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Sistema evolutivo eficiente para aprendizagem estrutural de redes Bayesianas; Efficient evolutionary system for learning BN structures

Villanueva Talavera, Edwin Rafael
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 21/09/2012 Português
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Redes Bayesianas (RB) são ferramentas probabilísticas amplamente aceitas para modelar e fazer inferências em domínios sob incertezas. Uma das maiores dificuldades na construção de uma RB é determinar a sua estrutura de modelo, a qual representa a estrutura de interdependências entre as variáveis modeladas. A estimativa exata da estrutura de modelo a partir de dados observados é, de forma geral, impraticável já que o número de estruturas possíveis cresce de forma super-exponencial com o número de variáveis. Métodos eficientes de aprendizagem aproximada tornam-se, portanto, essenciais para a construção de RBs verossímeis. O presente trabalho apresenta o Sistema Evolutivo Eficiente para Aprendizagem Estrutural de RBs, ou abreviadamente, EES-BN. Duas etapas de aprendizagem compõem EES-BN. A primeira etapa é encarregada de reduzir o espaço de busca mediante a aprendizagem de uma superestrutura. Para tal fim foram desenvolvidos dois métodos efetivos: Opt01SS e OptHPC, ambos baseados em testes de independência. A segunda etapa de EES-BN é um esquema de busca evolutiva que aproxima a estrutura do modelo respeitando as restrições estruturais aprendidas na superestrutura. Três blocos principais integram esta etapa: recombinação...

Precipitates segmentation from scanning electron microscope images through machine learning techniques

Papa, João P.; Pereira, Clayton R.; De Albuquerque, Victor H. C.; Silva, Cleiton C.; Falcão, Alexandre X.; Tavares, João Manuel R. S.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 456-468
Português
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The presence of precipitates in metallic materials affects its durability, resistance and mechanical properties. Hence, its automatic identification by image processing and machine learning techniques may lead to reliable and efficient assessments on the materials. In this paper, we introduce four widely used supervised pattern recognition techniques to accomplish metallic precipitates segmentation in scanning electron microscope images from dissimilar welding on a Hastelloy C-276 alloy: Support Vector Machines, Optimum-Path Forest, Self Organizing Maps and a Bayesian classifier. Experimental results demonstrated that all classifiers achieved similar recognition rates with good results validated by an expert in metallographic image analysis. © 2011 Springer-Verlag Berlin Heidelberg.

Learning overhypotheses with hierarchical Bayesian models

Kemp, C.; Perfors, A.; Tenenbaum, J.
Fonte: Wiley-Blackwell Publishing Publicador: Wiley-Blackwell Publishing
Tipo: Artigo de Revista Científica
Publicado em //2007 Português
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Inductive learning is impossible without overhypotheses, or constraints on the hypotheses considered by the learner. Some of these overhypotheses must be innate, but we suggest that hierarchical Bayesian models can help to explain how the rest are acquired. To illustrate this claim, we develop models that acquire two kinds of overhypotheses – overhypotheses about feature variability (e.g. the shape bias in word learning) and overhypotheses about the grouping of categories into ontological kinds like objects and substances.; Charles Kemp, Amy Perfors and Joshua B. Tenenbaum

Indirect evidence and the poverty of the stimulus: the case of anaphoric one

Foraker, S.; Regier, T.; Khetarpal, N.; Perfors, A.; Tenenbaum, J.
Fonte: Cognitive Science Society; United States Publicador: Cognitive Science Society; United States
Tipo: Conference paper
Publicado em //2007 Português
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It is widely held that children’s linguistic input underdetermines the correct grammar, and that language learning must therefore be guided by innate linguistic constraints. In contrast, a recent counterproposal holds that apparently impoverished input may contain indirect sources of evidence that allow the child to learn without such constraints. Here, we support this latter view by showing that a Bayesian model can learn a standard “poverty-of-stimulus” example, anaphoric one, from realistic input without a constraint traditionally assumed to be necessary, by relying on indirect evidence. Our demonstration does however assume other linguistic knowledge; thus we reduce the problem of learning anaphoric one to that of learning this other knowledge. We discuss whether this other knowledge may itself be acquired without linguistic constraints.; Stephani Foraker, Terry Regier, Naveen Khetarpal, Amy Perfors and Joshua B. Tenenbaum

