Probabilistic databases play a crucial role in the management and understanding of uncertain data. However, incorporating probabilities into the semantics of incomplete databases has posed many challenges, forcing systems to sacrifice modeling power, scalability, or restrict the class of relational algebra formula under which they are closed. We propose an alternative approach where the underlying relational database always represents a single world, and an external factor graph encodes a distribution over possible worlds; Markov chain Monte Carlo (MCMC) inference is then used to recover this uncertainty to a desired level of fidelity. Our approach allows the efficient evaluation of arbitrary queries over probabilistic databases with arbitrary dependencies expressed by graphical models with structure that changes during inference. MCMC sampling provides efficiency by hypothesizing modifications to possible worlds rather than generating entire worlds from scratch. Queries are then run over the portions of the world that change, avoiding the onerous cost of running full queries over each sampled world. A significant innovation of this work is the connection between MCMC sampling and materialized view maintenance techniques: we find empirically that using view maintenance techniques is several orders of magnitude faster than naively querying each sampled world. We also demonstrate our system's ability to answer relational queries with aggregation, and demonstrate additional scalability through the use of parallelization.
Although there is a vast body of work on probabilistic databases, graphical models have largely been ignored until recently. The work of @cite_21 @cite_19 casts query evaluation as inference in a graphical model and BayesStore @cite_17 makes explicit use of Bayesian networks to represent uncertainty in the database. While expressive, generative Bayesian networks have difficulty representing the types of dependencies handled automatically in discriminative models @cite_4 , motivating a database approach to linear chain conditional random fields @cite_13 . We, however, present a more general representation based on factor graphs, an umbrella framework for both Bayesian networks and conditional random fields. Perhaps more importantly we directly address the problem of scalable query evaluation in these representations|with an MCMC sampler|whereas previous systems based on graphical models are severely restricted by this bottleneck. Furthermore our approach can easily evaluate any relational algebra query without the need to close the graphical model under the semantics of each operator.
@cite_4 @cite_21 @cite_19 @cite_13 @cite_17
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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. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach. Most tasks require a person or an automated system to reason -- to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs. Due to numerous applications producing noisy data, e.g., sensor data, experimental data, data from uncurated sources, information extraction, etc., there has been a surge of interest in the development of probabilistic databases. Most probabilistic database models proposed to date, however, fail to meet the challenges of real-world applications on two counts: (1) they often restrict the kinds of uncertainty that the user can represent; and (2) the query processing algorithms often cannot scale up to the needs of the application. In this work, we define a probabilistic database model, PrDB, that uses graphical models, a state-of-the-art probabilistic modeling technique developed within the statistics and machine learning community, to model uncertain data. We show how this results in a rich, complex yet compact probabilistic database model, which can capture the commonly occurring uncertainty models (tuple uncertainty, attribute uncertainty), more complex models (correlated tuples and attributes) and allows compact representation (shared and schema-level correlations). In addition, we show how query evaluation in PrDB translates into inference in an appropriately augmented graphical model. This allows us to easily use any of a myriad of exact and approximate inference algorithms developed within the graphical modeling community. While probabilistic inference provides a generic approach to solving queries, we show how the use of shared correlations, together with a novel inference algorithm that we developed based on bisimulation, can speed query processing significantly. We present a comprehensive experimental evaluation of the proposed techniques and show that even with a few shared correlations, significant speedups are possible.