ALBERT — All Library Books, journals and Electronic Records Telegrafenberg

1

Electronic Resource

Efficient Approximations for the Marginal Likelihood of Bayesian Networks with Hidden Variables (1997)

Maxwell Chickering, David ; Heckerman, David

Springer

Machine learning 29 (1997), S. 181-212

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ISSN: 0885-6125

Keywords: Bayesian model averaging ; model selection ; multinomial mixtures ; clustering ; unsupervised learning ; Laplace approximation

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Abstract We discuss Bayesian methods for model averaging and model selection among Bayesian-network models with hidden variables. In particular, we examine large-sample approximations for the marginal likelihood of naive-Bayes models in which the root node is hidden. Such models are useful for clustering or unsupervised learning. We consider a Laplace approximation and the less accurate but more computationally efficient approximation known as the Bayesian Information Criterion (BIC), which is equivalent to Rissanen's (1987) Minimum Description Length (MDL). Also, we consider approximations that ignore some off-diagonal elements of the observed information matrix and an approximation proposed by Cheeseman and Stutz (1995). We evaluate the accuracy of these approximations using a Monte-Carlo gold standard. In experiments with artificial and real examples, we find that (1) none of the approximations are accurate when used for model averaging, (2) all of the approximations, with the exception of BIC/MDL, are accurate for model selection, (3) among the accurate approximations, the Cheeseman–Stutz and Diagonal approximations are the most computationally efficient, (4) all of the approximations, with the exception of BIC/MDL, can be sensitive to the prior distribution over model parameters, and (5) the Cheeseman–Stutz approximation can be more accurate than the other approximations, including the Laplace approximation, in situations where the parameters in the maximum a posteriori configuration are near a boundary.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1007469629108

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2

Electronic Resource

Learning Bayesian Networks: The Combination of Knowledge and Statistical Data (1995)

Heckerman, David ; Geiger, Dan ; Chickering, David M.

Springer

Machine learning 20 (1995), S. 197-243

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ISSN: 0885-6125

Keywords: Bayesian networks ; learning ; Dirichlet ; likelihood equivalence ; maximum branching ; heuristic search

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Abstract We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption of likelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—a prior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at most k = 1 parent. For the general case (k 〉 1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1022623210503

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3

Electronic Resource

Learning Bayesian networks: The combination of knowledge and statistical data (1995)

Heckerman, David ; Geiger, Dan ; Chickering, David M.

Springer

Machine learning 20 (1995), S. 197-243

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ISSN: 0885-6125

Keywords: Bayesian networks ; learning ; Dirichlet ; likelihood equivalence ; maximum branching ; heuristic search

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Abstract We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption oflikelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—aprior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at mostk=1 parent. For the general case (k〉1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00994016

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4

Electronic Resource

Bayesian Networks for Data Mining (1997)

Heckerman, David

Springer

Data mining and knowledge discovery 1 (1997), S. 79-119

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ISSN: 1573-756X

Keywords: Bayesian networks ; Bayesian statistics ; learning ; missing data ; classification ; regression ; clustering ; causal discovery

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science

Notes: Abstract A Bayesian network is a graphical model that encodesprobabilistic relationships among variables of interest. When used inconjunction with statistical techniques, the graphical model hasseveral advantages for data modeling. One, because the model encodesdependencies among all variables, it readily handles situations wheresome data entries are missing. Two, a Bayesian network can be used tolearn causal relationships, and hence can be used to gain understanding about a problem domain and to predict the consequencesof intervention. Three, because the model has both a causal andprobabilistic semantics, it is an ideal representation for combiningprior knowledge (which often comes in causal form) and data. Four,Bayesian statistical methods in conjunction with Bayesian networksoffer an efficient and principled approach for avoiding theoverfitting of data. In this paper, we discuss methods for constructing Bayesian networks from prior knowledge and summarizeBayesian statistical methods for using data to improve these models.With regard to the latter task, we describe methods for learning boththe parameters and structure of a Bayesian network, includingtechniques for learning with incomplete data. In addition, we relateBayesian-network methods for learning to techniques for supervised andunsupervised learning. We illustrate the graphical-modeling approachusing a real-world case study.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1009730122752

