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Redes probabilísticas: aprendendo estruturas e atualizando probabilidades; Probabilistic networks: learning structures and updating probabilities

Faria, Rodrigo Candido
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 28/05/2014 Português
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Redes probabilísticas são modelos muito versáteis, com aplicabilidade crescente em diversas áreas. Esses modelos são capazes de estruturar e mensurar a interação entre variáveis, permitindo que sejam realizados vários tipos de análises, desde diagnósticos de causas para algum fenômeno até previsões sobre algum evento, além de permitirem a construção de modelos de tomadas de decisões automatizadas. Neste trabalho são apresentadas as etapas para a construção dessas redes e alguns métodos usados para tal, dando maior ênfase para as chamadas redes bayesianas, uma subclasse de modelos de redes probabilísticas. A modelagem de uma rede bayesiana pode ser dividida em três etapas: seleção de variáveis, construção da estrutura da rede e estimação de probabilidades. A etapa de seleção de variáveis é usualmente feita com base nos conhecimentos subjetivos sobre o assunto estudado. A construção da estrutura pode ser realizada manualmente, levando em conta relações de causalidade entre as variáveis selecionadas, ou semi-automaticamente, através do uso de algoritmos. A última etapa, de estimação de probabilidades, pode ser feita seguindo duas abordagens principais: uma frequentista, em que os parâmetros são considerados fixos...

Using Mechanistic Bayesian Networks to Identify Downstream Targets of the Sonic Hedgehog Pathway

Shah, Abhik; Tenzen, Toyoaki; Woolf, Peter J; McMahon, Andrew P.
Fonte: BioMed Central Publicador: BioMed Central
Tipo: Artigo de Revista Científica
Português
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Background: The topology of a biological pathway provides clues as to how a pathway operates, but rationally using this topology information with observed gene expression data remains a challenge. Results: We introduce a new general-purpose analytic method called Mechanistic Bayesian Networks (MBNs) that allows for the integration of gene expression data and known constraints within a signal or regulatory pathway to predict new downstream pathway targets. The MBN framework is implemented in an open-source Bayesian network learning package, the Python Environment for Bayesian Learning (PEBL). We demonstrate how MBNs can be used by modeling the early steps of the sonic hedgehog pathway using gene expression data from different developmental stages and genetic backgrounds in mouse. Using the MBN approach we are able to automatically identify many of the known downstream targets of the hedgehog pathway such as Gas1 and Gli1, along with a short list of likely targets such as Mig12. Conclusions: The MBN approach shown here can easily be extended to other pathways and data types to yield a more mechanistic framework for learning genetic regulatory models.; Molecular and Cellular Biology; Stem Cell and Regenerative Biology

Input Warping for Bayesian Optimization of Non-Stationary Functions

Snoek, Jasper; Swersky, Kevin; Zemel, Rich; Adams, Ryan Prescott
Fonte: Journal of Machine Learning Research Publicador: Journal of Machine Learning Research
Tipo: Conference Paper
Português
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Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness of Bayesian optimization. Although Gaussian processes provide a flexible prior over functions, there are various classes of functions that remain difficult to model. One of the most frequently occurring of these is the class of non-stationary functions. The optimization of the hyperparameters of machine learning algorithms is a problem domain in which parameters are often manually transformed a priori, for example by optimizing in “log-space”, to mitigate the effects of spatially-varying length scale. We develop a methodology for automatically learning a wide family of bijective transformations or warpings of the input space using the Beta cumulative distribution function. We further extend the warping framework to multi-task Bayesian optimization so that multiple tasks can be warped into a jointly stationary space. On a set of challenging benchmark optimization tasks, we observe that the inclusion of warping greatly improves on the state-of-the-art, producing better results faster and more reliably.; Engineering and Applied Sciences

A scoring function for learning Bayesian networks based on mutual information and conditional independence tests

