Robert B. Gramacy

NeurIPS Conference 2022 Conference Paper

Triangulation candidates for Bayesian optimization

• Robert B. Gramacy
• Annie Sauer
• Nathan Wycoff

Bayesian optimization involves "inner optimization" over a new-data acquisition criterion which is non-convex/highly multi-modal, may be non-differentiable, or may otherwise thwart local numerical optimizers. In such cases it is common to replace continuous search with a discrete one over random candidates. Here we propose using candidates based on a Delaunay triangulation of the existing input design. We detail the construction of these "tricands" and demonstrate empirically how they outperform both numerically optimized acquisitions and random candidate-based alternatives, and are well-suited for hybrid schemes, on benchmark synthetic and real simulation experiments.

UAI Conference 2010 Conference Paper

Gaussian Process Structural Equation Models with Latent Variables

• Ricardo Bezerra de Andrade e Silva
• Robert B. Gramacy

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 wellstudied, 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.

ICML Conference 2004 Conference Paper

Parameter space exploration with Gaussian process trees

• Robert B. Gramacy
• Herbert K. H. Lee
• William G. Macready