Indirect evidence and the poverty of the stimulus: The case of anaphoric one

Foraker, S.; Regier, T.; Khetarpal, N.; Perfors, A.; Tenenbaum, J.
Fonte: Elsevier Science Inc Publicador: Elsevier Science Inc
Tipo: Artigo de Revista Científica
Publicado em //2009 Português
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It is widely held that children’s linguistic input underdetermines the correct grammar, and that language learning must therefore be guided by innate linguistic constraints. Here, we show that a Bayesian model can learn a standard poverty-of-stimulus example, anaphoric one, from realistic input by relying on indirect evidence, without a linguistic constraint assumed to be necessary. Our demonstration does, however, assume other linguistic knowledge; thus, we reduce the problem of learning anaphoric one to that of learning this other knowledge. We discuss whether this other knowledge may itself be acquired without linguistic constraints.; Stephani Foraker, Terry Regier, Naveen Khetarpal, Amy Perfors and Joshua Tenenbaum

Language evolution is shaped by the structure of the world: an iterated learning analysis

Perfors, A.; Navarro, D.
Fonte: Cognitive Science Society; Austin, TX, USA Publicador: Cognitive Science Society; Austin, TX, USA
Tipo: Conference paper
Publicado em //2011 Português
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Human languages vary in many ways, but also show striking cross-linguistic universals. Why do these universals exist? Recent theoretical results demonstrate that Bayesian learners transmitting language to each other through iterated learning will converge on a distribution of languages that depends only on their prior biases about language and the quantity of data transmitted at each point; the structure of the world being communicated about plays no role (Griffiths & Kalish, 2005, 2007). We revisit these findings and show that when certain assumptions about the independence of languages and the world are abandoned, learners will converge to languages that depend on the structure of the world as well as their prior biases. These theoretical results are supported with a series of experiments showing that when human learners acquire language through iterated learning, the ultimate structure of those languages is shaped by the structure of the meanings to be communicated.; Amy Perfors, Daniel Navarro

Linear-Nonlinear-Poisson Neuron Networks Perform Bayesian Inference On Boltzmann Machines

Shao, Louis Yuanlong
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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One conjecture in both deep learning and classical connectionist viewpoint is that the biological brain implements certain kinds of deep networks as its back-end. However, to our knowledge, a detailed correspondence has not yet been set up, which is important if we want to bridge between neuroscience and machine learning. Recent researches emphasized the biological plausibility of Linear-Nonlinear-Poisson (LNP) neuron model. We show that with neurally plausible settings, the whole network is capable of representing any Boltzmann machine and performing a semi-stochastic Bayesian inference algorithm lying between Gibbs sampling and variational inference.; Comment: Submitted to International Conference of Learning Representation (ICLR) 2013

A new parameter Learning Method for Bayesian Networks with Qualitative Influences

Feelders, Ad
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/06/2012 Português
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We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified qualitative influences correspond to certain order restrictions on the parameters in the network. These parameters may therefore be estimated using constrained maximum likelihood estimation. We propose an alternative method, based on the isotonic regression. The constrained maximum likelihood estimates are fairly complicated to compute, whereas computation of the isotonic regression estimates only requires the repeated application of the Pool Adjacent Violators algorithm for linear orders. Therefore, the isotonic regression estimator is to be preferred from the viewpoint of computational complexity. Through experiments on simulated and real data, we show that the new learning method is competitive in performance to the constrained maximum likelihood estimator, and that both estimators improve on the standard estimator.; Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence (UAI2007)

Marginal Pseudo-Likelihood Learning of Markov Network structures

Pensar, Johan; Nyman, Henrik; Niiranen, Juha; Corander, Jukka
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the assumption of chordality which ensures that efficient scoring methods can be used. In general, non-chordal graphs have intractable normalizing constants which renders the calculation of Bayesian and other scores difficult beyond very small-scale systems. Recently, there has been a surge of interest towards the use of regularized pseudo-likelihood methods for structural learning of large-scale Markov network models, as such an approach avoids the assumption of chordality. The currently available methods typically necessitate the use of a tuning parameter to adapt the level of regularization for a particular dataset, which can be optimized for example by cross-validation. Here we introduce a Bayesian version of pseudo-likelihood scoring of Markov networks, which enables an automatic regularization through marginalization over the nuisance parameters in the model. We prove consistency of the resulting MPL estimator for the network structure via comparison with the pseudo information criterion. Identification of the MPL-optimal network on a prescanned graph space is considered with both greedy hill climbing and exact pseudo-Boolean optimization algorithms. We find that for reasonable sample sizes the hill climbing approach most often identifies networks that are at a negligible distance from the restricted global optimum. Using synthetic and existing benchmark networks...