Campos Ib????ez, Luis Miguel
Fonte: MIT Press Publicador: MIT Press
Tipo: Artigo de Revista Científica
Português
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We propose a new scoring function for learning Bayesian networks from data using score+search algorithms. This is based on the concept of mutual information and exploits some well-known properties of this measure in a novel way. Essentially, a statistical independence test based on the chi-square distribution, associated with the mutual information measure, together with a property of additive decomposition of this measure, are combined in order to measure the degree of interaction between each variable and its parent variables in the network. The result is a non-Bayesian scoring function called MIT (mutual information tests) which belongs to the family of scores based on information theory. The MIT score also represents a penalization of the Kullback-Leibler divergence between the joint probability distributions associated with a candidate network and with the available data set. Detailed results of a complete experimental evaluation of the proposed scoring function and its comparison with the well-known K2, BDeu and BIC/MDL scores are also presented.

Using bayesian networks and parameterized questions in independent study

Descalço, Luís; Carvalho, Paula; Cruz, João Pedro; Oliveira, Paula; Seabra, Dina
Fonte: IATED Publicador: IATED
Tipo: Conferência ou Objeto de Conferência
Português
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The teaching paradigm is changing from a traditional model of teachers as suppliers of knowledge and toward a model of teachers as advisers who carefully observe students, identify their learning needs, and help them in their independent study. In this new paradigm, computers and communication technology can be effective, not only as means for knowledge transmission, but also as tools for automatically providing feedback and diagnosis in the learning process. We present an approach integrating parameterized questions from two computer systems (Megua and PmatE), combined with a Web application (Siacua) implementing a Bayesian user model, using already many hundreds of questions from each of the two systems. Our approach allows the students a certain level of independence and provides some orientation in their independent study, by giving feedback about answers to questions and also about the general progress in the study subject. This progress is shown in the form of progress bars computed by Bayesian networks where nodes represent “concepts” and knowledge evidences. Teachers use Megua for creating and organizing their own database of (parameterized) questions, make them available for students, and for seeing the progress of each student or class in every topic being studied.

Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters

Wang, Ziyu; de Freitas, Nando
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/06/2014 Português
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Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard. While reasonable practical solutions have been advanced, they can often fail to find the best optima. Surprisingly, there is little theoretical analysis of this crucial problem in the literature. To address this, we derive a cumulative regret bound for Bayesian optimisation with Gaussian processes and unknown kernel hyper-parameters in the stochastic setting. The bound, which applies to the expected improvement acquisition function and sub-Gaussian observation noise, provides us with guidelines on how to design hyper-parameter estimation methods. A simple simulation demonstrates the importance of following these guidelines.; Comment: 16 pages, 1 figure

Dynamic Bayesian Multinets

Bilmes, Jeff A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/01/2013 Português
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In this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how information-theoretic criterion functions can be used to induce sparse, discriminative, and class-conditional network structures that yield an optimal approximation to the class posterior probability, and therefore are useful for the classification task. Using a new structure learning heuristic, the resulting models are tested on a medium-vocabulary isolated-word speech recognition task. It is demonstrated that these discriminatively structured dynamic Bayesian multinets, when trained in a maximum likelihood setting using EM, can outperform both HMMs and other dynamic Bayesian networks with a similar number of parameters.; Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000)

BayesPy: Variational Bayesian Inference in Python

Luttinen, Jaakko
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of implementing the variational Bayesian update equations, the user can construct models faster and in a less error-prone way. Simple syntax, flexible model construction and efficient inference make BayesPy suitable for both average and expert Bayesian users. It also supports some advanced methods such as stochastic and collapsed variational inference.; Comment: Submitted to Journal of Machine Learning Research - Machine Learning Open Source Software

Update Rules for Parameter Estimation in Bayesian Networks

Bauer, Eric; Koller, Daphne; Singer, Yoram
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/02/2013 Português
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This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for parameter estimation that encompasses both on-line learning, where the model is continuously adapted to new data cases as they arrive, and the more traditional batch learning, where a pre-accumulated set of samples is used in a one-time model selection process. In the batch case, our framework encompasses both the gradient projection algorithm and the EM algorithm for Bayesian networks. The framework also leads to new on-line and batch parameter update schemes, including a parameterized version of EM. We provide both empirical and theoretical results indicating that parameterized EM allows faster convergence to the maximum likelihood parameters than does standard EM.; Comment: Appears in Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence (UAI1997)

