
Bayesian ErrorBars for Belief Net Inference
A Bayesian Belief Network (BN) is a model of a joint distribution over a...
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Reparameterization trick for discrete variables
Lowvariance gradient estimation is crucial for learning directed graphi...
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Efficient Inference in Large Discrete Domains
In this paper we examine the problem of inference in Bayesian Networks w...
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Investigation of Variances in Belief Networks
The belief network is a wellknown graphical structure for representing ...
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The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables
The reparameterization trick enables optimizing large scale stochastic c...
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Bayesian Conditional Transformation Models
Recent developments in statistical regression methodology establish flex...
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Simultaneous MeanVariance Regression
We propose simultaneous meanvariance regression for the linear estimati...
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Improved Mean and Variance Approximations for Belief Net Responses via Network Doubling
A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing conditional distributions. The parameters are viewed as random variables to quantify uncertainty about their values. Belief nets are used to compute responses to queries; i.e., conditional probabilities of interest. A query is a function of the parameters, hence a random variable. Van Allen et al. (2001, 2008) showed how to quantify uncertainty about a query via a delta method approximation of its variance. We develop more accurate approximations for both query mean and variance. The key idea is to extend the query mean approximation to a "doubled network" involving two independent replicates. Our method assumes complete data and can be applied to discrete, continuous, and hybrid networks (provided discrete variables have only discrete parents). We analyze several improvements, and provide empirical studies to demonstrate their effectiveness.
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