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Bayesian Nonparametric Kernel-Learning

Oliva, Junier; Dubey, Avinava; Poczos, Barnabas; Schneider, Jeff; Xing, Eric P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/06/2015 Português
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Kernel methods are ubiquitous tools in machine learning. They have proven to be effective in many domains and tasks. Yet, kernel methods often require the user to select a predefined kernel to build an estimator with. However, there is often little reason for the a priori selection of a kernel. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly effected by the choice of kernel. Furthermore, when directly applying kernel methods, one typically needs to compute a $N \times N$ Gram matrix of pairwise kernel evaluations to work with a dataset of $N$ instances. The computation of this Gram matrix precludes the direct application of kernel methods on large datasets. In this paper we introduce Bayesian nonparmetric kernel (BaNK) learning, a generic, data-driven framework for scalable learning of kernels. We show that this framework can be used for performing both regression and classification tasks and scale to large datasets. Furthermore, we show that BaNK outperforms several other scalable approaches for kernel learning on a variety of real world datasets.

Bayesian Inference in Sparse Gaussian Graphical Models

Orchard, Peter; Agakov, Felix; Storkey, Amos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/09/2013 Português
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One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bayesian inference of sparse structures of Gaussian graphical models (GGMs). One is based on a simple modification of the cutting-edge block Gibbs sampler for sparse GGMs, which results in significant computational gains in high dimensions. The other method is based on a specific construction of the Hamiltonian Monte Carlo sampler, which results in further significant improvements. We compare our fully Bayesian approaches with the popular regularisation-based graphical LASSO, and demonstrate significant advantages of the Bayesian treatment under the same computing costs. We apply the methods to a broad range of simulated data sets, and a real-life financial data set.

Monte Carlo Bayesian Reinforcement Learning

Wang, Yi; Won, Kok Sung; Hsu, David; Lee, Wee Sun
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/06/2012 Português
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Bayesian reinforcement learning (BRL) encodes prior knowledge of the world in a model and represents uncertainty in model parameters by maintaining a probability distribution over them. This paper presents Monte Carlo BRL (MC-BRL), a simple and general approach to BRL. MC-BRL samples a priori a finite set of hypotheses for the model parameter values and forms a discrete partially observable Markov decision process (POMDP) whose state space is a cross product of the state space for the reinforcement learning task and the sampled model parameter space. The POMDP does not require conjugate distributions for belief representation, as earlier works do, and can be solved relatively easily with point-based approximation algorithms. MC-BRL naturally handles both fully and partially observable worlds. Theoretical and experimental results show that the discrete POMDP approximates the underlying BRL task well with guaranteed performance.; Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012)

Smoothness and Structure Learning by Proxy

Yackley, Benjamin; Lane, Terran
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/06/2012 Português
Relevância na Pesquisa
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As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data into account. For instance, Bayesian networks, the model chosen in this paper, have a super-exponentially large search space for a fixed number of variables. One possible method to alleviate this problem is to use a proxy, such as a Gaussian Process regressor, in place of the true scoring function, training it on a selection of sampled networks. We prove here that the use of such a proxy is well-founded, as we can bound the smoothness of a commonly-used scoring function for Bayesian network structure learning. We show here that, compared to an identical search strategy using the network?s exact scores, our proxy-based search is able to get equivalent or better scores on a number of data sets in a fraction of the time.; Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012)

Bayesian Multicategory Support Vector Machines

Zhang, Zhihua; Jordan, Michael I.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/06/2012 Português
Relevância na Pesquisa
37.360273%
We show that the multi-class support vector machine (MSVM) proposed by Lee et. al. (2004), can be viewed as a MAP estimation procedure under an appropriate probabilistic interpretation of the classifier. We also show that this interpretation can be extended to a hierarchical Bayesian architecture and to a fully-Bayesian inference procedure for multi-class classification based on data augmentation. We present empirical results that show that the advantages of the Bayesian formalism are obtained without a loss in classification accuracy.; Comment: Appears in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (UAI2006)

Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithm

Friedman, Nir; Nachman, Iftach; Pe'er, Dana
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/01/2013 Português
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Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem using standard heuristic search techniques. Since the search space is extremely large, such search procedures can spend most of the time examining candidates that are extremely unreasonable. This problem becomes critical when we deal with data sets that are large either in the number of instances, or the number of attributes. In this paper, we introduce an algorithm that achieves faster learning by restricting the search space. This iterative algorithm restricts the parents of each variable to belong to a small subset of candidates. We then search for a network that satisfies these constraints. The learned network is then used for selecting better candidates for the next iteration. We evaluate this algorithm both on synthetic and real-life data. Our results show that it is significantly faster than alternative search procedures without loss of quality in the learned structures.; Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999)

Learning Bayesian Networks with Restricted Causal Interactions

Neil, Julian R.; Wallace, Chris S.; Korb, Kevin B.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/01/2013 Português
Relevância na Pesquisa
37.380051%
A major problem for the learning of Bayesian networks (BNs) is the exponential number of parameters needed for conditional probability tables. Recent research reduces this complexity by modeling local structure in the probability tables. We examine the use of log-linear local models. While log-linear models in this context are not new (Whittaker, 1990; Buntine, 1991; Neal, 1992; Heckerman and Meek, 1997), for structure learning they are generally subsumed under a naive Bayes model. We describe an alternative interpretation, and use a Minimum Message Length (MML) (Wallace, 1987) metric for structure learning of networks exhibiting causal independence, which we term first-order networks (FONs). We also investigate local model selection on a node-by-node basis.; Comment: Appears in Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (UAI1999)

Advances in Learning Bayesian Networks of Bounded Treewidth

Nie, Siqi; Maua, Denis Deratani; de Campos, Cassio Polpo; Ji, Qiang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
37.380051%
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 tables

Bayesian representation learning with oracle constraints

Karaletsos, Theofanis; Belongie, Serge; Rätsch, Gunnar
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
37.380051%
Representation learning systems typically rely on massive amounts of labeled data in order to be trained to high accuracy. Recently, high-dimensional parametric models like neural networks have succeeded in building rich representations using either compressive, reconstructive or supervised criteria. However, the semantic structure inherent in observations is oftentimes lost in the process. Human perception excels at understanding semantics but cannot always be expressed in terms of labels. Thus, \emph{oracles} or \emph{human-in-the-loop systems}, for example crowdsourcing, are often employed to generate similarity constraints using an implicit similarity function encoded in human perception. In this work we propose to combine \emph{generative unsupervised feature learning} with a \emph{probabilistic treatment of oracle information like triplets} in order to transfer implicit privileged oracle knowledge into explicit nonlinear Bayesian latent factor models of the observations. We use a fast variational algorithm to learn the joint model and demonstrate applicability to a well-known image dataset. We show how implicit triplet information can provide rich information to learn representations that outperform previous metric learning approaches as well as generative models without this side-information in a variety of predictive tasks. In addition...

Data mining for censored time-to-event data: A Bayesian network model for predicting cardiovascular risk from electronic health record data

Bandyopadhyay, Sunayan; Wolfson, Julian; Vock, David M.; Vazquez-Benitez, Gabriela; Adomavicius, Gediminas; Elidrisi, Mohamed; Johnson, Paul E.; O'Connor, Patrick J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/04/2014 Português
Relevância na Pesquisa
37.381897%
Models for predicting the risk of cardiovascular events based on individual patient characteristics are important tools for managing patient care. Most current and commonly used risk prediction models have been built from carefully selected epidemiological cohorts. However, the homogeneity and limited size of such cohorts restricts the predictive power and generalizability of these risk models to other populations. Electronic health data (EHD) from large health care systems provide access to data on large, heterogeneous, and contemporaneous patient populations. The unique features and challenges of EHD, including missing risk factor information, non-linear relationships between risk factors and cardiovascular event outcomes, and differing effects from different patient subgroups, demand novel machine learning approaches to risk model development. In this paper, we present a machine learning approach based on Bayesian networks trained on EHD to predict the probability of having a cardiovascular event within five years. In such data, event status may be unknown for some individuals as the event time is right-censored due to disenrollment and incomplete follow-up. Since many traditional data mining methods are not well-suited for such data...