Bayesian Network Structure Learning Using Quantum Annealing

O'Gorman, Bryan; Perdomo-Ortiz, Alejandro; Babbush, Ryan; Aspuru-Guzik, Alan; Smelyanskiy, Vadim
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We introduce a method for the problem of learning the structure of a Bayesian network using the quantum adiabatic algorithm. We do so by introducing an efficient reformulation of a standard posterior-probability scoring function on graphs as a pseudo-Boolean function, which is equivalent to a system of 2-body Ising spins, as well as suitable penalty terms for enforcing the constraints necessary for the reformulation; our proposed method requires $\mathcal O(n^2)$ qubits for $n$ Bayesian network variables. Furthermore, we prove lower bounds on the necessary weighting of these penalty terms. The logical structure resulting from the mapping has the appealing property that it is instance-independent for a given number of Bayesian network variables, as well as being independent of the number of data cases.

Bayesian test of significance for conditional independence: The multinomial model

Andrade, Pablo de Morais; Stern, Julio Michael; Pereira, Carlos Alberto de Bragança
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/06/2013 Português
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Conditional independence tests (CI tests) have received special attention lately in Machine Learning and Computational Intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of Probabilistic Graphical Models (PGM)--which includes Bayesian Networks (BN) models--CI tests are especially important for the task of learning the PGM structure from data. In this paper, we propose the Full Bayesian Significance Test (FBST) for tests of conditional independence for discrete datasets. FBST is a powerful Bayesian test for precise hypothesis, as an alternative to frequentist's significance tests (characterized by the calculation of the \emph{p-value}).; Comment: 24 pages, 33 figures

A Bayesian encourages dropout

Maeda, Shin-ichi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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Dropout is one of the key techniques to prevent the learning from overfitting. It is explained that dropout works as a kind of modified L2 regularization. Here, we shed light on the dropout from Bayesian standpoint. Bayesian interpretation enables us to optimize the dropout rate, which is beneficial for learning of weight parameters and prediction after learning. The experiment result also encourages the optimization of the dropout.

Learning networks determined by the ratio of prior and data

Ueno, Maomi
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/03/2012 Português
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Recent reports have described that the equivalent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymptotic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size determine the penalty of adding arcs in learning Bayesian networks. The number of arcs increases monotonically as the ESS increases; the number of arcs monotonically decreases as the ESS decreases. Furthermore, the marginal likelihood score provides a unified expression of various score metrics by changing prior knowledge.; Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010)

Improving parameter learning of Bayesian nets from incomplete data

Corani, Giorgio; De Campos, Cassio P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/10/2011 Português
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This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood estimate. We argue that choosing the maximum log-likelihood estimate (as well as the maximum penalized log-likelihood and the maximum a posteriori estimate) has severe drawbacks, being affected both by overfitting and model uncertainty. Two ideas are discussed to overcome these issues: a maximum entropy approach and a Bayesian model averaging approach. Both ideas can be easily applied on top of EM, while the entropy idea can be also implemented in a more sophisticated way, through a dedicated non-linear solver. A vast set of experiments shows that these ideas produce significantly better estimates and inferences than the traditional and widely used maximum (penalized) log-likelihood and maximum a posteriori estimates. In particular, if EM is adopted as optimization engine, the model averaging approach is the best performing one; its performance is matched by the entropy approach when implemented using the non-linear solver. The results suggest that the applicability of these ideas is immediate (they are easy to implement and to integrate in currently available inference engines) and that they constitute a better way to learn Bayesian network parameters.

