Angelika Kimmig

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.

On the Efficient Execution of ProbLog Programs

The past few years have seen a surge of interest in the field of probabilistic logic learning or 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 mutually independent probabilities that they 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.

The magic of logical inference in probabilistic programming

Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use backward reasoning based on SLD resolution for inference. While these methods are typically computationally efficient, they often can neither handle infinite and/or continuous distributions, nor evidence. To overcome these limitations, we introduce distributional clauses, a variation and extension of Satos distribution semantics. We also contribute a novel approximate inference method that integrates forward reasoning with importance sampling, a well-known technique for probabilistic inference. To achieve efficiency, we integrate two logic programming techniques to direct forward sampling. Magic sets are used to focus on relevant parts of the program, while the integration of backward reasoning allows one to identify and avoid regions of the sample space that are inconsistent with the evidence.

Parameter Learning in Probabilistic Databases: A Least Squares Approach

We introduce the problem of learning the parameters of the probabilistic database ProbLog. Given the observed success probabilities of a set of queries, we compute the probabilities attached to facts that have a low approximation error on the training examples as well as on unseen examples. Assuming Gaussian error terms on the observed success probabilities, this naturally leads to a least squares optimization problem. Our approach, called LeProbLog, is able to learn both from queries and from proofs and even from both simultaneously. This makes it flexible and allows faster training in domains where the proofs are available. Experiments on real world data show the usefulness and effectiveness of this least squares calibration of probabilistic databases.

Lifted graphical models: a survey

Lifted graphical models provide a language for expressing dependencies between different types of entities, their attributes, and their diverse relations, as well as techniques for probabilistic reasoning in such multi-relational domains. In this survey, we review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We discuss inference algorithms, including lifted inference algorithms, that efficiently compute the answers to probabilistic queries over such models. We also review work in learning lifted graphical models from data. There is a growing need for statistical relational models (whether they go by that name or another), as we are inundated with data which is a mix of structured and unstructured, with entities and relations extracted in a noisy manner from text, and with the need to reason effectively with this data. We hope that this synthesis of ideas from many different research groups will provide an accessible starting point for new researchers in this expanding field.

A flexible framework for probabilistic models of social trust

In social networks, notions such as trust, fondness, or respect between users can be expressed by associating a strength with each tie. This provides a view of social interaction as a weighted graph. Sociological models for such weighted networks can differ significantly in their basic motivations and intuitions. In this paper, we present a flexible framework for probabilistic modeling of social networks that allows one to represent these different models and more. The framework, probabilistic soft logic (PSL), is particularly well-suited for this domain, as it combines a declarative, first-order logic-based syntax for describing relational models with a soft-logic representation, which maps naturally to the non-discrete strength of social trust. We demonstrate the flexibility and effectiveness of PSL for trust prediction using two different approaches: a structural balance model based on social triangles, and a social status model based on a consistent status hierarchy. We test these models on real social network data and find that PSL is an effective tool for trust prediction.

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.

Probabilistic Explanation Based Learning

Explanation based learning produces generalized explanations from examples. These explanations are typically built in a deductive manner and they aim to capture the essential characteristics of the examples. Probabilistic explanation based learning extends this idea to probabilistic logic representations, which have recently become popular within the field of statistical relational learning. The task is now to find the most likely explanation why one (or more) example(s) satisfy a given concept. These probabilistic and generalized explanations can then be used to discover similarexamples and to reason by analogy. So, whereas traditional explanation based learning is typically used for speed-up learning, probabilistic explanation based learning is used for discovering new knowledge. Probabilistic explanation based learning has been implemented in a recently proposed probabilistic logic called ProbLog, and it has been applied to a challenging application in discovering relationships of interest in large biological networks.

Subgraph pattern matching over uncertain graphs with identity linkage uncertainty

There is a growing need for methods that can represent and query uncertain graphs. These uncertain graphs are often the result of an information extraction and integration system that attempts to extract an entity graph or a knowledge graph from multiple unstructured sources [25], [7]. Such an integration typically leads to identity uncertainty, as different data sources may use different references to the same underlying real-world entities. Integration usually also introduces additional uncertainty on node attributes and edge existence. In this paper, we propose the notion of a probabilistic entity graph (PEG), a formal model that uniformly and systematically addresses these three types of uncertainty. A PEG is a probabilistic graph model that defines a distribution over possible graphs at the entity level. We introduce a general framework for constructing a PEG given uncertain data at the reference level and develop efficient algorithms to answer subgraph pattern matching queries in this setting. Our algorithms are based on two novel ideas: context-aware path indexing and reduction by join-candidates, which drastically reduce the query search space. A comprehensive experimental evaluation shows that our approach outperforms baseline implementations by orders of magnitude.

Algebraic model counting

Weighted model counting (WMC) is a well-known inference task on knowledge bases, and the basis for some of the most efficient techniques for probabilistic inference in graphical models. We introduce algebraic model counting (AMC), a generalization of WMC to a semiring structure that provides a unified view on a range of tasks and existing results. We show that AMC generalizes many well-known tasks in a variety of domains such as probabilistic inference, soft constraints and network and database analysis. Furthermore, we investigate AMC from a knowledge compilation perspective and show that all AMC tasks can be evaluated using sd-DNNF circuits, which are strictly more succinct, and thus more efficient to evaluate, than direct representations of sets of models. We identify further characteristics of AMC instances that allow for evaluation on even more succinct circuits.