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5

Electronic Resource

A comparison of scientific and engineering criteria for Bayesian model selection (2000)

Chickering, David Maxwell ; Heckerman, David

Springer

Statistics and computing 10 (2000), S. 55-62

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ISSN: 1573-1375

Keywords: model selection ; model averaging ; Bayesian selection criteria

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract Given a set of possible models for variables X and a set of possible parameters for each model, the Bayesian “estimate” of the probability distribution for X given observed data is obtained by averaging over the possible models and their parameters. An often-used approximation for this estimate is obtained by selecting a single model and averaging over its parameters. The approximation is useful because it is computationally efficient, and because it provides a model that facilitates understanding of the domain. A common criterion for model selection is the posterior probability of the model. Another criterion for model selection, proposed by San Martini and Spezzafari (1984), is the predictive performance of a model for the next observation to be seen. From the standpoint of domain understanding, both criteria are useful, because one identifies the model that is most likely, whereas the other identifies the model that is the best predictor of the next observation. To highlight the difference, we refer to the posterior-probability and alternative criteria as the scientific criterion (SC) and engineering criterion (EC), respectively. When we are interested in predicting the next observation, the model-averaged estimate is at least as good as that produced by EC, which itself is at least as good as the estimate produced by SC. We show experimentally that, for Bayesian-network models containing discrete variables only, the predictive performance of the model average can be significantly better than those of single models selected by either criterion, and that differences between models selected by the two criterion can be substantial.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008936501289

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6

Electronic Resource

Pressure release superleak sound modes in He II (1980)

Heckerman, David ; Rosenbaum, Ralph ; Putterman, Seth ; [et al.]

Springer

Journal of low temperature physics 38 (1980), S. 629-640

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ISSN: 1573-7357

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: The sound modes of He II in a waveguide partially packed with superleak are investigated for the case of a free surface within the waveguide. In the limit of zero vapor density, two propagating modes are found: one a gravity wave whose velocity depends on the superfluid fraction, and the other a temperature wave which is analogous to adiabatic U-tube osculations. With finite vapor the U-tube mode in pure 4He mixes strongly with the vapor sound; however, in 3He-4He mixtures it is uncoupled from the vapor and is observable. Experimental results are in qualitative agreement with the theory.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00115493

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7

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Linear mixed model for heritability estimation that explicitly addresses environmental variation (2016)

Heckerman, David ; Gurdasani, Deepti ; Kadie, Carl ; [et al.]

National Academy of Sciences

In: PNAS - Proceedings of the National Academy of Sciences of the United States of America. 2016; 113(27): 7377-7382. Published 2016 Jul 05. doi: 10.1073/pnas.1510497113.

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Publication Date: 2016-07-05

Description: The linear mixed model (LMM) is now routinely used to estimate heritability. Unfortunately, as we demonstrate, LMM estimates of heritability can be inflated when using a standard model. To help reduce this inflation, we used a more general LMM with two random effects—one based on genomic variants and one based on easily measured spatial location as a proxy for environmental effects. We investigated this approach with simulated data and with data from a Uganda cohort of 4,778 individuals for 34 phenotypes including anthropometric indices, blood factors, glycemic control, blood pressure, lipid tests, and liver function tests. For the genomic random effect, we used identity-by-descent estimates from accurately phased genome-wide data. For the environmental random effect, we constructed a covariance matrix based on a Gaussian radial basis function. Across the simulated and Ugandan data, narrow-sense heritability estimates were lower using the more general model. Thus, our approach addresses, in part, the issue of “missing heritability” in the sense that much of the heritability previously thought to be missing was fictional. Software is available at https://github.com/MicrosoftGenomics/FaST-LMM.

Print ISSN: 0027-8424

Electronic ISSN: 1091-6490

Topics: Biology , Medicine , Natural Sciences in General