Open Access
June 2014 Laplace Approximation for Logistic Gaussian Process Density Estimation and Regression
Jaakko Riihimäki, Aki Vehtari
Bayesian Anal. 9(2): 425-448 (June 2014). DOI: 10.1214/14-BA872


Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximate Bayesian inference for LGP density estimation in a grid using Laplace’s method to integrate over the non-Gaussian posterior distribution of latent function values and to determine the covariance function parameters with type-II maximum a posteriori (MAP) estimation. We demonstrate that Laplace’s method with MAP is sufficiently fast for practical interactive visualisation of 1D and 2D densities. Our experiments with simulated and real 1D data sets show that the estimation accuracy is close to a Markov chain Monte Carlo approximation and state-of-the-art hierarchical infinite Gaussian mixture models. We also construct a reduced-rank approximation to speed up the computations for dense 2D grids, and demonstrate density regression with the proposed Laplace approach.


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Jaakko Riihimäki. Aki Vehtari. "Laplace Approximation for Logistic Gaussian Process Density Estimation and Regression." Bayesian Anal. 9 (2) 425 - 448, June 2014.


Published: June 2014
First available in Project Euclid: 26 May 2014

zbMATH: 1327.62248
MathSciNet: MR3217002
Digital Object Identifier: 10.1214/14-BA872

Keywords: approximate inference , Density estimation , density regression , Gaussian process , Laplace’s method , logistic transformation

Rights: Copyright © 2014 International Society for Bayesian Analysis

Vol.9 • No. 2 • June 2014
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