Improved learning of Bayesian networks

Kocka, Tomas; Castelo, Robert
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/01/2013 Português
Relevância na Pesquisa
37.381897%
The search space of Bayesian Network structures is usually defined as Acyclic Directed Graphs (DAGs) and the search is done by local transformations of DAGs. But the space of Bayesian Networks is ordered by DAG Markov model inclusion and it is natural to consider that a good search policy should take this into account. First attempt to do this (Chickering 1996) was using equivalence classes of DAGs instead of DAGs itself. This approach produces better results but it is significantly slower. We present a compromise between these two approaches. It uses DAGs to search the space in such a way that the ordering by inclusion is taken into account. This is achieved by repetitive usage of local moves within the equivalence class of DAGs. We show that this new approach produces better results than the original DAGs approach without substantial change in time complexity. We present empirical results, within the framework of heuristic search and Markov Chain Monte Carlo, provided through the Alarm dataset.; Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI2001)

Bayesian image segmentations by Potts prior and loopy belief propagation

Tanaka, Kazuyuki; Kataoka, Shun; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou-Ting
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
37.381897%
This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in LBP's for Potts models influence our hyperparameter estimation procedures.; Comment: 24 pages, 9 figures

Tree Exploration for Bayesian RL Exploration

Dimitrakakis, Christos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
37.381897%
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time. This is because the resulting planning task takes the form of a dynamic programming problem on a belief tree with an infinite number of states. The second type employs relatively simple algorithm which are shown to suffer small regret within a distribution-free framework. This paper presents a lower bound and a high probability upper bound on the optimal value function for the nodes in the Bayesian belief tree, which are analogous to similar bounds in POMDPs. The bounds are then used to create more efficient strategies for exploring the tree. The resulting algorithms are compared with the distribution-free algorithm UCB1, as well as a simpler baseline algorithm on multi-armed bandit problems.; Comment: 13 pages, 1 figure. Slightly extended and corrected version (notation errors and lower bound calculation) of homonymous paper presented at the conference of Computational Intelligence for Modelling, Control and Automation 2008 (CIMCA'08)

Preference elicitation and inverse reinforcement learning

Rothkopf, Constantin; Dimitrakakis, Christos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
37.380051%
We state the problem of inverse reinforcement learning in terms of preference elicitation, resulting in a principled (Bayesian) statistical formulation. This generalises previous work on Bayesian inverse reinforcement learning and allows us to obtain a posterior distribution on the agent's preferences, policy and optionally, the obtained reward sequence, from observations. We examine the relation of the resulting approach to other statistical methods for inverse reinforcement learning via analysis and experimental results. We show that preferences can be determined accurately, even if the observed agent's policy is sub-optimal with respect to its own preferences. In that case, significantly improved policies with respect to the agent's preferences are obtained, compared to both other methods and to the performance of the demonstrated policy.; Comment: 13 pages, 4 figures; ECML 2011

Convex Point Estimation using Undirected Bayesian Transfer Hierarchies

Elidan, Gal; Packer, Ben; Heitz, Geremy; Koller, Daphne
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/06/2012 Português
Relevância na Pesquisa
37.380051%
When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be difficult and computationally demanding, it is often desirable to use posterior point estimates that facilitate (relatively) efficient prediction. However, the hierarchical Bayes framework does not always lend itself naturally to this maximum aposteriori goal. In this work we propose an undirected reformulation of hierarchical Bayes that relies on priors in the form of similarity measures. We introduce the notion of "degree of transfer" weights on components of these similarity measures, and show how they can be automatically learned within a joint probabilistic framework. Importantly, our reformulation results in a convex objective for many learning problems, thus facilitating optimal posterior point estimation using standard optimization techniques. In addition, we no longer require proper priors, allowing for flexible and straightforward specification of joint distributions over transfer hierarchies. We show that our framework is effective for learning models that are part of transfer hierarchies for two real-life tasks: object shape modeling using Gaussian density estimation and document classification.; Comment: Appears in Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence (UAI2008)

Freeze-Thaw Bayesian Optimization

Swersky, Kevin; Snoek, Jasper; Adams, Ryan Prescott
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/06/2014 Português
Relevância na Pesquisa
37.380051%
In this paper we develop a dynamic form of Bayesian optimization for machine learning models with the goal of rapidly finding good hyperparameter settings. Our method uses the partial information gained during the training of a machine learning model in order to decide whether to pause training and start a new model, or resume the training of a previously-considered model. We specifically tailor our method to machine learning problems by developing a novel positive-definite covariance kernel to capture a variety of training curves. Furthermore, we develop a Gaussian process prior that scales gracefully with additional temporal observations. Finally, we provide an information-theoretic framework to automate the decision process. Experiments on several common machine learning models show that our approach is extremely effective in practice.

