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Tutorial
Mon Dec 07 02:30 AM -- 05:00 AM (PST)
(Track1) There and Back Again: A Tale of Slopes and Expectations
Marc Deisenroth · Cheng Soon Ong
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Integration and differentiation play key roles in machine learning.

We take a tour of some old and new results on methods and algorithms for integration and differentiation, in particular, for calculating expectations and slopes. We review numerical and Monte-Carlo integration for calculating expectations. We discuss the change-of-variables method leading to normalizing flows and discuss inference in time series to get there''. To get`back again'', we review gradients for calculating slopes by the chain rule and automatic differentiation, the basis for backpropagation in neural networks. We discuss backpropagation in three settings: in probabilistic graphical models, through an equality constraint, and with an inequality constraint.

To complete the round-trip, we explore algorithms for calculating gradients of expectations, the basis of methods for variational inference, reinforcement learning, and experimental design.