Computing Multi-Relational Sufficient Statistics for Large Databases

Databases contain information about which relationships do and do not hold among entities. To make this information accessible for statistical analysis requires computing sufficient statistics that combine information from different database tables. Such statistics may involve any number of {\em positive and negative} relationships. With a naive enumeration approach, computing sufficient statistics for negative relationships is feasible only for small databases. We solve this problem with a new dynamic programming algorithm that performs a virtual join, where the requisite counts are computed without materializing join tables. Contingency table algebra is a new extension of relational algebra, that facilitates the efficient implementation of this M\"obius virtual join operation. The M\"obius Join scales to large datasets (over 1M tuples) with complex schemas. Empirical evaluation with seven benchmark datasets showed that information about the presence and absence of links can be exploited in feature selection, association rule mining, and Bayesian network learning.Comment: 11pages, 8 figures, 8 tables, CIKM'14,November 3--7, 2014, Shanghai, Chin

An Answer Explanation Model for Probabilistic Database Queries

Following the availability of huge amounts of uncertain data, coming from diverse ranges of applications such as sensors, machine learning or mining approaches, information extraction and integration, etc. in recent years, we have seen a revival of interests in probabilistic databases. Queries over these databases result in probabilistic answers. As the process of arriving at these answers is based on the underlying stored uncertain data, we argue that from the standpoint of an end user, it is helpful for such a system to give an explanation on how it arrives at an answer and on which uncertainty assumptions the derived answer is based. In this way, the user with his/her own knowledge can decide how much confidence to place in this probabilistic answer. \ud The aim of this paper is to design such an answer explanation model for probabilistic database queries. We report our design principles and show the methods to compute the answer explanations. One of the main contributions of our model is that it fills the gap between giving only the answer probability, and giving the full derivation. Furthermore, we show how to balance verifiability and influence of explanation components through the concept of verifiable views. The behavior of the model and its computational efficiency are demonstrated through an extensive performance study

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

Node Classification in Uncertain Graphs

In many real applications that use and analyze networked data, the links in the network graph may be erroneous, or derived from probabilistic techniques. In such cases, the node classification problem can be challenging, since the unreliability of the links may affect the final results of the classification process. If the information about link reliability is not used explicitly, the classification accuracy in the underlying network may be affected adversely. In this paper, we focus on situations that require the analysis of the uncertainty that is present in the graph structure. We study the novel problem of node classification in uncertain graphs, by treating uncertainty as a first-class citizen. We propose two techniques based on a Bayes model and automatic parameter selection, and show that the incorporation of uncertainty in the classification process as a first-class citizen is beneficial. We experimentally evaluate the proposed approach using different real data sets, and study the behavior of the algorithms under different conditions. The results demonstrate the effectiveness and efficiency of our approach