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14
Dependency networks for inference, collaborative filtering, and data visualization
 Journal of Machine Learning Research
"... We describe a graphical model for probabilistic relationshipsan alternative tothe Bayesian networkcalled a dependency network. The graph of a dependency network, unlike aBayesian network, is potentially cyclic. The probability component of a dependency network, like aBayesian network, is a set of ..."
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Cited by 159 (10 self)
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We describe a graphical model for probabilistic relationshipsan alternative tothe Bayesian networkcalled a dependency network. The graph of a dependency network, unlike aBayesian network, is potentially cyclic. The probability component of a dependency network, like aBayesian network, is a set of conditional distributions, one for each nodegiven its parents. We identify several basic properties of this representation and describe a computationally e cient procedure for learning the graph and probability components from data. We describe the application of this representation to probabilistic inference, collaborative ltering (the task of predicting preferences), and the visualization of acausal predictive relationships.
A Bayesian Approach to Causal Discovery
, 1997
"... We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraintbased approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that t ..."
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Cited by 79 (1 self)
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We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraintbased approach. Both approaches rely on the Causal Markov assumption, but the two differ significantly in theory and practice. An important difference between the approaches is that the constraintbased approach uses categorical information about conditionalindependence constraints in the domain, whereas the Bayesian approach weighs the degree to which such constraints hold. As a result, the Bayesian approach has three distinct advantages over its constraintbased counterpart. One, conclusions derived from the Bayesian approach are not susceptible to incorrect categorical decisions about independence facts that can occur with data sets of finite size. Two, using the Bayesian approach, finer distinctions among model structuresboth quantitative and qualitativecan be made. Three, information from several models can be combined to make better inferences and to better ...
On the Dirichlet Prior and Bayesian Regularization
 In Advances in Neural Information Processing Systems 15
, 2002
"... A common objective in learning a model from data is to recover its network structure, while the model parameters are of minor interest. For example, we may wish to recover regulatory networks from highthroughput data sources. In this paper we examine how Bayesian regularization using a Dirichle ..."
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Cited by 22 (2 self)
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A common objective in learning a model from data is to recover its network structure, while the model parameters are of minor interest. For example, we may wish to recover regulatory networks from highthroughput data sources. In this paper we examine how Bayesian regularization using a Dirichlet prior over the model parameters affects the learned model structure in a domain with discrete variables. Surprisingly, a weak prior in the sense of smaller equivalent sample size leads to a strong regularization of the model structure (sparse graph) given a sufficiently large data set. In particular, the empty graph is obtained in the limit of a vanishing strength of prior belief. This is diametrically opposite to what one may expect in this limit, namely the complete graph from an (unregularized) maximum likelihood estimate. Since the prior affects the parameters as expected, the prior strength balances a "tradeoff" between regularizing the parameters or the structure of the model. We demonstrate the benefits of optimizing this tradeoff in the sense of predictive accuracy.
Transferring Prior Information Between Models Using Imaginary Data
, 2001
"... . Bayesian modeling is limited by our ability to formulate prior distributions that adequately represent our actual prior beliefs  a task that is especially difficult for realistic models with many interacting parameters. I show here how a prior distribution formulated for a simpler, more easily ..."
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Cited by 6 (0 self)
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. Bayesian modeling is limited by our ability to formulate prior distributions that adequately represent our actual prior beliefs  a task that is especially difficult for realistic models with many interacting parameters. I show here how a prior distribution formulated for a simpler, more easily understood model can be used to modify the prior distribution of a more complex model. This is done by generating imaginary data from the simpler "donor" model, which is conditioned on in the more complex "recipient" model, effectively transferring the donor model's wellspecified prior information to the recipient model. Such prior information transfers are also useful when comparing two complex models for the same data. Bayesian model comparison based on the Bayes factor is very sensitive to the prior distributions for each model's parameters, with the result that the wrong model may be favoured simply because the prior for the right model was not carefully formulated. This problem can be alleviated by modifying each model's prior to potentially incorporate prior information transferred from the other model. I discuss how these techniques can be implemented by simple Monte Carlo and by Markov chain Monte Carlo with annealed importance sampling. Demonstrations on models for twoway contingency tables and on graphical models for categorical data show that prior information transfer can indeed overcome deficiencies in prior specification for complex models.
