Scalable Statistical Modeling and Query Processing over Large Scale Uncertain Databases

The past decade has witnessed a large number of novel applications that generate imprecise, uncertain and incomplete data. Examples include monitoring infrastructures such as RFIDs, sensor networks and web-based applications such as information extraction, data integration, social networking and so on. In my dissertation, I addressed several challenges in managing such data and developed algorithms for efficiently executing queries over large volumes of such data. Specifically, I focused on the following challenges. First, for meaningful analysis of such data, we need the ability to remove noise and infer useful information from uncertain data. To address this challenge, I first developed a declarative system for applying dynamic probabilistic models to databases and data streams. The output of such probabilistic modeling is probabilistic data, i.e., data annotated with probabilities of correctness/existence. Often, the data also exhibits strong correlations. Although there is prior work in managing and querying such probabilistic data using probabilistic databases, those approaches largely assume independence and cannot handle probabilistic data with rich correlation structures. Hence, I built a probabilistic database system that can manage large-scale correlations and developed algorithms for efficient query evaluation. Our system allows users to provide uncertain data as input and to specify arbitrary correlations among the entries in the database. In the back end, we represent correlations as a forest of junction trees, an alternative representation for probabilistic graphical models (PGM). We execute queries over the probabilistic database by transforming them into message passing algorithms (inference) over the junction tree. However, traditional algorithms over junction trees typically require accessing the entire tree, even for small queries. Hence, I developed an index data structure over the junction tree called INDSEP that allows us to circumvent this process and thereby scalably evaluate inference queries, aggregation queries and SQL queries over the probabilistic database. Finally, query evaluation in probabilistic databases typically returns output tuples along with their probability values. However, the existing query evaluation model provides very little intuition to the users: for instance, a user might want to know Why is this tuple in my result? or Why does this output tuple have such high probability? or Which are the most influential input tuples for my query ?'' Hence, I designed a query evaluation model, and a suite of algorithms, that provide users with explanations for query results, and enable users to perform sensitivity analysis to better understand the query results

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

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

Problem-Solving Knowledge Mining from Users’\ud Actions in an Intelligent Tutoring System

In an intelligent tutoring system (ITS), the domain expert should provide\ud relevant domain knowledge to the tutor so that it will be able to guide the\ud learner during problem solving. However, in several domains, this knowledge is\ud not predetermined and should be captured or learned from expert users as well as\ud intermediate and novice users. Our hypothesis is that, knowledge discovery (KD)\ud techniques can help to build this domain intelligence in ITS. This paper proposes\ud a framework to capture problem-solving knowledge using a promising approach\ud of data and knowledge discovery based on a combination of sequential pattern\ud mining and association rules discovery techniques. The framework has been implemented\ud and is used to discover new meta knowledge and rules in a given domain\ud which then extend domain knowledge and serve as problem space allowing\ud the intelligent tutoring system to guide learners in problem-solving situations.\ud Preliminary experiments have been conducted using the framework as an alternative\ud to a path-planning problem solver in CanadarmTutor