<ul data-eligibleForWebStory="false"><li>This paper discusses the consistency of sparse grid quadrature for integrating high dimensional distributions.</li><li>A transport map is learned to normalize the distribution to a noise distribution on the unit cube using neural ordinary differential equations.</li><li>The generative map is integrated numerically with the quantity of interest using Clenshaw-Curtis sparse grid quadrature.</li><li>The paper proves that all error terms can be controlled in the sense of PAC learning, ensuring that the numerical integral approximates the theoretical value with small error as the data set size grows and the network capacity increases.</li></ul>

Consistency of Learned Sparse Grid Quadrature Rules using NeuralODEs

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