45 research outputs found
Parameter Learning of Logic Programs for Symbolic-Statistical Modeling
We propose a logical/mathematical framework for statistical parameter
learning of parameterized logic programs, i.e. definite clause programs
containing probabilistic facts with a parameterized distribution. It extends
the traditional least Herbrand model semantics in logic programming to
distribution semantics, possible world semantics with a probability
distribution which is unconditionally applicable to arbitrary logic programs
including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM
algorithm, the graphical EM algorithm, that runs for a class of parameterized
logic programs representing sequential decision processes where each decision
is exclusive and independent. It runs on a new data structure called support
graphs describing the logical relationship between observations and their
explanations, and learns parameters by computing inside and outside probability
generalized for logic programs. The complexity analysis shows that when
combined with OLDT search for all explanations for observations, the graphical
EM algorithm, despite its generality, has the same time complexity as existing
EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside
algorithm for PCFGs, and the one for singly connected Bayesian networks that
have been developed independently in each research field. Learning experiments
with PCFGs using two corpora of moderate size indicate that the graphical EM
algorithm can significantly outperform the Inside-Outside algorithm
Introduction to the special issue on probability, logic and learning
Recently, the combination of probability, logic and learning has received considerable attention in the artificial intelligence and machine learning communities; see e.g. Getoor and Taskar (2007); De Raedt et al. (2008). Computational logic often plays a major role in these developments since it forms the theoretical backbone for much of the work in probabilistic programming and logical and relational learning. Contemporary work in this area is often application- and experiment-driven, but is also concerned with the theoretical foundations of formalisms and inference procedures and with advanced implementation technology that scales well
DNF Sampling for ProbLog Inference
Inference in probabilistic logic languages such as ProbLog, an extension of
Prolog with probabilistic facts, is often based on a reduction to a
propositional formula in DNF. Calculating the probability of such a formula
involves the disjoint-sum-problem, which is computationally hard. In this work
we introduce a new approximation method for ProbLog inference which exploits
the DNF to focus sampling. While this DNF sampling technique has been applied
to a variety of tasks before, to the best of our knowledge it has not been used
for inference in probabilistic logic systems. The paper also presents an
experimental comparison with another sampling based inference method previously
introduced for ProbLog.Comment: Online proceedings of the Joint Workshop on Implementation of
Constraint Logic Programming Systems and Logic-based Methods in Programming
Environments (CICLOPS-WLPE 2010), Edinburgh, Scotland, U.K., July 15, 201
Probabilistic Logic Programming with Beta-Distributed Random Variables
We enable aProbLog---a probabilistic logical programming approach---to reason
in presence of uncertain probabilities represented as Beta-distributed random
variables. We achieve the same performance of state-of-the-art algorithms for
highly specified and engineered domains, while simultaneously we maintain the
flexibility offered by aProbLog in handling complex relational domains. Our
motivation is that faithfully capturing the distribution of probabilities is
necessary to compute an expected utility for effective decision making under
uncertainty: unfortunately, these probability distributions can be highly
uncertain due to sparse data. To understand and accurately manipulate such
probability distributions we need a well-defined theoretical framework that is
provided by the Beta distribution, which specifies a distribution of
probabilities representing all the possible values of a probability when the
exact value is unknown.Comment: Accepted for presentation at AAAI 201
Random-World Semantics and Syntactic Independence for Expressive Languages
We consider three desiderata for a language combining logic and probability: logical expressivity, random-world semantics, and the existence of a useful syntactic condition for probabilistic independence. Achieving these three desiderata simultaneously is nontrivial. Expressivity can be achieved by using a formalism similar to a programming language, but standard approaches to combining programming languages with probabilities sacrifice random-world semantics. Naive approaches to restoring random-world semantics undermine syntactic independence criteria. Our main result is a syntactic independence criterion that holds for a broad class of highly expressive logics under random-world semantics. We explore various examples including Bayesian networks, probabilistic context-free grammars, and an example from Mendelian genetics. Our independence criterion supports a case-factor inference technique that reproduces both variable elimination for BNs and the inside algorithm for PCFGs
On the Implementation of the Probabilistic Logic Programming Language ProbLog
The past few years have seen a surge of interest in the field of
probabilistic logic learning and statistical relational learning. In this
endeavor, many probabilistic logics have been developed. ProbLog is a recent
probabilistic extension of Prolog motivated by the mining of large biological
networks. In ProbLog, facts can be labeled with probabilities. These facts are
treated as mutually independent random variables that indicate whether these
facts belong to a randomly sampled program. Different kinds of queries can be
posed to ProbLog programs. We introduce algorithms that allow the efficient
execution of these queries, discuss their implementation on top of the
YAP-Prolog system, and evaluate their performance in the context of large
networks of biological entities.Comment: 28 pages; To appear in Theory and Practice of Logic Programming
(TPLP
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