中科院数学与系统科学研究院

数学研究所

计算机科学研讨班

报告人： Prof.Thomas Ehrhard  (University Paris Diderot, France)

题  目：Why and how to compute derivatives of probabilistic programs?

时  间：2019.10.28（星期一）, 14:00-15:00

地  点：数学院南楼N205室

摘  要：Probabilistic programming is becoming more and more important not only to improve the efficiency of algorithms, but also in Bayesian inference and Machine Learning. More than 10 years ago, we have developed the model of probabilistic coherence spaces where probabilistic programs are interpreted as power series with non-negative coefficients and, more recently, we have extended this interpretation to "continuous data types" such as the real line. Such series can be differentiated although probabilistic coherence spaces are not a model of the differential lambda-calculus. We will explain how these derivatives can be defined in the model, give examples of such derivatives and suggest some possible interpretations and applications.

报告人简历：

Thomas Ehrhard has been a CNRS (the French National Centre for Scientific Research) Senior Researcher in Computer Science at the Institut d’Informatique Fondamentale (Institute for Fondamental Computer Science, IRIF) of University Paris Diderot (Paris 7) and CNRS since 2001. He was the deputy director of IRIF from 2016 to 2018, after being the director of the PPS Laboratory (Proofs, Programs and Systems, Univ Paris Diderot and CNRS) from 2009 to 2016. His research concerns mainly the mathematical interpretation of proofs and programs. His main contributions include:

？  a theory of sequential computations which, contrarily to the more familiar game models, does not specify the order of evaluation (Strong Stability and Hypercoherences)

？  new logical systems with indexed formulas representing partial denotations of programs (Indexed Linear Logic)

？  models of Linear Logic using infinite dimensional vector spaces (K？the Spaces and Finiteness Spaces)

？  extension of the lambda-calculus and of Linear Logic with differentiation (Differential Lambda-Calculus, Differential Linear Logic, Taylor Expansion of lambda-terms etc)

？  generalization of CCS processes from words to trees  (CCS for trees, Branching Process Calculus)

？  semantics of probabilistic programs by linear and ？ analytic functions ？ acting on distributions (Probabilistic Coherence Spaces, Stable Functions on Cones etc).

He has written about 60 papers, mainly on the topics above, and supervised 15 PhD students. He has served in program committees of some of the main international conferences in his research field : LICS, ICALP, FOSSACS etc.