Statistical Relational Models Research Articles

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.

Symmetry-Aware Marginal Density Estimation

The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to outperform standard estimators by several orders of magnitude. The developed theory and algorithms apply to a broad class of probabilistic models including statistical relational models considered not susceptible to lifted probabilistic inference.

RockIt: Exploiting Parallelism and Symmetry for MAP Inference in Statistical Relational Models

RockIt is a maximum a-posteriori (MAP) query engine for statistical relational models. MAP inference in graphical models is an optimization problem which can be compiled to integer linear programs (ILPs).We describe several advances in translating MAP queries to ILP instances and present the novel meta-algorithm cutting plane aggregation (CPA). CPA exploits local context-specific symmetries and bundles up sets of linear constraints. The resulting counting constraints lead to more compact ILPs and make the symmetry of the ground model more explicit to state-of-the-art ILP solvers. Moreover, RockIt parallelizes most parts of the MAP inference pipeline taking advantage of ubiquitous shared-memory multi-core architectures. We report on extensive experiments with Markov logic network (MLN) benchmarks showing that RockIt outperforms the state-of-the-art systems Alchemy, Markov TheBeast, and Tuffy both in terms of efficiency and quality of results.

Structure Learning for Markov Logic Networks with Many Descriptive Attributes

Many machine learning applications that involve relational databases incorporate first-order logic and probability. Markov Logic Networks (MLNs) are a prominent statistical relational model that consist of weighted first order clauses. Many of the current state-of-the-art algorithms for learning MLNs have focused on relatively small datasets with few descriptive attributes, where predicates are mostly binary and the main task is usually prediction of links between entities. This paper addresses what is in a sense a complementary problem: learning the structure of an MLN that models the distribution of discrete descriptive attributes on medium to large datasets, given the links between entities in a relational database. Descriptive attributes are usually nonbinary and can be very informative, but they increase the search space of possible candidate clauses. We present an efficient new algorithm for learning a directed relational model (parametrized Bayes net), which produces an MLN structure via a standard moralization procedure for converting directed models to undirected models. Learning MLN structure in this way is 200-1000 times faster and scores substantially higher in predictive accuracy than benchmark algorithms on three relational databases.

BayesStore

Several real-world applications need to effectively manage and reason about large amounts of data that are inherently uncertain. For instance, pervasive computing applications must constantly reason about volumes of noisy sensory readings for a variety of reasons, including motion prediction and human behavior modeling. Such probabilistic data analyses require sophisticated machine-learning tools that can effectively model the complex spatio/temporal correlation patterns present in uncertain sensory data. Unfortunately, to date, most existing approaches to probabilistic database systems have relied on somewhat simplistic models of uncertainty that can be easily mapped onto existing relational architectures: Probabilistic information is typically associated with individual data tuples, with only limited or no support for effectively capturing and reasoning about complex data correlations. In this paper, we introduce BayesStore, a novel probabilistic data management architecture built on the principle of handling statistical models and probabilistic inference tools as first-class citizens of the database system. Adopting a machine-learning view, BAYESSTORE employs concise statistical relational models to effectively encode the correlation patterns between uncertain data, and promotes probabilistic inference and statistical model manipulation as part of the standard DBMS operator repertoire to support efficient and sound query processing. We present BAYESSTORE's uncertainty model based on a novel, first-order statistical model , and we redefine traditional query processing operators, to manipulate the data and the probabilistic models of the database in an efficient manner. Finally, we validate our approach, by demonstrating the value of exploiting data correlations during query processing, and by evaluating a number of optimizations which significantly accelerate query processing.

Understanding tuberculosis epidemiology using structured statistical models

Molecular epidemiological studies can provide novel insights into the transmission of infectious diseases such as tuberculosis. Typically, risk factors for transmission are identified using traditional hypothesis-driven statistical methods such as logistic regression. However, limitations become apparent in these approaches as the scope of these studies expand to include additional epidemiological and bacterial genomic data. Here we examine the use of Bayesian models to analyze tuberculosis epidemiology. We begin by exploring the use of Bayesian networks (BNs) to identify the distribution of tuberculosis patient attributes (including demographic and clinical attributes). Using existing algorithms for constructing BNs from observational data, we learned a BN from data about tuberculosis patients collected in San Francisco from 1991 to 1999. We verified that the resulting probabilistic models did in fact capture known statistical relationships. Next, we examine the use of newly introduced methods for representing and automatically constructing probabilistic models in structured domains. We use statistical relational models (SRMs) to model distributions over relational domains. SRMs are ideally suited to richly structured epidemiological data. We use a data-driven method to construct a statistical relational model directly from data stored in a relational database. The resulting model reveals the relationships between variables in the data and describes their distribution. We applied this procedure to the data on tuberculosis patients in San Francisco from 1991 to 1999, their Mycobacterium tuberculosis strains, and data on contact investigations. The resulting statistical relational model corroborated previously reported findings and revealed several novel associations. These models illustrate the potential for this approach to reveal relationships within richly structured data that may not be apparent using conventional statistical approaches. We show that Bayesian methods, in particular statistical relational models, are an important tool for understanding infectious disease epidemiology.

061-PA12 Knowledge, attitudes and practices of lay people about tuberculosis in Cali, Colombia

Molecular epidemiological studies can provide novel insights into the transmission of infectious diseases such as tuberculosis. Typically, risk factors for transmission are identified using traditional hypothesis-driven statistical methods such as logistic regression. However, limitations become apparent in these approaches as the scope of these studies expand to include additional epidemiological and bacterial genomic data. Here we examine the use of Bayesian models to analyze tuberculosis epidemiology. We begin by exploring the use of Bayesian networks (BNs) to identify the distribution of tuberculosis patient attributes (including demographic and clinical attributes). Using existing algorithms for constructing BNs from observational data, we learned a BN from data about tuberculosis patients collected in San Francisco from 1991 to 1999. We verified that the resulting probabilistic models did in fact capture known statistical relationships. Next, we examine the use of newly introduced methods for representing and automatically constructing probabilistic models in structured domains. We use statistical relational models (SRMs) to model distributions over relational domains. SRMs are ideally suited to richly structured epidemiological data. We use a data-driven method to construct a statistical relational model directly from data stored in a relational database. The resulting model reveals the relationships between variables in the data and describes their distribution. We applied this procedure to the data on tuberculosis patients in San Francisco from 1991 to 1999, their Mycobacterium tuberculosis strains, and data on contact investigations. The resulting statistical relational model corroborated previously reported findings and revealed several novel associations. These models illustrate the potential for this approach to reveal relationships within richly structured data that may not be apparent using conventional statistical approaches. We show that Bayesian methods, in particular statistical relational models, are an important tool for understanding infectious disease epidemiology.