Asymptotics of Discrete MDL for Online Prediction

Poland, Jan; Hutter, Marcus
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/06/2005 Português
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Minimum Description Length (MDL) is an important principle for induction and prediction, with strong relations to optimal Bayesian learning. This paper deals with learning non-i.i.d. processes by means of two-part MDL, where the underlying model class is countable. We consider the online learning framework, i.e. observations come in one by one, and the predictor is allowed to update his state of mind after each time step. We identify two ways of predicting by MDL for this setup, namely a static} and a dynamic one. (A third variant, hybrid MDL, will turn out inferior.) We will prove that under the only assumption that the data is generated by a distribution contained in the model class, the MDL predictions converge to the true values almost surely. This is accomplished by proving finite bounds on the quadratic, the Hellinger, and the Kullback-Leibler loss of the MDL learner, which are however exponentially worse than for Bayesian prediction. We demonstrate that these bounds are sharp, even for model classes containing only Bernoulli distributions. We show how these bounds imply regret bounds for arbitrary loss functions. Our results apply to a wide range of setups, namely sequence prediction, pattern classification, regression, and universal induction in the sense of Algorithmic Information Theory among others.; Comment: 34 pages

Learning Optimal Augmented Bayes Networks

Hamine, Vikas; Helman, Paul
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/09/2005 Português
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Naive Bayes is a simple Bayesian classifier with strong independence assumptions among the attributes. This classifier, desipte its strong independence assumptions, often performs well in practice. It is believed that relaxing the independence assumptions of a naive Bayes classifier may improve the classification accuracy of the resulting structure. While finding an optimal unconstrained Bayesian Network (for most any reasonable scoring measure) is an NP-hard problem, it is possible to learn in polynomial time optimal networks obeying various structural restrictions. Several authors have examined the possibilities of adding augmenting arcs between attributes of a Naive Bayes classifier. Friedman, Geiger and Goldszmidt define the TAN structure in which the augmenting arcs form a tree on the attributes, and present a polynomial time algorithm that learns an optimal TAN with respect to MDL score. Keogh and Pazzani define Augmented Bayes Networks in which the augmenting arcs form a forest on the attributes (a collection of trees, hence a relaxation of the stuctural restriction of TAN), and present heuristic search methods for learning good, though not optimal, augmenting arc sets. The authors, however, evaluate the learned structure only in terms of observed misclassification error and not against a scoring metric...

Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC

Frigola, Roger; Lindsten, Fredrik; Schön, Thomas B.; Rasmussen, Carl E.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

Near-Optimal Target Learning With Stochastic Binary Signals

Chakraborty, Mithun; Das, Sanmay; Magdon-Ismail, Malik
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/02/2012 Português
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We study learning in a noisy bisection model: specifically, Bayesian algorithms to learn a target value V given access only to noisy realizations of whether V is less than or greater than a threshold theta. At step t = 0, 1, 2, ..., the learner sets threshold theta t and observes a noisy realization of sign(V - theta t). After T steps, the goal is to output an estimate V^ which is within an eta-tolerance of V . This problem has been studied, predominantly in environments with a fixed error probability q < 1/2 for the noisy realization of sign(V - theta t). In practice, it is often the case that q can approach 1/2, especially as theta -> V, and there is little known when this happens. We give a pseudo-Bayesian algorithm which provably converges to V. When the true prior matches our algorithm's Gaussian prior, we show near-optimal expected performance. Our methods extend to the general multiple-threshold setting where the observation noisily indicates which of k >= 2 regions V belongs to.

Learning Bayesian Network Parameters with Prior Knowledge about Context-Specific Qualitative Influences

Feelders, Ad; van der Gaag, Linda C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/07/2012 Português
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We present a method for learning the parameters of a Bayesian network with prior knowledge about the signs of influences between variables. Our method accommodates not just the standard signs, but provides for context-specific signs as well. We show how the various signs translate into order constraints on the network parameters and how isotonic regression can be used to compute order-constrained estimates from the available data. Our experimental results show that taking prior knowledge about the signs of influences into account leads to an improved fit of the true distribution, especially when only a small sample of data is available. Moreover, the computed estimates are guaranteed to be consistent with the specified signs, thereby resulting in a network that is more likely to be accepted by experts in its domain of application.; Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005)

Convex Structure Learning for Bayesian Networks: Polynomial Feature Selection and Approximate Ordering

