We propose Edward, a Turing-complete probabilistic programming language. Edward builds on two compositional representations—random variables and inference. By treating inference as a first class citizen, on a par with modeling, we show that probabilistic programming can be as flexible and computationally efficient as traditional deep learning. For flexibility, Edward makes it easy to fit the sa...

We introduce a notion of probability to the graph programming language GP2 which resolves nondeterministic choices of graph transformation rules and their matches. With our programming model Probabilistic GP2 (P-GP2), rule and match decisions are assigned uniform distributions over their domains. In this paper, we present an implementation of P-GP2 as an extension of an existing GP2 compiler. A...

In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to spec­ ify the probability structure. We consider the case in which probabilistic information is not available. Instead of using probability intervals, we allow for the specification of the probabilities of disjunctions. Because mini­ mal ...

We extend cc to allow the specification of a discrete probability distribution for random variables. We demonstrate the expressiveness of pcc by synthesizing combinators for default reasoning. We extend pcc uniformly over time, to get a synchronous reactive probabilistic programming language, Timed pcc. We describe operational and denotational models for pcc (and Timed pcc). The key feature of ...

We present a new approach to probabilistic logic programs with a possible worlds semantics. Classical program clauses are extended by a subinterval of [0; 1] that describes the range for the conditional probability of the head of a clause given its body. We show that deduction in the defined probabilistic logic programs is computationally more complex than deduction in classical logic programs....

PRISM is a probabilistic programming language based on Prolog augmented with primitives to represent probabilistic choice. PRISM is implemented using a combination of low level support from a modified version of B-Prolog, source level program transformation, and libraries for probabilistic inference and learning implemented in the imperative language C. More recently, developers of probabilisti...

This paper considers a multi-objective portfolio selection problem imposed by gaining of portfolio, divided yield and risk control in an ambiguous investment environment, in which the return and risk are characterized by probabilistic numbers. Based on the theory of possibility, a new multi-objective portfolio optimization model with gaining of portfolio, divided yield and risk control is propo...

Abstract We present d3p , a software package designed to help fielding runtime efficient widely-applicable Bayesian inference under differential privacy guarantees. achieves general applicability wide range of probabilistic modelling problems by implementing the differentially private variational algorithm, allowing users fit any parametric model with differentiable density function. adopts pro...

We consider a programming language that can manipulate both classical and quantum information. Our is type-safe designed for variational programming, which hybrid classical-quantum computational paradigm. The subsystem of the Probabilistic FixPoint Calculus (PFPC), lambda calculus with mixed-variance recursive types, term recursion probabilistic choice. first-order linear type system two subsys...