Probabilistic properties of deterministic systems

Deterministic and probabilistic discrepancies

In this paper, we compare some deterministic and probabilistic techniques in the study of upper bounds in problems related to certain mean square discrepancie with respect to balls in the d-dimensional unit torus, and show that the quality of these techniques depends in an intricate way on the dimension d under consideration.

Probabilistic Deterministic Infinite Automata

We propose a novel Bayesian nonparametric approach to learning with probabilistic deterministic finite automata (PDFA). We define and develop a sampler for a PDFA with an infinite number of states which we call the probabilistic deterministic infinite automata (PDIA). Posterior predictive inference in this model, given a finite training sequence, can be interpreted as averaging over multiple PD...

Probabilistic Deterministic Infinite Automata

We propose a novel Bayesian nonparametric approach to learning with probabilistic deterministic finite automata (PDFA). We define a PDFA with an infinite number of states (probabilistic deterministic infinite automata, or PDIA) and show how to average over its connectivity structure and state-specific emission distributions. Given a finite training sequence, posterior inference in the PDIA can ...

Probabilistic Programming Languages: Independent Choices and Deterministic Systems

Pearl [2000, p. 26] attributes to Laplace [1814] the idea of a probabilistic model as a deterministic system with stochastic inputs. Pearl defines causal models in terms of deterministic systems with stochastic inputs. In this paper, I show how deterministic systems with (independent) probabilistic inputs can also be seen as the basis of modern probabilistic programming languages. Probabilistic...

Probabilistic Crowding: Deterministic Crowding with Probabilistic Replacement