We provide provably privacy-preserving versions of belief propagation, Gibbs sampling, and other local algorithms -- distributed multiparty protocols in which each party or vertex learns only its final local value, and absolutely nothing else.

We present a new local approximation algorithm for computing MAP and log-partition function for arbitrary exponential family distribution represented by a finite-valued pair-wise Markov random field (MRF), say G. Our algorithm is based on decomposing G into appropriately chosen small components; computing estimates locally in each of these components and then producing a good global solution. We prove that the algorithm can provide approximate solution within arbitrary accuracy when $G$ excludes some finite sized graph as its minor and G has bounded degree: all Planar graphs with bounded degree are examples of such graphs. The running time of the algorithm is $\Theta(n)$ (n is the number of nodes in G), with constant dependent on accuracy, degree of graph and size of the graph that is excluded as a minor (constant for Planar graphs). Our algorithm for minor-excluded graphs uses the decomposition scheme of Klein, Plotkin and Rao (1993). In general, our algorithm works with any decomposition scheme and provides quantifiable approximation guarantee that depends on the decomposition scheme.

Adaptation to other initially unknown agents often requires computing an effective counter-strategy. In the Bayesian paradigm, one must find a good counter-strategy to the inferred posterior of the other agents' behavior. In the experts paradigm, one may want to choose experts that are good counter-strategies to the other agents' expected behavior. In this paper we introduce a technique for computing robust counter-strategies for adaptation in multiagent scenarios under a variety of paradigms. The strategies can take advantage of a suspected tendency in the decisions of the other agents, while bounding the worst-case performance when the tendency is not observed. The technique involves solving a modified game, and therefore can make use of recently developed algorithms for solving very large extensive games. We demonstrate the effectiveness of the technique in two-player Texas Hold'em. We show that the computed poker strategies are substantially more robust than best response counter-strategies, while still exploiting a suspected tendency. We also compose the generated strategies in an experts algorithm showing a dramatic improvement in performance over using simple best responses.

Our task, at time t, is to compute an estimate V; of V5 for each state .9.

Two algorithmic implementations of the method are formalized.

We introduce a hierarchical Bayesian model for the discovery of putative regulators from gene expression data only. The hierarchy incorporates the knowledge that there are just a few regulators that by themselves only regulate a handful of genes. This is implemented through a so-called spike-and-slab prior, a mixture of Gaussians with different widths, with mixing weights from a hierarchical Bernoulli model. For efficient inference we implemented expectation propagation. Running the model on a malaria parasite data set, we found four genes with significant homology to transcription factors in an amoebe, one RNA regulator and three genes of unknown function (out of the top ten genes considered).

We propose a novel method for {\em linear} dimensionality reduction of manifold modeled data. First, we show that with a small number $M$ of {\em random projections} of sample points in $\reals^N$ belonging to an unknown $K$-dimensional Euclidean manifold, the intrinsic dimension (ID) of the sample set can be estimated to high accuracy. Second, we rigorously prove that using only this set of random projections, we can estimate the structure of the underlying manifold. In both cases, the number random projections required is linear in $K$ and logarithmic in $N$, meaning that $K

Rare category detection is an open challenge for active learning, especially in the de-novo case (no labeled examples), but of significant practical importance for data mining - e.g.

We propose to investigate test statistics for testing homogeneity based on kernel Fisher discriminant analysis. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed alternatives is assessed. Finally, experimental evidenceof the performance of the proposed approach on both artificial and real datasets is provided.

Active learning sequentially selects unlabeled instances to label with the goal of reducing the effort needed to learn a good classifier. Most previous studies in active learning have focused on selecting one unlabeled instance at one time while retraining in each iteration. However, single instance selection systems are unable to exploit a parallelized labeler when one is available. Recently a few batch mode active learning approaches have been proposed that select a set of most informative unlabeled instances in each iteration, guided by some heuristic scores. In this paper, we propose a discriminative batch mode active learning approach that formulates the instance selection task as a continuous optimization problem over auxiliary instance selection variables. The optimization is formuated to maximize the discriminative classification performance of the target classifier, while also taking the unlabeled data into account. Although the objective is not convex, we can manipulate a quasi-Newton method to obtain a good local solution. Our empirical studies on UCI datasets show that the proposed active learning is more effective than current state-of-the art batch mode active learning algorithms.