The essential idea is fast approximation by sampling in trees.

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 study the relation between notions of game-theoretic equilibria which are based on stability under a set of deviations, and empirical equilibria which are reached by rational players. Rational players are modelled by players using no regret algorithms, which guarantee that their payoff in the long run is almost as much as the most they could hope to achieve by consistently deviating from the algorithm's suggested action. We show that for a given set of deviations over the strategy set of a player, it is possible to efficiently approximate fixed points of a given deviation if and only if there exist efficient no regret algorithms resistant to the deviations. Further, we show that if all players use a no regret algorithm, then the empirical distribution of their plays converges to an equilibrium.

We propose a new approach for dealing with the estimation of the location of change-points in one-dimensional piecewise constant signals observed in white noise. Our approach consists in reframing this task in a variable selection context. We use a penalized least-squares criterion with a l1-type penalty for this purpose. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of the change-points. Then, we explain how to implement this method in practice by combining the LAR algorithm and a reduced version of the dynamic programming algorithm and we apply it to synthetic and real data.

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.

We investigate a new, convex relaxation of an expectation-maximization (EM) variant that approximates a standard objective while eliminating local minima. First, a cautionary result is presented, showing that any convex relaxation of EM over hidden variables must give trivial results if any dependence on the missing values is retained. Although this appears to be a strong negative outcome, we then demonstrate how the problem can be bypassed by using equivalence relations instead ofvalue assignments over hidden variables. In particular, we develop new algorithms for estimating exponential conditional models that only require equivalence relationinformation over the variable values. This reformulation leads to an exact expression for EM variants in a wide range of problems. We then develop a semidefinite relaxation that yields global training by eliminating local minima.

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.

Statistical tests of independence have been associated with a broad variety of dependence measures. Classical tests such as Spearman's,0 and Kendall's 7' are widely applied, however they are not