Confidence Statements for Ordering Quantiles

This work proposes Quor, a simple yet effective nonparametric method to compare independent samples with respect to corresponding quantiles of their populations. The method is solely based on the order statistics of the samples, and independence is its only requirement. All computations are performed using exact distributions with no need for any asymptotic considerations, and yet can be run using a fast quadratic-time dynamic programming idea. Computational performance is essential in high-dimensional domains, such as gene expression data. We describe the approach and discuss on the most important assumptions, building a parallel with assumptions and properties of widely used techniques for the same problem. Experiments using real data from biomedical studies are performed to empirically compare Quor and other methods in a classification task over a selection of high-dimensional data sets

Advances in Learning Bayesian Networks of Bounded Treewidth

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table

Solving Limited Memory Influence Diagrams

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and $10^{64}$ solutions. We show that the problem is NP-hard even if the underlying graph structure of the problem has small treewidth and the variables take on a bounded number of states, but that a fully polynomial time approximation scheme exists for these cases. Moreover, we show that the bound on the number of states is a necessary condition for any efficient approximation scheme.Comment: 43 pages, 8 figure

Ordering Quantiles through Confidence Statements

Ranking variables according to their relevance to predict an outcome is an important task in biomedicine. For instance, such ranking can be used for selecting a smaller number of genes for then applying other sophisticated experiments only on genes identified as important. A nonparametric method called Quor is designed to provide a confidence value for the order of arbitrary quantiles of different populations using independent samples. This confidence may provide insights about possible differences among groups and yields a ranking of importance for the variables. Computations are efficient and use exact distributions with no need for asymptotic considerations. Experiments with simulated data and with multiple real -omics data sets are performed, and they show advantages and disadvantages of the method. Quor has no assumptions but independence of samples, thus it might be a better option when assumptions of other methods cannot be asserted. The software is publicly available on CRAN

Integração de evidências em redes credais e a regra de Jeffrey

              As redes credais provêm um esquema para a representação de modelosprobabilísticos imprecisos. Os algoritmos de inferência usualmente empregados emredes credais computam o intervalo da probabilidade posterior de um evento de inter-esse dadas evidências do tipo específica - evidências que descrevem o estado atual deum conjunto de variáveis. Estes algoritmos não realizam raciocínio evidencial no casoem que as evidências devem ser processadas segundo a regra de condicionamento pro-posta por R.C. Jeffrey. Considerando isto este artigo descreve um procedimento paraintegrar evidências com a regra de Jeffrey quando da realização de inferências emredes credais

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Nesta dissetação tratamos de geometria computacional no cenário dinâmico. Neste contexto, desejamos manter estruturas de dados que permitam que um determinado atributo geométrico possa ser calculado a qualquer instante, com o conjunto de dados sendo alterado por inserções e remoções. estudamos quatro problemas clássicos de geometria computacional no cenário dinâmico: busca por regiões, localização de pontos, fecho convexo e par de pontos mais próximos. Nossa abordagem é principalmente teórica, mostrando estruturas de dados dinâmicas que permitem que inserções, remoções e consultas sobre os atributos geométricos sejam feitas eficientemente. Tipicamente esperamos que tais operações sejam feitas em tempo polilogarítmico no tamanho da entrada. Apresentamos também implementações de alguns dos algoritmos e estruturas de dados tratadas para o problema da busca por regiões e o problema do fecho convexoThis work handles computational geometry problems in their dinamic versions. In this context, we want to mantain data structures supporting queries about geometric attributes at any time, with the data set being updated by insertions and delections of objects. We studied four classic problems of computational geometry in the dinamic scenario: range searching, point location, convex hull and the closest pair points. Our approach is mainly theoretical, showing dinamic data structues supporting insertions., delections and queries about geometric atributes efficiently. Tipically we expect these operations to be executed in polylogarithmic time on the size of the set. We present implementations for some algorithms and data structures in the range searching problem and the convex hull problem addressed in this dissertatio

Local Computation in Credal Networks

The goal of this contribution is to discuss local computation in credal networks — graphical models that can represent imprecise and indeterminate probability values. We analyze the inference problem in credal networks, discuss how inference algorithms can benefit from local computation, and suggest that local computation can be particularly important in approximate inference algorithms