This paper introduces and illustrates BLOG, a formal language for defining probability models over worlds with unknown objects and identity uncertainty. BLOG unifies and extends several existing approaches. Subject to certain acyclicity constraints, every BLOG model specifies a unique probability distribution over first-order model structures that can contain varying and unbounded numbers of objects. Furthermore, complete inference algorithms exist for a large fragment of the language. We also introduce a probabilistic form of Skolemization for handling evidence. 1

Many datasets of interest today are best described as a linked collection of interrelated objects. These may represent homogeneous networks, in which there is a single-object type and link type, or richer, heterogeneous networks, in which there may be multiple object and link types (and possibly other semantic information). Examples of homogeneous networks include single mode social networks, such as people connected by friendship links, or the WWW, a collection of linked web pages. Examples of heterogeneous networks include those in medical domains describing patients, diseases, treatments and contacts, or in bibliographic domains describing publications, authors, and venues. Link mining refers to data mining techniques that explicitly consider these links when building predictive or descriptive models of the linked data. Commonly addressed link mining tasks include object ranking, group detection, collective classification, link prediction and subgraph discovery. While network analysis has been studied in depth in particular areas such as social network analysis, hypertext mining, and web analysis, only recently has there been a cross-fertilization of ideas among these different communities. This is an exciting, rapidly expanding area. In this article, we review some of the common emerging themes. 1.

Many real-world domains exhibit rich relational structure and stochasticity and motivate the development of models that combine predicate logic with probabilities. These models describe probabilistic influences between attributes of objects that are related to each other through known domain relationships. To keep these models succinct, each such influence is considered independent of others, which is called the assumption of “independence of causal influences ” (ICI). In this paper, we describe a language that consists of quantified conditional influence statements and captures most relational probabilistic models based on directed graphs. The influences due to different statements are combined using a set of combining rules such as Noisy-OR. We motivate and introduce multi-level combining rules, where the lower level rules combine the influences due to different ground instances of the same statement, and the upper level rules combine the influences due to different statements. We present algorithms and empirical results for parameter learning in the presence of such combining rules. Specifically, we derive and implement algorithms based on gradient descent and expectation maximization for different combining rules and evaluate them on synthetic data and on a real-world task. The results demonstrate that the algorithms are able to learn both the conditional probability distributions of the influence statements and the parameters of the combining rules. 1.

The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation. This paper extends BLOG by adopting generative processes over function spaces — known as nonparametrics in the Bayesian literature. We introduce syntax for reasoning about arbitrary collections of objects, and their properties, in an intuitive manner. By exploiting exchangeability, distributions over unknown objects and their attributes are cast as Dirichlet processes, which resolve difficulties in model selection and inference caused by varying numbers of objects. We demonstrate these concepts with application to citation matching. 1

Abstract — We present a declarative framework for collective deduplication of entity references in the presence of constraints. Constraints occur naturally in many data cleaning domains and can improve the quality of deduplication. An example of a constraint is “each paper has a unique publication venue”; iftwo paper references are duplicates, then their associated conference references must be duplicates as well. Our framework supports collective deduplication, meaning that we can dedupe both paper references and conference references collectively in the example above. Our framework is based on a simple declarative Datalogstyle language with precise semantics. Most previous work on deduplication either ignore constraints or use them in an ad-hoc domain-specific manner. We also present efficient algorithms to support the framework. Our algorithms have precise theoretical guarantees for a large subclass of our framework. We show, using a prototype implementation, that our algorithms scale to very large datasets. We provide thorough experimental results over real-world data demonstrating the utility of our framework for high-quality and scalable deduplication. I.

Abstract. Two general techniques for implementing a domain-specific language (DSL) with less overhead are the finally-tagless embedding of object programs and the direct-style representation of side effects. We use these techniques to build a DSL for probabilistic programming, for expressing countable probabilistic models and performing exact inference and importance sampling on them. Our language is embedded as an ordinary OCaml library and represents probability distributions as ordinary OCaml programs. We use delimited continuations to reify probabilistic programs as lazy search trees, which inference algorithms may traverse without imposing any interpretive overhead on deterministic parts of a model. We thus take advantage of the existing OCaml implementation to achieve competitive performance and ease of use. Inference algorithms can easily be embedded in probabilistic programs themselves.

Stochastic logic programs combine ideas from probabilistic grammars with the expressive power of definite clause logic; as such they can be considered as an extension of probabilistic context-free grammars. Motivated by an analogy with learning tree-bank grammars, we study how to learn stochastic logic programs from proof-trees. Using proof-trees as examples imposes strong logical constraints on the structure of the target stochastic logic program. These constraints can be integrated in the least general generalization (lgg) operator, which is employed to traverse the search space. Our implementation employs a greedy search guided by the maximum likelihood principle and failure-adjusted maximization. We also report on a number of simple experiments that show the promise of the approach.

This paper describes the system that we submitted to the “Learning Language in Logic” Challenge of extracting directed genic interactions from sentences in Medline abstracts. The system uses Markov Logic, a framework that combines log-linear models and First Order Logic, to create a set of weighted clauses which can classify pairs of gene named entities as genic interactions. These clauses are based on chains of syntactic and semantic relations in the parse or Discourse Representation Structure (drs) of a sentence, respectively. Our submitted results achieved 52.6 % F-Measure on the dataset without and 54.3 % on the dataset with coreferences. After adding explicit clauses which model noninteraction we were able to improve these numbers to 68.4 % and 64.7%, respectively.

We unify f-divergences, Bregman divergences, surrogate regret bounds, proper scoring rules, cost curves, ROC-curves and statistical information. We do this by systematically studying integral and variational representations of these various objects and in so doing identify their primitives which all are related to cost-sensitive binary classification. As well as developing relationships between generative and discriminative views of learning, the new machinery leads to tight and more general surrogate regret bounds and generalised Pinsker inequalities relating f-divergences to variational divergence. The new viewpoint also illuminates existing algorithms: it provides a new derivation of Support Vector Machines in terms of divergences and relates Maximum Mean Discrepancy to Fisher Linear Discriminants.

Inthetraditionallinkpredictionproblem, asnapshotofasocial network is used as a starting point to predict, by means of graph-theoretic measures, the links that are likely to appear in the future. In this paper, we introduce cold start link prediction as the problem of predicting the structure of a social network when the network itself is totally missing while some other information regarding the nodes is available. Weproposeatwo-phasemethodbasedonthebootstrap probabilistic graph. The first phase generates an implicit social network under the form of a probabilistic graph. The second phase applies probabilistic graph-based measures to produce the final prediction. We assess our method empirically over a large data collection obtained from Flickr, using interest groups as the initial information. The experiments confirm the effectiveness of our approach.