Sets", we consider the problem of retrieving items from a concept or cluster, given a query consisting of a few items from that cluster. We formulate this as a Bayesian inference problem and describe avery simple algorithm for solving it. Our algorithm uses a modelbased concept of a cluster and ranks items using a score which evaluates the marginal probability that each item belongs to a cluster containing the query items. For exponential family models with conjugate priors this marginal probability is a simple function of sufficient statistics. We focus on sparse binary data and show that our score can be evaluated exactly usinga single sparse matrix multiplication, making it possible to apply our algorithm to very large datasets. We evaluate our algorithm on three datasets: retrieving movies from EachMovie, finding completions of author sets from the NIPS dataset, and finding completions of sets of words appearing in the Grolier encyclopedia.

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 reinforcementlearning problem into a sequence of single-stage reinforcement learningsubproblems, 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 probleminto 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 ofthe proposed algorithm is that a plethora of classification methods can be applied to find policies in the reinforcement learning problem.

We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network.

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.

Humans are extremely adept at learning new skills by imitating the actions ofothers. A progression of imitative abilities has been observed in children, ranging from imitation of simple body movements to goalbased imitationbased on inferring intent. In this paper, we show that the problem of goal-based imitation can be formulated as one of inferring goals and selecting actions using a learned probabilistic graphical model of the environment. We first describe algorithms for planning actions to achieve a goal state using probabilistic inference. We then describe how planning can be used to bootstrap the learning of goal-dependent policies byutilizing feedback from the environment. The resulting graphical model is then shown to be powerful enough to allow goal-based imitation. Usinga simple maze navigation task, we illustrate how an agent can infer the goals of an observed teacher and imitate the teacher even when the goals are uncertain and the demonstration is incomplete.

In supervised learning scenarios, feature selection has been studied widely in the literature. Selecting features in unsupervised learning scenarios is a much harder problem, due to the absence of class labels that would guide the search for relevant information. And, almost all of previous unsupervised feature selection methods are "wrapper" techniques that require a learning algorithm to evaluate the candidate feature subsets. In this paper, we propose a "filter" method for feature selection which is independent of any learning algorithm. Our method can be performed in either supervised or unsupervised fashion. The proposed method is based on the observation that, in many real world classification problems, data from the same class are often close to each other. The importance of a feature is evaluated by its power of locality preserving, or,Laplacian Score. We compare our method with data variance (unsupervised) and Fisher score (supervised) on two data sets. Experimental results demonstrate the effectiveness and efficiency of our algorithm.

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. Alimitation 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 forapproximate posterior inference in this model, which is complicated bythe 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 wayof visualizing and exploring this and other unstructured data sets.

Hybrid "CMOL" integrated circuits, combining CMOS subsystem with nanowire crossbars and simple two-terminal nanodevices, promise to extend the exponential Moore-Law development of microelectronics into the sub-10-nm range. We are developing neuromorphic network ("CrossNet") architectures for this future technology, in which neural cell bodies are implemented in CMOS, nanowires are used as axons and dendrites, while nanodevices (bistable latching switches) are used as elementary synapses. We have shown how CrossNets may be trained to perform pattern recovery and classification despite the limitations imposed by the CMOL hardware.

The problem of computing a resample estimate for the reconstruction error in PCA is reformulated as an inference problem with the help of the replica method. Using the expectation consistent (EC) approximation, theintractable inference problem can be solved efficiently using only two variational parameters. A perturbative correction to the result is computed and an alternative simplified derivation is also presented.

Previous work has demonstrated that the image variations of many objects (human faces in particular) under variable lighting can be effectively modeled by low dimensional linear spaces.