7 research outputs found
Adaptive Multiple Importance Sampling for Gaussian Processes
In applications of Gaussian processes where quantification of uncertainty is
a strict requirement, it is necessary to accurately characterize the posterior
distribution over Gaussian process covariance parameters. Normally, this is
done by means of standard Markov chain Monte Carlo (MCMC) algorithms. Motivated
by the issues related to the complexity of calculating the marginal likelihood
that can make MCMC algorithms inefficient, this paper develops an alternative
inference framework based on Adaptive Multiple Importance Sampling (AMIS). This
paper studies the application of AMIS in the case of a Gaussian likelihood, and
proposes the Pseudo-Marginal AMIS for non-Gaussian likelihoods, where the
marginal likelihood is unbiasedly estimated. The results suggest that the
proposed framework outperforms MCMC-based inference of covariance parameters in
a wide range of scenarios and remains competitive for moderately large
dimensional parameter spaces.Comment: 27 page
ALGORITHMS FOR CONSTRAINT-BASED LEARNING OF BAYESIAN NETWORK STRUCTURES WITH LARGE NUMBERS OF VARIABLES
Bayesian networks (BNs) are highly practical and successful tools for modeling probabilistic knowledge. They can be constructed by an expert, learned from data, or by a combination of the two. A popular approach to learning the structure of a BN is the constraint-based search (CBS) approach, with the PC algorithm being a prominent example. In recent years, we have been experiencing a data deluge. We have access to more data, big and small, than ever before. The exponential nature of BN algorithms, however, hinders large-scale analysis. Developments in parallel and distributed computing have made the computational power required for large-scale data processing widely available, yielding opportunities for developing parallel and distributed algorithms for BN learning and inference. In this dissertation, (1) I propose two MapReduce versions of the PC algorithm, aimed at solving an increasingly common case: data is not necessarily massive in the number of records, but more and more so in the number of variables. (2) When the number of data records is small, the PC algorithm experiences problems in independence testing. Empirically, I explore a contradiction in the literature on how to resolve the case of having insufficient data when testing the independence of two variables: declare independence or dependence. (3) When BNs learned from data become complex in terms of graph density, they may require more parameters than we can feasibly store. I propose and evaluate five approaches to pruning a BN structure to guarantee that it will be tractable for storage and inference. I follow this up by proposing three approaches to improving the classification accuracy of a BN by modifying its structure
Adaptive importance sampling for estimation in structured domains
Sampling is an important tool for estimating large, complex sums and integrals over highdimensional spaces. For instance, importance sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we want to have a sampling distribution that provides optimal-variance estimators. In this paper, we present methods that improve the sampling distribution by systematically adapting it as we obtain information from the samples. We present a stochastic-gradient-descent method for sequentially updating the sampling distribution based on the direct minimization of the variance. We also present other stochastic-gradient-descent methods based on the minimization of typical notions of distance between the current sampling distribution and approximations of the target, optimal distribution. We finally validate and compare the different methods empirically by applying them to the problem of action evaluation in influence diagrams.
Adaptive Importance Sampling for Estimation in Structured Domains
Sampling is an important tool for estimating large, complex sums and integrals over highdimensional spaces. For instance, importance sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we want to have a sampling distribution that provides optimal-variance estimators. In this paper, we present methods that improve the sampling distribution by systematically adapting it as we obtain information from the samples. We present a stochastic-gradient-descent method for sequentially updating the sampling distribution based on the direct minimization of the variance. We also present other stochastic-gradient-descent methods based on the minimization of typical notions of distance between the current sampling distribution and approximations of the target, optimal distribution. We finally validate and compare the different methods empirically by applying them to the problem of action evaluation in influence diagrams. 1 INTRODUCT..