Bayesian kernel mixtures for counts
Antonio Canale & David B. Dunson
Presented by Yingjian Wang
Apr. 29, 2011
Outline
• Existed models for counts and their
drawbacks;
• Univariate rounded kernel mixture priors;
• Simulation of the univariate model;
• Multivariate rounded kernel mixture
priors;
• Experiment with the multivariate model;
Modeling of counts
• Mixture of Poissons:
a) Not a nonparametric way;
b) Only accounts for cases where the
variance is greater than the mean;
Modeling of counts (2)
• DP mixture of Poissons/Multinomial kernel:
a) It is non-parametric but, still has the problem of
not suitable for under-disperse cases;
b) If with multinomial kernel, the dimension of the
probability vector is equal to the number of support
points, causes overfitting.
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Modeling of counts (3)
• DP with Poisson base measure:
a) There is no allowance for smooth deviations from
the base;
• Motivation: The continuous densities can be
accurately approximated using Gaussian kernels.
• Idea: Use kernels induced through rounding of
continuous kernels.
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Univariate rounded kernel
discrete :
y ~ p
g ()  h ()
continuous:
y* ~ f
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Univariate rounded kernel (2)
• Existence:
• Consistence: (the mapping g(.) maintains KL
neighborhoods.)
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Examples of rounded kernels
• Rounded Gaussian kernel:
• Other kernels:
log-normal, gamma, Weibull densities.
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Eliciting the thresholds
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A Gibbs sampling algorithm
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Experiment with univariate model
• Two scenarios:
• Two standards:
• Results:
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Extension to multivariate model
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Telecommunication data
• Data from 2050 SIM cards, with multivariate:
yi=[yi1, yi2, yi3, yi4, yi5],
Compare the RMG with generalized additive model (GAM):
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