20 research outputs found
Slice sampling covariance hyperparameters of latent Gaussian models
The Gaussian process (GP) is a popular way to specify dependencies between
random variables in a probabilistic model. In the Bayesian framework the
covariance structure can be specified using unknown hyperparameters.
Integrating over these hyperparameters considers different possible
explanations for the data when making predictions. This integration is often
performed using Markov chain Monte Carlo (MCMC) sampling. However, with
non-Gaussian observations standard hyperparameter sampling approaches require
careful tuning and may converge slowly. In this paper we present a slice
sampling approach that requires little tuning while mixing well in both strong-
and weak-data regimes.Comment: 9 pages, 4 figures, 4 algorithms. Minor corrections to previous
version. This version to appear in Advances in Neural Information Processing
Systems (NIPS) 23, 201
Elliptical slice sampling
Many probabilistic models introduce strong dependencies between variables
using a latent multivariate Gaussian distribution or a Gaussian process. We
present a new Markov chain Monte Carlo algorithm for performing inference in
models with multivariate Gaussian priors. Its key properties are: 1) it has
simple, generic code applicable to many models, 2) it has no free parameters,
3) it works well for a variety of Gaussian process based models. These
properties make our method ideal for use while model building, removing the
need to spend time deriving and tuning updates for more complex algorithms.Comment: 8 pages, 6 figures, appearing in AISTATS 2010 (JMLR: W&CP volume 6).
Differences from first submission: some minor edits in response to feedback
Gaussian Process Structural Equation Models with Latent Variables
In a variety of disciplines such as social sciences, psychology, medicine and
economics, the recorded data are considered to be noisy measurements of latent
variables connected by some causal structure. This corresponds to a family of
graphical models known as the structural equation model with latent variables.
While linear non-Gaussian variants have been well-studied, inference in
nonparametric structural equation models is still underdeveloped. We introduce
a sparse Gaussian process parameterization that defines a non-linear structure
connecting latent variables, unlike common formulations of Gaussian process
latent variable models. The sparse parameterization is given a full Bayesian
treatment without compromising Markov chain Monte Carlo efficiency. We compare
the stability of the sampling procedure and the predictive ability of the model
against the current practice.Comment: 12 pages, 6 figure
A New Monte Carlo Based Algorithm for the Gaussian Process Classification Problem
Gaussian process is a very promising novel technology that has been applied
to both the regression problem and the classification problem. While for the
regression problem it yields simple exact solutions, this is not the case for
the classification problem, because we encounter intractable integrals. In this
paper we develop a new derivation that transforms the problem into that of
evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we
develop a new Monte Carlo procedure that evaluates these integrals. It is based
on some aspects of bootstrap sampling and acceptancerejection. The proposed
approach has beneficial properties compared to the existing Markov Chain Monte
Carlo approach, such as simplicity, reliability, and speed