Online Learning of Non-Stationary Networks, with Application to Financial Data

Hongo, Yasunori
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Tese de Doutorado
Publicado em //2012 Português
Relevância na Pesquisa
37.380051%

In this paper, we propose a new learning algorithm for non-stationary Dynamic Bayesian Networks is proposed. Although a number of effective learning algorithms for non-stationary DBNs have previously been proposed and applied in Signal Pro- cessing and Computational Biology, those algorithms are based on batch learning algorithms that cannot be applied to online time-series data. Therefore, we propose a learning algorithm based on a Particle Filtering approach so that we can apply that algorithm to online time-series data. To evaluate our algorithm, we apply it to the simulated data set and the real-world financial data set. The result on the simulated data set shows that our algorithm performs accurately makes estimation and detects change. The result applying our algorithm to the real-world financial data set shows several features, which are suggested in previous research that also implies the effectiveness of our algorithm.

; Thesis

Efficient Bayesian Nonparametric Methods for Model-Free Reinforcement Learning in Centralized and Decentralized Sequential Environments

Liu, Miao
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2014 Português
Relevância na Pesquisa
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As a growing number of agents are deployed in complex environments for scientific research and human well-being, there are increasing demands for designing efficient learning algorithms for these agents to improve their control polices. Such policies must account for uncertainties, including those caused by environmental stochasticity, sensor noise and communication restrictions. These challenges exist in missions such as planetary navigation, forest firefighting, and underwater exploration. Ideally, good control policies should allow the agents to deal with all the situations in an environment and enable them to accomplish their mission within the budgeted time and resources. However, a correct model of the environment is not typically available in advance, requiring the policy to be learned from data. Model-free reinforcement learning (RL) is a promising candidate for agents to learn control policies while engaged in complex tasks, because it allows the control policies to be learned directly from a subset of experiences and with time efficiency. Moreover, to ensure persistent performance improvement for RL, it is important that the control policies be concisely represented based on existing knowledge, and have the flexibility to accommodate new experience. Bayesian nonparametric methods (BNPMs) both allow the complexity of models to be adaptive to data...

Machine Learning with Dirichlet and Beta Process Priors: Theory and Applications

Paisley, John William
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação Formato: 14589534 bytes; application/pdf
Publicado em //2010 Português
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Bayesian nonparametric methods are useful for modeling data without having to define the complexity of the entire model a priori, but rather allowing for this complexity to be determined by the data. Two problems considered in this dissertation are the number of components in a mixture model, and the number of factors in a latent factor model, for which the Dirichlet process and the beta process are the two respective Bayesian nonparametric priors selected for handling these issues.

The flexibility of Bayesian nonparametric priors arises from the prior's definition over an infinite dimensional parameter space. Therefore, there are theoretically an infinite number of latent components and an infinite number of latent factors. Nevertheless, draws from each respective prior will produce only a small number of components or factors that appear in a given data set. As mentioned, the number of these components and factors, and their corresponding parameter values, are left for the data to decide.

This dissertation is split between novel practical applications and novel theoretical results for these priors. For the Dirichlet process, we investigate stick-breaking representations for the finite Dirichlet process and their application to novel sampling techniques...

Learning from experience using a decision-theoretic intelligent agent in multi-agent systems

Sahin, Ferat; Bay, John
Fonte: IEEE Publicador: IEEE
Tipo: Proceedings
Português
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This paper proposes a decision-theoretic intelligent agent model to solve a herding problem and studies the learning from experience capabilities of the agent model. The proposed intelligent agent model is designed by combining Bayesian networks (BN) and influence diagrams (ID). The online Bayesian network learning method is proposed to accomplish the learning from experience. Intelligent agent software, IntelliAgent, is written to realize the proposed intelligent agent model and to simulate the agents in a problem domain. The same software is then used to simulate the herding problem with one sheep and one dog. Simulation results show that the proposed intelligent agent is successful in establishing a goal (herding) and learning other agents' behaviors.; Copyright 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.; Mountain Workshop on Soft Computing in Industrial Applications Virginia Tech, Blacksburg, Virginia, June25-27,2001