PreMoLab

Date: Thursday May 24, 2012. Speaker: K.V. Borontsov

Abstract: In Combinatorial Theory of Overfitting the problem of bounding generalization ability of a learning algorithm is considered in a following discrete framework. Given a binary error matrix with rows corresponding to objects and columns corresponding to hypotheses. The “one” in a matrix cell means that a given hypothesis is wrong for a given object. One tries to find a hypothesis that makes errors as few as possible provided that only a subset of rows is observable. All partitions of an object set into an observable training sample and a hidden testing sample of fixed lengths are assumed to be equiprobable. This only probabilistic assumption is sufficient to bound the probability of overfitting and the complete cross-validation functional. Combinatorial approach enables to capture information from error matrix in most explicit and exhaustive way, thus resulting to very tight and in some cases exact generalization bounds. Some applications of combinatorial generalization bounds to learning algorithm design are considered including rule induction and prototype selection for distance-based classifiers.

Date: Thursday May 17, 2012. Speakers: Burnaev Evgeny (IITP, PreMoLab, Datadvance) and Panov Maxim (IITP, Datadvance)

Abstract: Problem of adaptive design of regression experiments is considered. Some approaches to its solution based on Gaussian process regression are proposed. Various criteria for construction of regression experiments are investigated.

Date: Thursday May 10, 2012 Speaker: Yuri Dorn

Abstract: In our talk we describe the Braess Paradox and traffic management tools, s.t. traffic lights and road tolls, in equilibrium models (BMW and Nesterov-de Palma stationary dynamic models). The capability of this tools to take away the transportation system from inefficient traffic flow distribution will be consider. We will show, that in the original Braess Paradox case the ability of traffic lights to manage equilibrium traffic distribution are very limited. On the other hand road tolls are very efficient in this case.

Date: Thursday May 3, 2012 Speaker: Yuri Golubev

Abstract: This paper analyzes the so-called exponential weighting method for Gaussian regression model. Special attention is given to the case that the component estimators are projections into arbitrary subspaces, such as those spanned by subsets of explanatory of explanatory variables in a given design. The main idea in this paper is to relate the unbiased risk estimate of the mixture estimator to estimates of the risk achieved by the components. This results in simple and elegant bounds on the risk in the form of oracle inequalities. Connections between the model selection approach and the exponential weighting will be discussed.

The source file of the paper can be be downloaded from http://www.stat.yale.edu/~arb4/publications.html.