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dc.contributor.authorCao, Jian
dc.contributor.authorDurante, Daniele
dc.contributor.authorGenton, Marc G.
dc.date.accessioned2020-09-14T12:01:40Z
dc.date.available2020-09-14T12:01:40Z
dc.date.issued2020-09-03
dc.identifier.urihttp://hdl.handle.net/10754/665127
dc.description.abstractPredictive models for binary data are fundamental in various fields, ranging from spatial statistics to machine learning. In such settings, the growing complexity of the phenomena to be analyzed has motivated a variety of flexible specifications that avoid strong parametric assumptions when defining the relationship between the observed predictors and the binary response data. A widely-implemented solution within this class expresses the probability parameter via a probit mapping of a Gaussian process indexed by the predictors. However, unlike for continuous settings with Gaussian responses, there is a lack of closed-form results for predictive distributions in binary models with Gaussian process priors. Markov chain Monte Carlo methods and approximate solutions provide common options to address this issue, but state-of-the-art strategies are either computationally intractable or lead to low-quality approximations in moderate-to-high dimensions. In this article, we aim to cover this gap by deriving closed-form expressions for the predictive probabilities in probit Gaussian processes that rely either on cumulative distribution functions of multivariate Gaussians or on functionals of multivariate truncated normals. To evaluate such quantities we develop novel scalable solutions based on tile-low-rank Monte Carlo methods for computing multivariate Gaussian probabilities and on accurate variational approximations of multivariate truncated normal densities. Closed-form expressions for the marginal likelihood and for the conditional distribution of the Gaussian process given the binary responses are also discussed. As illustrated in simulations and in a real-world environmental application, the proposed methods can scale to dimensions where state-of-the-art solutions are impractical.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2009.01471
dc.rightsArchived with thanks to arXiv
dc.titleScalable computation of predictive probabilities in probit models with Gaussian process priors
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Group
dc.contributor.departmentStatistics Program
dc.eprint.versionPre-print
dc.contributor.institutionDepartment of Decision Sciences and Bocconi Institute for Data Science and Analytics, Bocconi University, Italy.
dc.identifier.arxivid2009.01471
kaust.personCao, Jian
kaust.personGenton, Marc G.
refterms.dateFOA2020-09-14T12:02:32Z


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