Guo, Yuhong; Schuurmans, Dale
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/06/2012 Português
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We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and parameters can be learned efficiently, even without restricting the size of the parent sets. We then consider the problem of optimizing the variable order for a given set of features. This is still a computationally hard problem, but we present a convex relaxation that yields an optimal 'soft' ordering in polynomial time. One novel aspect of the approach is that we do not perform a discrete search over DAG structures, nor over variable orders, but instead solve a continuous relaxation that can then be rounded to obtain a valid network structure. We conduct an experimental comparison against standard structure search procedures over standard objectives, which cope with local minima, and evaluate the advantages of using convex relaxations that reduce the effects of local minima.; Comment: Appears in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (UAI2006)

A Kernel Approach to Tractable Bayesian Nonparametrics

Huszár, Ferenc; Lacoste-Julien, Simon
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick to inference in a parametric Bayesian model. For example, Gaussian process regression can be derived this way from Bayesian linear regression. Despite the success of the Gaussian process framework, the kernel trick is rarely explicitly considered in the Bayesian literature. In this paper, we aim to fill this gap and demonstrate the potential of applying the kernel trick to tractable Bayesian parametric models in a wider context than just regression. As an example, we present an intuitive Bayesian kernel machine for density estimation that is obtained by applying the kernel trick to a Gaussian generative model in feature space.; Comment: acknowledgements added to previous version, content otherwise unchanged

PAC-Bayesian Inequalities for Martingales

Seldin, Yevgeny; Laviolette, François; Cesa-Bianchi, Nicolò; Shawe-Taylor, John; Auer, Peter
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where martingales are encountered. We also present a comparison inequality that bounds the expectation of a convex function of a martingale difference sequence shifted to the [0,1] interval by the expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma's inequality.

BPR: Bayesian Personalized Ranking from Implicit Feedback

Rendle, Steffen; Freudenthaler, Christoph; Gantner, Zeno; Schmidt-Thieme, Lars
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/05/2012 Português
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Item recommendation is the task of predicting a personalized ranking on a set of items (e.g. websites, movies, products). In this paper, we investigate the most common scenario with implicit feedback (e.g. clicks, purchases). There are many methods for item recommendation from implicit feedback like matrix factorization (MF) or adaptive knearest-neighbor (kNN). Even though these methods are designed for the item prediction task of personalized ranking, none of them is directly optimized for ranking. In this paper we present a generic optimization criterion BPR-Opt for personalized ranking that is the maximum posterior estimator derived from a Bayesian analysis of the problem. We also provide a generic learning algorithm for optimizing models with respect to BPR-Opt. The learning method is based on stochastic gradient descent with bootstrap sampling. We show how to apply our method to two state-of-the-art recommender models: matrix factorization and adaptive kNN. Our experiments indicate that for the task of personalized ranking our optimization method outperforms the standard learning techniques for MF and kNN. The results show the importance of optimizing models for the right criterion.; Comment: Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009)

A Bayesian Sampling Approach to Exploration in Reinforcement Learning

Asmuth, John; Li, Lihong; Littman, Michael L.; Nouri, Ali; Wingate, David
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/05/2012 Português
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We present a modular approach to reinforcement learning that uses a Bayesian representation of the uncertainty over models. The approach, BOSS (Best of Sampled Set), drives exploration by sampling multiple models from the posterior and selecting actions optimistically. It extends previous work by providing a rule for deciding when to resample and how to combine the models. We show that our algorithm achieves nearoptimal reward with high probability with a sample complexity that is low relative to the speed at which the posterior distribution converges during learning. We demonstrate that BOSS performs quite favorably compared to state-of-the-art reinforcement-learning approaches and illustrate its flexibility by pairing it with a non-parametric model that generalizes across states.; Comment: Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009)

Bayesian Nonparametric Modeling of Latent Structures

Xing, Zhengming
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2014 Português
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Unprecedented amount of data has been collected in diverse fields such as social network, infectious disease and political science in this information explosive era. The high dimensional, complex and heterogeneous data imposes tremendous challenges on traditional statistical models. Bayesian nonparametric methods address these challenges by providing models that can fit the data with growing complexity. In this thesis, we design novel Bayesian nonparametric models on dataset from three different fields, hyperspectral images analysis, infectious disease and voting behaviors.

First, we consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelength-dependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering the potential to significantly reduce the quantity of data that need be measured. We achieve this objective by employing Bayesian dictionary learning model, considering two distinct means of imposing sparse dictionary usage and drawing the dictionary elements from a Gaussian process prior, imposing structure on the wavelength dependence of the dictionary elements.

Second...