Nesting Probabilistic Inference

When doing inference in ProbLog, a probabilistic extension of Prolog, we extend SLD resolution with some additional bookkeeping. This additional information is used to compute the probabilistic results for a probabilistic query. In Prolog's SLD, goals are nested very naturally. In ProbLog's SLD, nesting probabilistic queries interferes with the probabilistic bookkeeping. In order to support nested probabilistic inference we propose the notion of a parametrised ProbLog engine. Nesting becomes possible by suspending and resuming instances of ProbLog engines. With our approach we realise several extensions of ProbLog such as meta-calls, negation, and answers of probabilistic goals.Comment: Online Proceedings of the 11th International Colloquium on Implementation of Constraint LOgic Programming Systems (CICLOPS 2011), Lexington, KY, U.S.A., July 10, 201

SkILL - a Stochastic Inductive Logic Learner

Probabilistic Inductive Logic Programming (PILP) is a rel- atively unexplored area of Statistical Relational Learning which extends classic Inductive Logic Programming (ILP). This work introduces SkILL, a Stochastic Inductive Logic Learner, which takes probabilistic annotated data and produces First Order Logic theories. Data in several domains such as medicine and bioinformatics have an inherent degree of uncer- tainty, that can be used to produce models closer to reality. SkILL can not only use this type of probabilistic data to extract non-trivial knowl- edge from databases, but it also addresses efficiency issues by introducing a novel, efficient and effective search strategy to guide the search in PILP environments. The capabilities of SkILL are demonstrated in three dif- ferent datasets: (i) a synthetic toy example used to validate the system, (ii) a probabilistic adaptation of a well-known biological metabolism ap- plication, and (iii) a real world medical dataset in the breast cancer domain. Results show that SkILL can perform as well as a deterministic ILP learner, while also being able to incorporate probabilistic knowledge that would otherwise not be considered

On Nesting Monte Carlo Estimators

Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation. We investigate the statistical implications of nesting MC estimators, including cases of multiple levels of nesting, and establish the conditions under which they converge. We derive corresponding rates of convergence and provide empirical evidence that these rates are observed in practice. We further establish a number of pitfalls that can arise from naive nesting of MC estimators, provide guidelines about how these can be avoided, and lay out novel methods for reformulating certain classes of nested expectation problems into single expectations, leading to improved convergence rates. We demonstrate the applicability of our work by using our results to develop a new estimator for discrete Bayesian experimental design problems and derive error bounds for a class of variational objectives.Comment: To appear at International Conference on Machine Learning 201

Probabilistic Programming Concepts

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been developed since more than 20 years

Probabilistic (logic) programming concepts

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position and survey state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been considered for over 20 years