902 research outputs found
Cutset Sampling for Bayesian Networks
The paper presents a new sampling methodology for Bayesian networks that
samples only a subset of variables and applies exact inference to the rest.
Cutset sampling is a network structure-exploiting application of the
Rao-Blackwellisation principle to sampling in Bayesian networks. It improves
convergence by exploiting memory-based inference algorithms. It can also be
viewed as an anytime approximation of the exact cutset-conditioning algorithm
developed by Pearl. Cutset sampling can be implemented efficiently when the
sampled variables constitute a loop-cutset of the Bayesian network and, more
generally, when the induced width of the networks graph conditioned on the
observed sampled variables is bounded by a constant w. We demonstrate
empirically the benefit of this scheme on a range of benchmarks
Cross-Fertilizing Strategies for Better EM Mountain Climbing and DA Field Exploration: A Graphical Guide Book
In recent years, a variety of extensions and refinements have been developed
for data augmentation based model fitting routines. These developments aim to
extend the application, improve the speed and/or simplify the implementation of
data augmentation methods, such as the deterministic EM algorithm for mode
finding and stochastic Gibbs sampler and other auxiliary-variable based methods
for posterior sampling. In this overview article we graphically illustrate and
compare a number of these extensions, all of which aim to maintain the
simplicity and computation stability of their predecessors. We particularly
emphasize the usefulness of identifying similarities between the deterministic
and stochastic counterparts as we seek more efficient computational strategies.
We also demonstrate the applicability of data augmentation methods for handling
complex models with highly hierarchical structure, using a high-energy
high-resolution spectral imaging model for data from satellite telescopes, such
as the Chandra X-ray Observatory.Comment: Published in at http://dx.doi.org/10.1214/09-STS309 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Parallel Adaptive Collapsed Gibbs Sampling
Rao-Blackwellisation is a technique that provably improves the performance of Gibbs sampling by summing-out variables from the PGM. However, collapsing variables is computationally expensive, since it changes the PGM structure introducing factors whose size is dependent upon the Markov blanket of the variable. Therefore, collapsing out several variables jointly is typically intractable in arbitrary PGM structures. This thesis proposes an adaptive approach for Rao-Blackwellisation, where additional parallel Markov chains are defined over different collapsed PGM structures. The collapsed variables are chosen based on their convergence diagnostics. Adding chains requires re-burn-in the chain, thus wasting samples. To address this, new chains are initialized from a mean field approximation for the distribution, that improves over time, thus reducing the burn-in period. The experiments on several UAI benchmarks shows that this approach is more accurate than state-of-the-art inference systems such as Merlin which have previously won the UAI inference challenge
Bayesian nonparametric panel Markov-switching GARCH models
This article proposes Bayesian nonparametric inference for panel Markov-switching GARCH models. The model incorporates series-specific hidden Markov chain processes that drive the GARCH parameters. To cope with the high-dimensionality of the parameter space, the article assumes soft parameter pooling through a hierarchical prior distribution and introduces cross sectional clustering through a Bayesian nonparametric prior distribution. An MCMC posterior approximation algorithm is developed and its efficiency is studied in simulations under alternative settings. An empirical application to financial returns data in the United States is offered with a portfolio performance exercise based on forecasts. A comparison shows that the Bayesian nonparametric panel Markov-switching GARCH model provides good forecasting performances and economic gains in optimal asset allocation
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