ICML 2015 论文列表

We introduce a new meta-algorithm for probabilistic inference in graphical models based on random projections. The key idea is to use approximate inference algorithms for an (exponentially) large number of samples, obtained by randomly projecting the original statistical model using universal hash functions. In the case where the approximate inference algorithm is a variational approximation, this approach can be viewed as interpolating between sampling-based and variational techniques. The number of samples used controls the trade-off between the accuracy of the approximate inference algorithm and the variance of the estimator. We show empirically that by using random projections, we can improve the accuracy of common approximate inference algorithms.

We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms introduced in Lessard et al. (2014), reducing algorithm convergence to verifying the stability of a dynamical system. This approach generalizes a number of existing results and obviates any assumptions about specific choices of algorithm parameters. On a numerical example, we demonstrate that minimizing the derived bound on the convergence rate provides a practical approach to selecting algorithm parameters for particular ADMM instances. We complement our upper bound by constructing a nearly-matching lower bound on the worst-case rate of convergence.

Language modelling is a fundamental building block of natural language processing. However, in practice the size of the vocabulary limits the distributions applicable for this task: specifically, one has to either resort to local optimization methods, such as those used in neural language models, or work with heavily constrained distributions. In this work, we take a step towards overcoming these difficulties. We present a method for global-likelihood optimization of a Markov random field language model exploiting long-range contexts in time independent of the corpus size. We take a variational approach to optimizing the likelihood and exploit underlying symmetries to greatly simplify learning. We demonstrate the efficiency of this method both for language modelling and for part-of-speech tagging.

Graph clustering is about identifying clusters of closely connected nodes, and is a fundamental technique of data analysis with many applications including community detection, VLSI network partitioning, collaborative filtering, and many others. In order to improve the scalability of existing graph clustering algorithms, we propose a novel divide and conquer framework for graph clustering, and establish theoretical guarantees of exact recovery of the clusters. One additional advantage of the proposed framework is that it can identify small clusters – the size of the smallest cluster can be of size o(\sqrtn), in contrast to Ω(\sqrtn) required by standard methods. Extensive experiments on synthetic and real-world datasets demonstrate the efficiency and effectiveness of our framework.

Subspace clustering groups data into several lowrank subspaces. In this paper, we propose a theoretical framework to analyze a popular optimization-based algorithm, Sparse Subspace Clustering (SSC), when the data dimension is compressed via some random projection algorithms. We show SSC provably succeeds if the random projection is a subspace embedding, which includes random Gaussian projection, uniform row sampling, FJLT, sketching, etc. Our analysis applies to the most general deterministic setting and is able to handle both adversarial and stochastic noise. It also results in the first algorithm for privacy-preserved subspace clustering.

In reinforcement learning, the notions of experience replay, and of planning as learning from replayed experience, have long been used to find good policies with minimal training data. Replay can be seen either as model-based reinforcement learning, where the store of past experiences serves as the model, or as a way to avoid a conventional model of the environment altogether. In this paper, we look more deeply at how replay blurs the line between model-based and model-free methods. First, we show for the first time an exact equivalence between the sequence of value functions found by a model-based policy-evaluation method and by a model-free method with replay. Second, we present a general replay method that can mimic a spectrum of methods ranging from the explicitly model-free (TD(0)) to the explicitly model-based (linear Dyna). Finally, we use insights gained from these relationships to design a new model-based reinforcement learning algorithm for linear function approximation. This method, which we call forgetful LSTD(lambda), improves upon regular LSTD(lambda) because it extends more naturally to online control, and improves upon linear Dyna because it is a multi-step method, enabling it to perform well even in non-Markov problems or, equivalently, in problems with significant function approximation.

We present a framework for biclustering and clustering where the observations are general labels. Our approach is based on the maximum likelihood estimator and its convex relaxation, and generalizes recent works in graph clustering to the biclustering setting. In addition to standard biclustering setting where one seeks to discover clustering structure simultaneously in two domain sets, we show that the same algorithm can be as effective when clustering structure only occurs in one domain. This allows for an alternative approach to clustering that is more natural in some scenarios. We present theoretical results that provide sufficient conditions for the recovery of the true underlying clusters under a generalized stochastic block model. These are further validated by our empirical results on both synthetic and real data.

MAD-Bayes (MAP-based Asymptotic Derivations) has been recently proposed as a general technique to derive scalable algorithm for Bayesian Nonparametric models. However, the combinatorial nature of objective functions derived from MAD-Bayes results in hard optimization problem, for which current practice employs heuristic algorithms analogous to k-means to find local minimum. In this paper, we consider the exemplar-based version of MAD-Bayes formulation for DP and Hierarchical DP (HDP) mixture model. We show that an exemplar-based MAD-Bayes formulation can be relaxed to a convex structural-regularized program that, under cluster-separation conditions, shares the same optimal solution to its combinatorial counterpart. An algorithm based on Alternating Direction Method of Multiplier (ADMM) is then proposed to solve such program. In our experiments on several benchmark data sets, the proposed method finds optimal solution of the combinatorial problem and significantly improves existing methods in terms of the exemplar-based objective.

A fundamental task in machine learning is to compare the performance of multiple algorithms. This is typically performed by frequentist tests (usually the Friedman test followed by a series of multiple pairwise comparisons). This implies dealing with null hypothesis significance tests and p-values, although the shortcomings of such methods are well known. First, we propose a nonparametric Bayesian version of the Friedman test using a Dirichlet process (DP) based prior. Our derivations show that, from a Bayesian perspective, the Friedman test is an inference for a multivariate mean based on an ellipsoid inclusion test. Second, we derive a joint procedure for the analysis of the multiple comparisons which accounts for their dependencies and which is based on the posterior probability computed through the DP. The proposed approach allows verifying the null hypothesis, not only rejecting it. Third, we apply our test to perform algorithms racing, i.e., the problem of identifying the best algorithm among a large set of candidates. We show by simulation that our approach is competitive both in terms of accuracy and speed in identifying the best algorithm.