Oblivious Bounds on the Probability of Boolean Functions

This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an exact characterization of optimal oblivious bounds, i.e. when the new probabilities are chosen independent of the probabilities of all other variables. Our motivation comes from the weighted model counting problem (or, equivalently, the problem of computing the probability of a Boolean function), which is #P-hard in general. By performing several dissociations, one can transform a Boolean formula whose probability is difficult to compute, into one whose probability is easy to compute, and which is guaranteed to provide an upper or lower bound on the probability of the original formula by choosing appropriate probabilities for the dissociated variables. Our new bounds shed light on the connection between previous relaxation-based and model-based approximations and unify them as concrete choices in a larger design space. We also show how our theory allows a standard relational database management system (DBMS) to both upper and lower bound hard probabilistic queries in guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281

Provenance Circuits for Trees and Treelike Instances (Extended Version)

Query evaluation in monadic second-order logic (MSO) is tractable on trees and treelike instances, even though it is hard for arbitrary instances. This tractability result has been extended to several tasks related to query evaluation, such as counting query results [3] or performing query evaluation on probabilistic trees [10]. These are two examples of the more general problem of computing augmented query output, that is referred to as provenance. This article presents a provenance framework for trees and treelike instances, by describing a linear-time construction of a circuit provenance representation for MSO queries. We show how this provenance can be connected to the usual definitions of semiring provenance on relational instances [20], even though we compute it in an unusual way, using tree automata; we do so via intrinsic definitions of provenance for general semirings, independent of the operational details of query evaluation. We show applications of this provenance to capture existing counting and probabilistic results on trees and treelike instances, and give novel consequences for probability evaluation.Comment: 48 pages. Presented at ICALP'1

Techniques for improving efficiency and scalability for the integration of information retrieval and databases

PhDThis thesis is on the topic of integration of Information Retrieval (IR) and Databases (DB), with particular focuses on improving efficiency and scalability of integrated IR and DB technology (IR+DB). The main purpose of this study is to develop efficient and scalable techniques for supporting integrated IR and DB technology, which is a popular approach today for handling complex queries over text and structured data. Our specific interest in this thesis is how to efficiently handle queries over large-scale text and structured data. The work is based on a technology that integrates probability theory and relational algebra, where retrievals for text and data are to be expressed in probabilistic logical programs such as probabilistic relational algebra or probabilistic Datalog. To support efficient processing of probabilistic logical programs, we proposed three optimization techniques that focus on aspects covered logical and physical layers, which include: scoring-driven query optimization using scoring expression, query processing with top-k incorporated pipeline, and indexing with relational inverted index. Specifically, scoring expressions are proposed for expressing the scoring or probabilistic semantics of implied scoring functions of PRA expressions, so that efficient query execution plan can be generated by rule-based scoring-driven optimizer. Secondly, to balance efficiency and effectiveness so that to improve query response time, we studied methods for incorporating topk algorithms into pipelined query execution engine for IR+DB systems. Thirdly, the proposed relational inverted index integrates IR-style inverted index and DB-style tuple-based index, which can be used to support efficient probability estimation and aggregation as well as conventional relational operations. Experiments were carried out to investigate the performances of proposed techniques. Experimental results showed that the efficiency and scalability of an IR+DB prototype have been improved, while the system can handle queries efficiently on considerable large data sets for a number of IR tasks

Learning Tuple Probabilities

Learning the parameters of complex probabilistic-relational models from labeled training data is a standard technique in machine learning, which has been intensively studied in the subfield of Statistical Relational Learning (SRL), but---so far---this is still an under-investigated topic in the context of Probabilistic Databases (PDBs). In this paper, we focus on learning the probability values of base tuples in a PDB from labeled lineage formulas. The resulting learning problem can be viewed as the inverse problem to confidence computations in PDBs: given a set of labeled query answers, learn the probability values of the base tuples, such that the marginal probabilities of the query answers again yield in the assigned probability labels. We analyze the learning problem from a theoretical perspective, cast it into an optimization problem, and provide an algorithm based on stochastic gradient descent. Finally, we conclude by an experimental evaluation on three real-world and one synthetic dataset, thus comparing our approach to various techniques from SRL, reasoning in information extraction, and optimization

The Design of Arbitrage-Free Data Pricing Schemes

Motivated by a growing market that involves buying and selling data over the web, we study pricing schemes that assign value to queries issued over a database. Previous work studied pricing mechanisms that compute the price of a query by extending a data seller's explicit prices on certain queries, or investigated the properties that a pricing function should exhibit without detailing a generic construction. In this work, we present a formal framework for pricing queries over data that allows the construction of general families of pricing functions, with the main goal of avoiding arbitrage. We consider two types of pricing schemes: instance-independent schemes, where the price depends only on the structure of the query, and answer-dependent schemes, where the price also depends on the query output. Our main result is a complete characterization of the structure of pricing functions in both settings, by relating it to properties of a function over a lattice. We use our characterization, together with information-theoretic methods, to construct a variety of arbitrage-free pricing functions. Finally, we discuss various tradeoffs in the design space and present techniques for efficient computation of the proposed pricing functions.Comment: full pape