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Exploiting parameter domain knowledge for learning in Bayesian networks
 Carnegie Mellon University
, 2005
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implied, of any sponsoring institution, the U.S. government or any other entity.
Dependent Dirichlet priors and optimal linear estimators for belief net parameters
, 2004
"... A Bayesian belief network is a model of a joint distribution over a finite set of variables, with a DAG structure representing immediate dependencies among the variables. For each node, a table of parameters (CPtable) represents local conditional probabilities, with rows indexed by conditioning even ..."
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Cited by 3 (0 self)
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A Bayesian belief network is a model of a joint distribution over a finite set of variables, with a DAG structure representing immediate dependencies among the variables. For each node, a table of parameters (CPtable) represents local conditional probabilities, with rows indexed by conditioning events (assignments to parents). CPtable rows are usually modeled as independent random vectors, each assigned a Dirichlet prior distribution. The assumption that rows are independent permits a relatively simple analysis but may not reflect actual prior opinion about the parameters. Rows representing similar conditioning events often have similar conditional probabilities. This paper introduces a more flexible family of “dependent Dirichlet ” prior distributions, where rows are not necessarily independent. Simple methods are developed to approximate the Bayes estimators of CPtable parameters with optimal linear estimators; i.e., linear combinations of sample proportions and prior means. This approach yields more efficient estimators by sharing information among rows. Improvements in efficiency can be substantial when a CPtable has many rows and samples sizes are small. 1
Computational aspects of Bayesian partition models
 In International Conference on Machine Learning (ICML 2005
, 2005
"... The conditional distribution of a discrete variable y, given another discrete variable x, is often specified by assigning one multinomial distribution to each state of x. The cost of this rich parametrization is the loss of statistical power in cases where the data actually fits a model with much fe ..."
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Cited by 3 (2 self)
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The conditional distribution of a discrete variable y, given another discrete variable x, is often specified by assigning one multinomial distribution to each state of x. The cost of this rich parametrization is the loss of statistical power in cases where the data actually fits a model with much fewer parameters. In this paper, we consider a model that partitions the state space of x into disjoint sets, and assigns a single Dirichletmultinomial to each set. We treat the partition as an unknown variable which is to be integrated away when the interest is in a coarser level task, e.g., variable selection or classification. Based on two different computational approaches, we present two exact algorithms for integration over partitions. Respective complexity bounds are derived in terms of detailed problem characteristics, including the size of the data and the size of the state space of x. Experiments on synthetic data demonstrate the applicability of the algorithms. 1.
Application of Bayesian Partition Models in Warranty Data Analysis
"... Automotive companies are forced to continuously extend and improve their product lineup. However, increasing diversity, higher design complexity, and shorter development cycles can produce new and unforeseen quality issues. Warranty data analysis helps quality engineers in their task of identifying ..."
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Automotive companies are forced to continuously extend and improve their product lineup. However, increasing diversity, higher design complexity, and shorter development cycles can produce new and unforeseen quality issues. Warranty data analysis helps quality engineers in their task of identifying the root cause of manufacturing or design related problems and in planning and implementing remedial actions. In this paper we show how Bayesian partition models can be used to support root cause investigations by applying Bayesian model comparison. We review product partition models, exemplify how partitions can be ranked, and illustrate their expressive power compared to Bayesian networks. Based on this, we outline a data analysis approach that considers dependencies, in particular taxonomic and partonomic relationships, among influencing variables and identifies the most likely semantically meaningful partitions that are close to the concept that actually caused a quality issue. The approach can be integrated seamlessly with interactive decision trees which have been successfully applied in our domain. An evaluation on test data and realworld case studies illustrate how the approach can be used by engineers to investigate causeeffect relationships and show that its application is not limited to the automotive domain. 1
Siemens
"... Building accurate models from a small amount of available training data can sometimes prove to be a great challenge. Expert domain knowledge can often be used to alleviate this burden. Parameter Sharing is one such important form of domain knowledge. Graphical models like HMMs, DBNs and Module Netwo ..."
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Building accurate models from a small amount of available training data can sometimes prove to be a great challenge. Expert domain knowledge can often be used to alleviate this burden. Parameter Sharing is one such important form of domain knowledge. Graphical models like HMMs, DBNs and Module Networks use different forms of Parameter Sharing to reduce the variance in the parameter estimates. The goal of this paper is to present a theoretical approach for learning in presence of several other types of Parameter Related Domain Knowledge that go beyond the ones in the above models. First, we introduce a General Parameter Sharing Framework that describes the models just mentioned, but allows for much finer grained parameter sharing assumptions. In this framework, we present sound procedures for parameter learning from both a Frequentist and a Bayesian point of view, from both complete and incomplete data, in the case where a domain expert specifies in advance the structure of the graphical model, and the subsets of parameters to be shared. Second, we describe a hierarchical extension of this framework based on Parameter Sharing Trees. Finally we present algorithms for using domain knowledge that specifies that certain groups of parameters share certain properties. In particular, we consider two kinds of constraints: first kind states certain groups of parameters share the same aggregate probability mass and second kind states the ratio of the parameters is preserved (shared) in several groups. As an example, we derive a novel form of parameter sharing for Bayesian Multinetworks. 1
Exploiting Parameter Related Domain Knowledge for Learning in Graphical Models Abstract
"... Building accurate models from a small amount of available training data can sometimes prove to be a great challenge. Expert domain knowledge can often be used to alleviate this burden. Parameter Sharing is one such important form of domain knowledge. Graphical models like HMMs, DBNs and Module Netwo ..."
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Building accurate models from a small amount of available training data can sometimes prove to be a great challenge. Expert domain knowledge can often be used to alleviate this burden. Parameter Sharing is one such important form of domain knowledge. Graphical models like HMMs, DBNs and Module Networks use different forms of Parameter Sharing to reduce the variance in the parameter estimates. The goal of this paper is to present a theoretical approach for learning in presence of several other types of Parameter Related Domain Knowledge that go beyond the ones in the above models. First, we introduce a General Parameter Sharing Framework that describes the models just mentioned, but allows for much finer grained parameter sharing assumptions. In this framework, we present sound procedures for parameter learning from both a Frequentist and a Bayesian point of view, from both complete and incomplete data, in the case where a domain expert specifies in advance the structure of the graphical model, and the subsets of parameters to be shared. Second, we describe a hierarchical extension of this framework based on Parameter Sharing Trees. Finally we present algorithms for using domain knowledge that specifies that certain groups of parameters share certain properties. In particular, we consider two kinds of constraints: first kind states certain groups of parameters share the same aggregate probability mass and second kind states the ratio of the parameters is preserved (shared) in several groups. As an example, we derive a novel form of parameter sharing for Bayesian Multinetworks. 1