Introduction to Quasi-Monte Carlo Sampling - Part 4

Speaker: Art Owen (Stanford University)

Type: Group Seminar

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Lecture 4 will return to the functional ANOVA and study measures of variable importance. The most important quantities there are Sobol' indices and the closely related Shapley effects, studied in joint work with Clementine Prieur. Estimating these can reveal when RQMC will work well, and in a somewhat circular fashion, RQMC is a very good way to estimate Sobol' indices. Some joint work with Masayoshi Mase and Benjamin Seiler finds a way to quantify variable importance in black box predictions, using the anchored decomposition, an alternative to the functional ANOVA. In joint work with Christopher Hoyt, Sobol' indices show that some deep neural networks used for classifying digits have a low mean dimension property despite having 784 inputs.