Learning from ambiguous training data is highly relevant in many applications. We present a new learning algorithm for classification problems where labels are associated with sets of pattern instead of individual patterns. This encompasses multiple instance learning as a special case. Our approach is based on a generalization of linear programming boosting and uses results from disjunctive programming to generate successively stronger linear relaxations of a discrete non-convex problem.

A common way of image denoising is to project a noisy image to the subspace of admissible images made for instance by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion.

We describe a new approximation algorithm for solving partially observable MDPs. Our bounded policy iteration approach searches through the space of bounded-size, stochastic finite state controllers, combining several advantages of gradient ascent (efficiency, search through restricted controller space) and policy iteration (less vulnerability to local optima).

We present a new method for calculating approximate marginals for probability distributions defined by graphs with cycles, based on a Gaussian entropybound combined with a semidefinite outer bound on the marginal polytope. This combination leads to a log-determinant maximization problemthat can be solved by efficient interior point methods [8]. As with the Bethe approximation and its generalizations [12], the optimizing arguments of this problem can be taken as approximations to the exact marginals. In contrast to Bethe/Kikuchi approaches, our variational problemis strictly convex and so has a unique global optimum. An additional desirable feature is that the value of the optimal solution is guaranteed to provide an upper bound on the log partition function. In experimental trials, the performance of the log-determinant relaxation is comparable to or better than the sum-product algorithm, and by a substantial marginfor certain problem classes. Finally, the zero-temperature limit of our log-determinant relaxation recovers a class of well-known semidefinite relaxations for integer programming [e.g., 3].

The connectivity of the nervous system of the nematode Caenorhabditis eleganshas been described completely, but the analysis of the neuronal basisof behavior in this system is just beginning. Here, we used an optimization algorithm to search for patterns of connectivity sufficient tocompute the sensorimotor transformation underlying C. elegans chemotaxis, a simple form of spatial orientation behavior in which turning probabilityis modulated by the rate of change of chemical concentration.

Approximate linear programming (ALP) has emerged recently as one of the most promising methods for solving complex factored MDPs with finite state spaces. In this work we show that ALP solutions are not limited only to MDPs with finite state spaces, but that they can also be applied successfully to factored continuous-state MDPs (CMDPs). We show how one can build an ALPbased approximation for such a model and contrast it to existing solution methods. We argue that this approach offers a robust alternative for solving high dimensional continuous-state space problems. The point is supported by experiments on three CMDP problems with 24-25 continuous state factors.

Optimal solutions to Markov Decision Problems (MDPs) are very sensitive withrespect to the state transition probabilities. In many practical problems, the estimation of those probabilities is far from accurate. Hence, estimation errors are limiting factors in applying MDPs to realworld problems.We propose an algorithm for solving finite-state and finite-action MDPs, where the solution is guaranteed to be robust with respect to estimation errors on the state transition probabilities.

We propose a nonlinear Canonical Correlation Analysis (CCA) method which works by coordinating or aligning mixtures of linear models. In the same way that CCA extends the idea of PCA, our work extends recent methodsfor nonlinear dimensionality reduction to the case where multiple embeddings of the same underlying low dimensional coordinates areobserved, each lying on a different high dimensional manifold. We also show that a special case of our method, when applied to only a single manifold, reduces to the Laplacian Eigenmaps algorithm. As with previous alignment schemes, once the mixture models have been estimated, all of the parameters of our model can be estimated in closed form without local optima in the learning. Experimental results illustrate the viability of the approach as a nonlinear extension of CCA.

A special case of particular relevance is known as multiple instance learning [5]

A common way of image denoising is to project a noisy image to the subspace ofadmissible images made for instance by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion.