Topic models, such as latent Dirichlet allocation (LDA), can be useful tools for the statistical analysis of document collections and other discrete data. The LDA model assumes that the words of each document arise from a mixture of topics, each of which is a distribution over the vocabulary. A limitation of LDA is the inability to model topic correlation even though, for example, a document about genetics is more likely to also be about disease than x-ray astronomy. This limitation stems from the use of the Dirichlet distribution to model the variability among the topic proportions. In this paper we develop the correlated topic model (CTM), where the topic proportions exhibit correlation via the logistic normal distribution [1]. We derive a mean-field variational inference algorithm for approximate posterior inference in this model, which is complicated by the fact that the logistic normal is not conjugate to the multinomial. The CTM gives a better fit than LDA on a collection of OCRed articles from the journal Science. Furthermore, the CTM provides a natural way of visualizing and exploring this and other unstructured data sets.

Clustering is a fundamental problem in machine learning and has been approached in many ways. Two general and quite different approaches include iteratively fitting a mixture model (e.g., using EM) and linking together pairs of training cases that have high affinity (e.g., using spectral methods). Pairwise clustering algorithms need not compute sufficient statistics and avoid poor solutions by directly placing similar examples in the same cluster. However, many applications require that each cluster of data be accurately described by a prototype or model, so affinity-based clustering - and its benefits - cannot be directly realized. We describe a technique called "affinity propagation", which combines the advantages of both approaches. The method learns a mixture model of the data by recursively propagating affinity messages. We demonstrate affinity propagation on the problems of clustering image patches for image segmentation and learning mixtures of gene expression models from microarray data. We find that affinity propagation obtains better solutions than mixtures of Gaussians, the K-medoids algorithm, spectral clustering and hierarchical clustering, and is both able to find a pre-specified number of clusters and is able to automatically determine the number of clusters. Interestingly, affinity propagation can be viewed as belief propagation in a graphical model that accounts for pairwise training case likelihood functions and the identification of cluster centers.

We discuss two intrinsic weaknesses of the spectral graph partitioning method, both of which have practical consequences. The first is that spectral embeddings tend to hide the best cuts from the commonly used hyperplane rounding method. Rather than cleaning up the resulting suboptimal cuts with local search, we recommend the adoption of flow-based rounding. The second weakness is that for many "power law" graphs, the spectral method produces cuts that are highly unbalanced, thus decreasing the usefulness of the method for visualization (see figure 4(b)) or as a basis for divide-and-conquer algorithms. These balance problems, which occur even though the spectral method's quotient-style objective function does encourage balance, can be fixed with a stricter balance constraint that turns the spectral mathematical program into an SDP that can be solved for million-node graphs by a method of Burer and Monteiro.

This paper proposes an algorithm to convert a T -stage stochastic decision problem with a continuous state space to a sequence of supervised learning problems. The optimization problem associated with the trajectory tree and random trajectory methods of Kearns, Mansour, and Ng, 2000, is solved using the Gauss-Seidel method. The algorithm breaks a multistage reinforcement learning problem into a sequence of single-stage reinforcement learning subproblems, each of which is solved via an exact reduction to a weighted-classification problem that can be solved using off-the-self methods. Thus the algorithm converts a reinforcement learning problem into simpler supervised learning subproblems. It is shown that the method converges in a finite number of steps to a solution that cannot be further improved by componentwise optimization. The implication of the proposed algorithm is that a plethora of classification methods can be applied to find policies in the reinforcement learning problem.

Given a directed graphical model with binary-valued hidden nodes and real-valued noisy observations, consider deciding upon the maximum a-posteriori (MAP) or the maximum posterior-marginal (MPM) assignment under the restriction that each node broadcasts only to its children exactly one single-bit message. We present a variational formulation, viewing the processing rules local to all nodes as degrees-of-freedom, that minimizes the loss in expected (MAP or MPM) performance subject to such online communication constraints. The approach leads to a novel message-passing algorithm to be executed offline, or before observations are realized, which mitigates the performance loss by iteratively coupling all rules in a manner implicitly driven by global statistics. We also provide (i) illustrative examples, (ii) assumptions that guarantee convergence and efficiency and (iii) connections to active research areas.

Predictive state representations (PSRs) are a method of modeling dynamical systems using only observable data, such as actions and observations, to describe their model. PSRs use predictions about the outcome of future tests to summarize the system state. The best existing techniques for discovery and learning of PSRs use a Monte Carlo approach to explicitly estimate these outcome probabilities. In this paper, we present a new algorithm for discovery and learning of PSRs that uses a gradient descent approach to compute the predictions for the current state. The algorithm takes advantage of the large amount of structure inherent in a valid prediction matrix to constrain its predictions. Furthermore, the algorithm can be used online by an agent to constantly improve its prediction quality; something that current state of the art discovery and learning algorithms are unable to do. We give empirical results to show that our constrained gradient algorithm is able to discover core tests using very small amounts of data, and with larger amounts of data can compute accurate predictions of the system dynamics.

In this paper we consider the problem of finding sets of points that conform to a given underlying model from within a dense, noisy set of observations. This problem is motivated by the task of efficiently linking faint asteroid detections, but is applicable to a range of spatial queries. We survey current tree-based approaches, showing a tradeoff exists between single tree and multiple tree algorithms. To this end, we present a new type of multiple tree algorithm that uses a variable number of trees to exploit the advantages of both approaches. We empirically show that this algorithm performs well using both simulated and astronomical data.

In this paper we derive an algorithm that computes the entire solution path of the support vector regression, with essentially the same computational cost as fitting one SVR model. We also propose an unbiased estimate for the degrees of freedom of the SVR model, which allows convenient selection of the regularization parameter.

We consider regularized least-squares (RLS) with a Gaussian kernel.

To escape from the curse of dimensionality, we claim that one can learn non-local functions, in the sense that the value and shape of the learned function at x must be inferred using examples that may be far from x. With this objective, we present a non-local nonparametric density estimator. It builds upon previously proposed Gaussian mixture models with regularized covariance matrices to take into account the local shape of the manifold. It also builds upon recent work on non-local estimators of the tangent plane of a manifold, which are able to generalize in places with little training data, unlike traditional, local, nonparametric models.