Robustly parameterised higher-order probabilistic models

Fredrik Dahlqvist (1) , Vincent Danos (2) , Ilias Garnier (3)

1 UCL-CS - Department of Computer science [University College of London]
2 ENS-PSL - École normale supérieure - Paris
3 School of Informatics [Edimbourg]

We present a method for constructing robustly parameterised families of higher-order probabil-istic models. Parameter spaces and models are represented by certain classes of functors in the category of Polish spaces. Maps from parameter spaces to models (parameterisations) are continuous and natural transformations between such functors. Naturality ensures that parameterised models are invariant by change of granularity – ie that parameterisations are intrinsic. Continuity ensures that models are robust with respect to their parameterisation. Our method allows one to build models from a set of basic functors among which the Giry probabilistic functor, spaces of cadlag trajectories (in continuous and discrete time), multisets and compact powersets. These functors can be combined by guarded composition, product and coproduct. Parameter spaces range over the polynomial closure of Giry-like functors. Thus we obtain a class of robust para-meterised models which includes the Dirichlet process, point processes and other classical objects of probability theory such as the de Finetti theorem. By extending techniques developed in prior work, we show how to reduce the questions of existence, uniqueness, naturality, and continuity of a parameterised model to combinatorial questions only involving finite spaces. 1998 ACM Subject Classification Semantics of programming languages

Mots clés: Category theory; Probability theory; Stochastic processes and Statistics

Domaines: Informatique [cs]; Mathématiques [math]

Fredrik Dahlqvist, Vincent Danos, Ilias Garnier. Robustly parameterised higher-order probabilistic models. 27th International Conference on Concurrency Theory, 2016, Québec City, Canada. ⟨10.4230/LIPIcs.CONCUR.2016.23⟩. ⟨hal-01429651⟩