20,562 research outputs found
Enabling scalable stochastic gradient-based inference for Gaussian processes by employing the Unbiased LInear System SolvEr (ULISSE)
In applications of Gaussian processes where quantification of uncertainty is
of primary interest, it is necessary to accurately characterize the posterior
distribution over covariance parameters. This paper proposes an adaptation of
the Stochastic Gradient Langevin Dynamics algorithm to draw samples from the
posterior distribution over covariance parameters with negligible bias and
without the need to compute the marginal likelihood. In Gaussian process
regression, this has the enormous advantage that stochastic gradients can be
computed by solving linear systems only. A novel unbiased linear systems solver
based on parallelizable covariance matrix-vector products is developed to
accelerate the unbiased estimation of gradients. The results demonstrate the
possibility to enable scalable and exact (in a Monte Carlo sense)
quantification of uncertainty in Gaussian processes without imposing any
special structure on the covariance or reducing the number of input vectors.Comment: 10 pages - paper accepted at ICML 201
Estimation methods for stochastic volatility models: a survey
Although stochastic volatility (SV) models have an intuitive appeal, their empirical application has been limited mainly due to difficulties involved in their estimation. The main problem is that the likelihood function is hard to evaluate. However, recently, several new estimation methods have been introduced and the literature on SV models has grown substantially. In this article, we review this literature. We describe the main estimators of the parameters and the underlying volatilities focusing on their advantages and limitations both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.Publicad
INLA or MCMC? A Tutorial and Comparative Evaluation for Spatial Prediction in log-Gaussian Cox Processes
We investigate two options for performing Bayesian inference on spatial
log-Gaussian Cox processes assuming a spatially continuous latent field: Markov
chain Monte Carlo (MCMC) and the integrated nested Laplace approximation
(INLA). We first describe the device of approximating a spatially continuous
Gaussian field by a Gaussian Markov random field on a discrete lattice, and
present a simulation study showing that, with careful choice of parameter
values, small neighbourhood sizes can give excellent approximations. We then
introduce the spatial log-Gaussian Cox process and describe MCMC and INLA
methods for spatial prediction within this model class. We report the results
of a simulation study in which we compare MALA and the technique of
approximating the continuous latent field by a discrete one, followed by
approximate Bayesian inference via INLA over a selection of 18 simulated
scenarios. The results question the notion that the latter technique is both
significantly faster and more robust than MCMC in this setting; 100,000
iterations of the MALA algorithm running in 20 minutes on a desktop PC
delivered greater predictive accuracy than the default \verb=INLA= strategy,
which ran in 4 minutes and gave comparative performance to the full Laplace
approximation which ran in 39 minutes.Comment: This replaces the previous version of the report. The new version
includes results from an additional simulation study, and corrects an error
in the implementation of the INLA-based method
Estimation methods for stochastic volatility models: a survey
The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome this problem, being at the same time, empirically feasible. As a consequence, several extensions of the SV models have been proposed and their empirical implementation is increasing. In this paper, we review the main estimators of the parameters and the volatility of univariate SV models proposed in the literature. We describe the main advantages and limitations of each of the methods both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S and P 500 stock price index
Bayesian Inference in Estimation of Distribution Algorithms
Metaheuristics such as Estimation of Distribution Algorithms and the Cross-Entropy method use probabilistic modelling and inference to generate candidate solutions in optimization problems. The model fitting task in this class of algorithms has largely been carried out to date based on maximum likelihood. An alternative approach that is prevalent in statistics and machine learning is to use Bayesian inference. In this paper, we provide a framework for the application of Bayesian inference techniques in probabilistic model-based optimization. Based on this framework, a simple continuous Bayesian Estimation of Distribution Algorithm is described. We evaluate and compare this algorithm experimentally with its maximum likelihood equivalent, UMDAG c
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