problem. The proposed algorithm has a linear complexity in the number of correspondences at a given outlier ratio. Concretely, we first decouple the rotation and the translation subproblems by utilizing the pairwise constraints, and then we solve the rotation subproblem using the branch-and-bound algorithm. Lastly, we estimate the translation based on the known rotation by using another branch-and-bound algorithm. The advantages of our method are demonstrated via thorough testing on both synthetic and real-world dataComment: 10 pages, 7figure

Simplicial volume and fillings of hyperbolic manifolds

Let M be a hyperbolic n-manifold whose cusps have torus cross-sections. In arXiv:0901.0056, the authors constructed a variety of nonpositively and negatively curved spaces as "2\pi-fillings" of M by replacing the cusps of M with compact "partial cones" of their boundaries. These 2\pi-fillings are closed pseudomanifolds, and so have a fundamental class. We show that the simplicial volume of any such 2\pi-filling is positive, and bounded above by Vol(M)/v_n, where v_n is the volume of a regular ideal hyperbolic n-simplex. This result generalizes the fact that hyperbolic Dehn filling of a 3-manifold does not increase hyperbolic volume. In particular, we obtain information about the simplicial volumes of some 4--dimensional homology spheres described by Ratcliffe and Tschantz, answering a question of Belegradek and establishing the existence of 4--dimensional homology spheres with positive simplicial volume.Comment: 22 pages; version 2 points out the application to the homology spheres of Ratcliffe and Tschantz, and makes some other small changes suggested by the refere

Bi-directional Weakly Supervised Knowledge Distillation for Whole Slide Image Classification

Computer-aided pathology diagnosis based on the classification of Whole Slide Image (WSI) plays an important role in clinical practice, and it is often formulated as a weakly-supervised Multiple Instance Learning (MIL) problem. Existing methods solve this problem from either a bag classification or an instance classification perspective. In this paper, we propose an end-to-end weakly supervised knowledge distillation framework (WENO) for WSI classification, which integrates a bag classifier and an instance classifier in a knowledge distillation framework to mutually improve the performance of both classifiers. Specifically, an attention-based bag classifier is used as the teacher network, which is trained with weak bag labels, and an instance classifier is used as the student network, which is trained using the normalized attention scores obtained from the teacher network as soft pseudo labels for the instances in positive bags. An instance feature extractor is shared between the teacher and the student to further enhance the knowledge exchange between them. In addition, we propose a hard positive instance mining strategy based on the output of the student network to force the teacher network to keep mining hard positive instances. WENO is a plug-and-play framework that can be easily applied to any existing attention-based bag classification methods. Extensive experiments on five datasets demonstrate the efficiency of WENO. Code is available at https://github.com/miccaiif/WENO.Comment: Accepted by NeurIPS 202