Chordal Decomposition in Rank Minimized Semidefinite Programs with Applications to Subspace Clustering

Semidefinite programs (SDPs) often arise in relaxations of some NP-hard problems, and if the solution of the SDP obeys certain rank constraints, the relaxation will be tight. Decomposition methods based on chordal sparsity have already been applied to speed up the solution of sparse SDPs, but methods for dealing with rank constraints are underdeveloped. This paper leverages a minimum rank completion result to decompose the rank constraint on a single large matrix into multiple rank constraints on a set of smaller matrices. The re-weighted heuristic is used as a proxy for rank, and the specific form of the heuristic preserves the sparsity pattern between iterations. Implementations of rank-minimized SDPs through interior-point and first-order algorithms are discussed. The problem of subspace clustering is used to demonstrate the computational improvement of the proposed method.Comment: 6 pages, 6 figure

Reducing Dueling Bandits to Cardinal Bandits

We present algorithms for reducing the Dueling Bandits problem to the conventional (stochastic) Multi-Armed Bandits problem. The Dueling Bandits problem is an online model of learning with ordinal feedback of the form "A is preferred to B" (as opposed to cardinal feedback like "A has value 2.5"), giving it wide applicability in learning from implicit user feedback and revealed and stated preferences. In contrast to existing algorithms for the Dueling Bandits problem, our reductions -- named \Doubler, \MultiSbm and \DoubleSbm -- provide a generic schema for translating the extensive body of known results about conventional Multi-Armed Bandit algorithms to the Dueling Bandits setting. For \Doubler and \MultiSbm we prove regret upper bounds in both finite and infinite settings, and conjecture about the performance of \DoubleSbm which empirically outperforms the other two as well as previous algorithms in our experiments. In addition, we provide the first almost optimal regret bound in terms of second order terms, such as the differences between the values of the arms

Similarity Learning for High-Dimensional Sparse Data

A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of the data. In this paper, we propose a method that can learn efficiently similarity measure from high-dimensional sparse data. The core idea is to parameterize the similarity measure as a convex combination of rank-one matrices with specific sparsity structures. The parameters are then optimized with an approximate Frank-Wolfe procedure to maximally satisfy relative similarity constraints on the training data. Our algorithm greedily incorporates one pair of features at a time into the similarity measure, providing an efficient way to control the number of active features and thus reduce overfitting. It enjoys very appealing convergence guarantees and its time and memory complexity depends on the sparsity of the data instead of the dimension of the feature space. Our experiments on real-world high-dimensional datasets demonstrate its potential for classification, dimensionality reduction and data exploration.Comment: 14 pages. Proceedings of the 18th International Conference on Artificial Intelligence and Statistics (AISTATS 2015). Matlab code: https://github.com/bellet/HDS

Bayesian Non-Exhaustive Classification A Case Study: Online Name Disambiguation using Temporal Record Streams

The name entity disambiguation task aims to partition the records of multiple real-life persons so that each partition contains records pertaining to a unique person. Most of the existing solutions for this task operate in a batch mode, where all records to be disambiguated are initially available to the algorithm. However, more realistic settings require that the name disambiguation task be performed in an online fashion, in addition to, being able to identify records of new ambiguous entities having no preexisting records. In this work, we propose a Bayesian non-exhaustive classification framework for solving online name disambiguation task. Our proposed method uses a Dirichlet process prior with a Normal * Normal * Inverse Wishart data model which enables identification of new ambiguous entities who have no records in the training data. For online classification, we use one sweep Gibbs sampler which is very efficient and effective. As a case study we consider bibliographic data in a temporal stream format and disambiguate authors by partitioning their papers into homogeneous groups. Our experimental results demonstrate that the proposed method is better than existing methods for performing online name disambiguation task.Comment: to appear in CIKM 201

Highly Scalable Algorithms for Robust String Barcoding

String barcoding is a recently introduced technique for genomic-based identification of microorganisms. In this paper we describe the engineering of highly scalable algorithms for robust string barcoding. Our methods enable distinguisher selection based on whole genomic sequences of hundreds of microorganisms of up to bacterial size on a well-equipped workstation, and can be easily parallelized to further extend the applicability range to thousands of bacterial size genomes. Experimental results on both randomly generated and NCBI genomic data show that whole-genome based selection results in a number of distinguishers nearly matching the information theoretic lower bounds for the problem