David Heckerman Microsoft Research Valencia 7 June 1, 2002
, 1999
"... Introduction to graphical models Introduction to graphical models ## Applications without data: Expert systems Applications without data: Expert systems Learning from data Learning from data ## Applications of learning Applications of learning Influence diagrams: Graphical models for Influence ..."
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Introduction to graphical models Introduction to graphical models ## Applications without data: Expert systems Applications without data: Expert systems Learning from data Learning from data ## Applications of learning Applications of learning Influence diagrams: Graphical models for Influence diagrams: Graphical models for decision making and causal reasoning decision making and causal reasoning Undirected Graph (UG; MRF; Markov Network) Undirected Graph (UG; MRF; Markov Network) Directed acyclic graph (DAG; Bayesian Network) Directed acyclic graph (DAG; Bayesian Network) Two popular classes of graphical models Two popular classes of graphical models X 1 X 2 X 3 X 1 X 2 X 3 Other types of graphical models Other types of graphical models X Y Z W Chain graphs: Directed cyclic graphs: Z Y ## Domain: X = (X Domain: X = (X 11 ,..., ,...,X X nn ) ) Graphical model = structure + collection of local Graphical model = structure + collection of local distributions distributions Stru
in Mathematics: A Regional Comparison Kenneth E. Hinson
"... Research on the comparison of educational aspirations among Black and White students has produced conflicting results. Some studies at the national level have shown that the level of educational aspirations for college between these two groups is similar, while other studies at the state, regional, ..."
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Research on the comparison of educational aspirations among Black and White students has produced conflicting results. Some studies at the national level have shown that the level of educational aspirations for college between these two groups is similar, while other studies at the state, regional, or local level have shown differences. The National Education Longitudinal Study (NELS: 88) database and its 1990 and 1992 followups were used to answer questions and test hypotheses about these differences. The NELS: 88 database is comprised of data initially collected on almost 25,000 eighth graders and over 22,000 parents together representing more 1,000 public and private schools. The study sample was comprised of approximately 1,500 Black and over 9,500 White high school seniors who were part of the tenth to twelfth grade cohort, attended public school, and remained in the same region between tenth and twelfth grade. Data were examined to determine if there were regional influences on the relationship between students' educational aspirations and their achievement in mathematics. Educational aspiration did not explain different amounts of variance in mathematics achievement across the four U.S. census regions. Region, however, was related to differences in White students' aspiration but indicated no differences for Blacks. Sex and mathematicscurriculum were related to differences in aspirations within race for both Black and White students. For both races and regardless of region, a greater proportion of females aspired to attend 4year college than males did. Students with aspirations, for 4year college or more, tended to score higher on mathematics achievement tests than those students with aspirations for less than 4year college. Whether students' tenthgrade a...
EXAMINING THE INCLINATION OF STUDENTS TO APPLY TO A POSTSECONDARY INSTITUTION IN THEIR SENIOR YEAR OF HIGH SCHOOL By
, 2008
"... To my wonderful husband, Tony, for his undying love and support ..."
Ranking by Dependenceâ€”A Fair Criteria
"... Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and informationtheoretic approaches, we first show that the pvalue and the mutual information can fail even in simplistic situations. We then propose ..."
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Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and informationtheoretic approaches, we first show that the pvalue and the mutual information can fail even in simplistic situations. We then propose two conditions for regularizing an estimator of dependence, which leads to a simple yet effective new measure. We discuss its advantages and compare it to wellestablished modelselection criteria. Apart from that, we derive a simple constraint for regularizing parameter estimates in a graphical model. This results in an analytical approximation for the optimal value of the equivalent sample size, which agrees very well with the more involved Bayesian approach in our experiments. 1
FirstGeneration Undergraduate Students and the Impacts of the First Year of College: Some Additional Evidence
"... Firstgeneration students are making significant gains towards access in higher education with enrollment numbers increasing over the past decade (Strayhorn, 2006). Yet the literature examining firstgeneration students has primarily focused on three distinct outcome measures: 1) college choice deci ..."
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Firstgeneration students are making significant gains towards access in higher education with enrollment numbers increasing over the past decade (Strayhorn, 2006). Yet the literature examining firstgeneration students has primarily focused on three distinct outcome measures: 1) college choice decisions and aspirations (e.g., Bui, 2002, 2005; Ceja, 2006; Gibbons & Shoffner,