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The main idea behind Bayesian quadrature (BQ) is to treat the integration task as an inference problem, i.e. to construct posterior measures over integrals $F = \int f(x)\,dx$. The choice of the model allows to encode prior knowledge about the integrand (e.g. smoothness).
In probabilistic models, one often is confronted with high dimensional integrals of positive functions that are concentrated in space. State-of-the-art numerical integration based on Markov-chain Monte Carlo (MCMC) may suffer from sample inefficiency and poor convergence diagnostics. In contrast, a BQ method with a suitably devised prior measure adapts to the shape of the integrand and efficiently selects informative nodes. However, BQ comes at a much higher computational cost than MCMC. My goal is to combine the strengths of MCMC integration and BQ to proceed on the path towards solving the long-standing problem of high-dimensional integration.
The main idea behind Bayesian quadrature (BQ) is to treat the integration task as an inference problem, i.e. to construct posterior measures over integrals $F = \int f(x)\,dx$. The choice of the model allows to encode prior knowledge about the integrand (e.g. smoothness).
In probabilistic models, one often is confronted with high dimensional integrals of positive functions that are concentrated in space. State-of-the-art numerical integration based on Markov-chain Monte Carlo (MCMC) may suffer from sample inefficiency and poor convergence diagnostics. In contrast, a BQ method with a suitably devised prior measure adapts to the shape of the integrand and efficiently selects informative nodes. However, BQ comes at a much higher computational cost than MCMC. My goal is to combine the strengths of MCMC integration and BQ to proceed on the path towards solving the long-standing problem of high-dimensional integration.
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35TH UNCERTAINTY IN ARTIFICIAL INTELLIGENCE CONFERENCE (UAI 2019) (2020): 712-721
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Stockinger G.,Janka H. -Th.,Kresse D., Melson T.,Ertl T.,Gabler M.,Gessner A.,Wongwathanarat A.,Tolstov A.,Leung S. -C., Nomoto K.,Heger A.
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