Robust Bayesian reinforcement learning through tight lower bounds

Dimitrakakis, Christos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
37.512798%
In the Bayesian approach to sequential decision making, exact calculation of the (subjective) utility is intractable. This extends to most special cases of interest, such as reinforcement learning problems. While utility bounds are known to exist for this problem, so far none of them were particularly tight. In this paper, we show how to efficiently calculate a lower bound, which corresponds to the utility of a near-optimal memoryless policy for the decision problem, which is generally different from both the Bayes-optimal policy and the policy which is optimal for the expected MDP under the current belief. We then show how these can be applied to obtain robust exploration policies in a Bayesian reinforcement learning setting.; Comment: Corrected version. 12 pages, 3 figures, 1 table

Estimating Continuous Distributions in Bayesian Classifiers

John, George H.; Langley, Pat
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/02/2013 Português
Relevância na Pesquisa
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When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated by a single Gaussian. In this paper we abandon the normality assumption and instead use statistical methods for nonparametric density estimation. For a naive Bayesian classifier, we present experimental results on a variety of natural and artificial domains, comparing two methods of density estimation: assuming normality and modeling each conditional distribution with a single Gaussian; and using nonparametric kernel density estimation. We observe large reductions in error on several natural and artificial data sets, which suggests that kernel estimation is a useful tool for learning Bayesian models.; Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995)

PAC-Bayesian Theorems for Domain Adaptation with Specialization to Linear Classifiers

Germain, Pascal; Habrard, Amaury; Laviolette, François; Morvant, Emilie
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/03/2015 Português
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In this paper, we provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different target distribution. On the one hand, we propose an improvement of the previous approach proposed by Germain et al. (2013), that relies on a novel distribution pseudodistance based on a disagreement averaging, allowing us to derive a new tighter PAC-Bayesian domain adaptation bound for the stochastic Gibbs classifier. We specialize it to linear classifiers, and design a learning algorithm which shows interesting results on a synthetic problem and on a popular sentiment annotation task. On the other hand, we generalize these results to multisource domain adaptation allowing us to take into account different source domains. This study opens the door to tackle domain adaptation tasks by making use of all the PAC-Bayesian tools.; Comment: Under review

Discriminative Bayesian Dictionary Learning for Classification

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/03/2015 Português
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We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.; Comment: 15 pages

ABC Reinforcement Learning

Dimitrakakis, Christos; Tziortziotis, Nikolaos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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This paper introduces a simple, general framework for likelihood-free Bayesian reinforcement learning, through Approximate Bayesian Computation (ABC). The main advantage is that we only require a prior distribution on a class of simulators (generative models). This is useful in domains where an analytical probabilistic model of the underlying process is too complex to formulate, but where detailed simulation models are available. ABC-RL allows the use of any Bayesian reinforcement learning technique, even in this case. In addition, it can be seen as an extension of rollout algorithms to the case where we do not know what the correct model to draw rollouts from is. We experimentally demonstrate the potential of this approach in a comparison with LSPI. Finally, we introduce a theorem showing that ABC is a sound methodology in principle, even when non-sufficient statistics are used.; Comment: Corrected version of paper appearing in ICML 2013

Nonparametric Bayesian Context Learning for Buried Threat Detection

Ratto, Christopher Ralph
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2012 Português
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This dissertation addresses the problem of detecting buried explosive threats (i.e., landmines and improvised explosive devices) with ground-penetrating radar (GPR) and hyperspectral imaging (HSI) across widely-varying environmental conditions. Automated detection of buried objects with GPR and HSI is particularly difficult due to the sensitivity of sensor phenomenology to variations in local environmental conditions. Past approahces have attempted to mitigate the effects of ambient factors by designing statistical detection and classification algorithms to be invariant to such conditions. These methods have generally taken the approach of extracting features that exploit the physics of a particular sensor to provide a low-dimensional representation of the raw data for characterizing targets from non-targets. A statistical classification rule is then usually applied to the features. However, it may be difficult for feature extraction techniques to adapt to the highly nonlinear effects of near-surface environmental conditions on sensor phenomenology, as well as to re-train the classifier for use under new conditions. Furthermore, the search for an invariant set of features ignores that possibility that one approach may yield best performance under one set of terrain conditions (e.g....