Approximating predicates and expressive queries on probabilistic databases

Abstract

We study complexity and approximation of queries in an expressive query language for probabilistic databases. The language studied supports the compositional use of confidence computation. It allows for a wide range of new use cases, such as the computation of conditional probabilities and of selections based on predicates that involve marginal and conditional probabilities. These features have important applications in areas such as data cleaning and the processing of sensor data. We establish techniques for efficiently computing approximate query results and for estimating the error incurred by queries. The central difficulty is due to selection predicates based on approximated values, which may lead to the unreliable selection of tuples. A database may contain certain singularities at which approximation of predicates cannot be achieved; however, the paper presents an algorithm that provides efficient approximation otherwise.

Anytime approximation in probabilistic databases

“…It was first shown by Karp, Luby, and Madras [33] that there is a fully polynomial-time randomised approximation scheme (FPTRAS) for DNF counting based on Monte Carlo simulation. This algorithm can be modified to compute the probability of a DNF over independent discrete random variables [12,25,34,46]. These techniques yield an efficiently computable unbiased estimator that in expectation returns the probability p of a DNF of n clauses such that computing the average of a polynomial number of such Monte Carlo steps (which are calls to the Karp-Luby unbiased estimator) is an ( , δ)-approximation for the probability (i.e., a relative approximation): If the averagep is taken over at least 3 · n · log(2/δ)/ 2 Monte Carlo steps, then Pr | p −p| ≥ · p ≤ δ.…”

k-nearest neighbors in uncertain graphs

“…These systems model data with relations and therefore, they cannot perform shortest path computations on graphs efficiently. Also, since computing exact answers to many typical SQL queries has been shown to have #P-complete data complexity [13], research has focused on computing approximate answers [25,34].…”

The trichotomy of HAVING queries on a probabilistic database

“…Koch [30] formalizes a language that allows predication on probabilities and discusses approximation algorithms for this richer language, though he does not consider HAVING aggregation. This is in part due to the fact that his aim is to create a fully compositional language for probabilistic databases [31].…”