Gaussian Process Networks

Abstract

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the {em marginal likelihood/} of the data given a candidate structure. This term can be computed in closed-form for standard parametric families (e.g., Gaussians), and can be approximated, at some computational cost, for some semi-parametric families (e.g., mixtures of Gaussians). We present a new family of continuous variable probabilistic networks that are based on {em Gaussian Process/} priors. These priors are semi-parametric in nature and can learn almost arbitrary noisy functional relations. Using these priors, we can directly compute marginal likelihoods for structure learning. The resulting method can discover a wide range of functional dependencies in multivariate data. We develop the Bayesian score of Gaussian Process Networks and describe how to learn them from data. We present empirical results on artificial data as well as on real-life domains with non-linear dependencies.

Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000)

References in corpus (4)

• Being Bayesian about Network Structure
• Learning Bayesian Networks: A Unification for Discrete and Gaussian Domains
• Learning Mixtures of DAG Models
• Structure and Parameter Learning for Causal Independence and Causal Interaction Models

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• Sparse Linear Identifiable Multivariate Modeling
• Testing whether linear equations are causal: A free probability theory approach
• The Gaussian Process Autoregressive Regression Model (GPAR)
• Boosting Synthetic Data Generation with Effective Nonlinear Causal Discovery
• On causally asymmetric versions of Occam's Razor and their relation to thermodynamics
• Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks
• The Effect of Noise Level on Causal Identification with Additive Noise Models
• Causal Identification with Additive Noise Models: Quantifying the Effect of Noise
• Gaussian Process Structural Equation Models with Latent Variables