2015/01/22 by Maurizio Filippone, Filippone, Maurizio, Raphael Engler +1 · 1 citation
Computer Science · Decision Sciences · Engineering · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Computation (stat.CO) #Control Systems and Identification #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #stat.CO #stat.ME #stat.ML
paper · pdf · doi:10.48550/arxiv.1501.05427
10 pages - paper accepted at ICML 2015
openalex publication_date 2015/01/22 · arxiv created 2015/09/03 · arxiv updated 2015/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.