We present a data-driven, probabilistic trajectory optimization framework for systems with unknown dynamics, called Probabilistic Differential Dynamic Programming (PDDP). PDDP takes into account uncertainty explicitly for dynamics models using Gaussian processes (GPs). Based on the second-order local approximation of the value function, PDDP performs Dynamic Programming around a nominal traject...

The field of Probabilistic Logic Programming (PLP) has seen significant advances in the last 20 years, with many proposals for languages that combine probability with logic programming. Since the start, the problem of learning probabilistic logic programs has been the focus of much attention and a special issue of Theory and Practice of Logic Programming on Probability, Logic, and Learning has ...

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....

Abstract Robust aiding of inertial navigation systems in GNSS-denied environments is critical for the removal accumulated error caused by drift and bias inherent sensors. One way to perform such an uses matching geophysical measurements, as gravimetry, gravity gradiometry or magnetometry, with a known geo-referenced map. Although simple concept, this map-matching procedure challenging:...