In this paper, we propose an efficient algorithm for estimating the natural policy gradient with parameter-based exploration; this algorithm samples directly in the parameter space. Unlike previous methods based on natural gradients, our algorithm calculates the natural policy gradient using the inverse of the exact Fisher information matrix. The computational cost of this algorithm is equal to that of conventional policy gradients whereas previous natural policy gradient methods have a prohibitive computational cost. Experimental results show that the proposed method outperforms several policy gradient methods.

We study worst-case bounds on the quality of any fixed point assignment of the max-product algorithm for Markov Random Fields (MRF). We start proving a bound independent of the MRF structure and parameters. Afterwards, we show how this bound can be improved for MRFs with particular structures such as bipartite graphs or grids. Our results provide interesting insight into the behavior of max-product. For example, we prove that max-product provides very good results (at least 90% of the optimal) on MRFs with large variable-disjoint cycles (MRFs in which all cycles are variable-disjoint, namely that they do not share any edge and in which each cycle contains at least 20 variables).

Clustering is a basic data mining task with a wide variety of applications. Not surprisingly, there exist many clustering algorithms. However, clustering is an ill defined problem - given a data set, it is not clear what a “correct” clustering for that set is. Indeed, different algorithms may yield dramatically different outputs for the same input sets. Faced with a concrete clustering task, a user needs to choose an appropriate clustering algorithm. Currently, such decisions are often made in a very ad hoc, if not completely random, manner. Given the crucial effect of the choice of a clustering algorithm on the resulting clustering, this state of affairs is truly regrettable. In this paper we address the major research challenge of developing tools for helping users make more informed decisions when they come to pick a clustering tool for their data. This is, of course, a very ambitious endeavor, and in this paper, we make some first steps towards this goal. We propose to address this problem by distilling abstract properties of the input-output behavior of different clustering paradigms. In this paper, we demonstrate how abstract, intuitive properties of clustering functions can be used to taxonomize a set of popular clustering algorithmic paradigms. On top of addressing deterministic clustering algorithms, we also propose similar properties for randomized algorithms and use them to highlight functional differences between different common implementations of k-means clustering. We also study relationships between the properties, independent of any particular algorithm. In particular, we strengthen Kleinbergs famous impossibility result, while providing a simpler proof.

This paper proposes a principled extension of the traditional single-layer flat sparse coding scheme, where a two-layer coding scheme is derived based on theoretical analysis of nonlinear functional approximation that extends recent results for local coordinate coding. The two-layer approach can be easily generalized to deeper structures in a hierarchical multiple-layer manner. Empirically, it is shown that the deep coding approach yields improved performance in benchmark datasets.

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the gamma-adapted-dimension, which is a simple function of the spectrum of a distribution's covariance matrix, and show distribution-specific upper and lower bounds on the sample complexity, both governed by the gamma-adapted-dimension of the source distribution. We conclude that this new quantity tightly characterizes the true sample complexity of large-margin classification. The bounds hold for a rich family of sub-Gaussian distributions.

In this paper we consider the fundamental problem of semi-supervised kernel function learning. We propose a general regularized framework for learning a kernel matrix, and then demonstrate an equivalence between our proposed kernel matrix learning framework and a general linear transformation learning problem. Our result shows that the learned kernel matrices parameterize a linear transformation kernel function and can be applied inductively to new data points. Furthermore, our result gives a constructive method for kernelizing most existing Mahalanobis metric learning formulations. To make our results practical for large-scale data, we modify our framework to limit the number of parameters in the optimization process. We also consider the problem of kernelized inductive dimensionality reduction in the semi-supervised setting. We introduce a novel method for this problem by considering a special case of our general kernel learning framework where we select the trace norm function as the regularizer. We empirically demonstrate that our framework learns useful kernel functions, improving the $k$-NN classification accuracy significantly in a variety of domains. Furthermore, our kernelized dimensionality reduction technique significantly reduces the dimensionality of the feature space while achieving competitive classification accuracies.

To understand the relationship between genomic variations among population and complex diseases, it is essential to detect eQTLs which are associated with phenotypic effects. However, detecting eQTLs remains a challenge due to complex underlying mechanisms and the very large number of genetic loci involved compared to the number of samples. Thus, to address the problem, it is desirable to take advantage of the structure of the data and prior information about genomic locations such as conservation scores and transcription factor binding sites. In this paper, we propose a novel regularized regression approach for detecting eQTLs which takes into account related traits simultaneously while incorporating many regulatory features. We first present a Bayesian network for a multi-task learning problem that includes priors on SNPs, making it possible to estimate the significance of each covariate adaptively. Then we find the maximum a posteriori (MAP) estimation of regression coefficients and estimate weights of covariates jointly. This optimization procedure is efficient since it can be achieved by using convex optimization and a coordinate descent procedure iteratively. Experimental results on simulated and real yeast datasets confirm that our model outperforms previous methods for finding eQTLs.

We propose a new probabilistic model for analyzing dynamic evolutions of relational data, such as additions, deletions and split & merge, of relation clusters like communities in social networks. Our proposed model abstracts observed time-varying object-object relationships into relationships between object clusters. We extend the infinite Hidden Markov model to follow dynamic and time-sensitive changes in the structure of the relational data and to estimate a number of clusters simultaneously. We show the usefulness of the model through experiments with synthetic and real-world data sets.

For over half a century, psychologists have been struck by how poor people are at expressing their internal sensations, impressions, and evaluations via rating scales. When individuals make judgments, they are incapable of using an absolute rating scale, and instead rely on reference points from recent experience. This relativity of judgment limits the usefulness of responses provided by individuals to surveys, questionnaires, and evaluation forms. Fortunately, the cognitive processes that transform internal states to responses are not simply noisy, but rather are influenced by recent experience in a lawful manner. We explore techniques to remove sequential dependencies, and thereby decontaminate a series of ratings to obtain more meaningful human judgments. In our formulation, decontamination is fundamentally a problem of inferring latent states (internal sensations) which, because of the relativity of judgment, have temporal dependencies. We propose a decontamination solution using a conditional random field with constraints motivated by psychological theories of relative judgment. Our exploration of decontamination models is supported by two experiments we conducted to obtain ground-truth rating data on a simple length estimation task. Our decontamination techniques yield an over 20% reduction in the error of human judgments.

We present a technique for exact simulation of Gaussian Markov random fields (GMRFs), which can be interpreted as locally injecting noise to each Gaussian factor independently, followed by computing the mean/mode of the perturbed GMRF. Coupled with standard iterative techniques for the solution of symmetric positive definite systems, this yields a very efficient sampling algorithm with essentially linear complexity in terms of speed and memory requirements, well suited to extremely large scale probabilistic models. Apart from synthesizing data under a Gaussian model, the proposed technique directly leads to an efficient unbiased estimator of marginal variances. Beyond Gaussian models, the proposed algorithm is also very useful for handling highly non-Gaussian continuously-valued MRFs such as those arising in statistical image modeling or in the first layer of deep belief networks describing real-valued data, where the non-quadratic potentials coupling different sites can be represented as finite or infinite mixtures of Gaussians with the help of local or distributed latent mixture assignment variables. The Bayesian treatment of such models most naturally involves a block Gibbs sampler which alternately draws samples of the conditionally independent latent mixture assignments and the conditionally multivariate Gaussian continuous vector and we show that it can directly benefit from the proposed methods.