Histograms and Wavelets on Probabilistic Data

TL;DR

This paper develops algorithms for creating histogram and wavelet summaries of probabilistic data, enabling efficient and accurate data approximation in uncertain databases, which improves query processing and data exploration.

Contribution

It introduces novel algorithms for probabilistic histograms and wavelets, extending dynamic programming techniques to optimize data summaries under uncertainty.

Findings

Algorithms outperform simple sampling methods in accuracy.

Proposed methods are computationally efficient.

Enhanced data summaries improve probabilistic query processing.

Abstract

There is a growing realization that uncertain information is a first-class citizen in modern database management. As such, we need techniques to correctly and efficiently process uncertain data in database systems. In particular, data reduction techniques that can produce concise, accurate synopses of large probabilistic relations are crucial. Similar to their deterministic relation counterparts, such compact probabilistic data synopses can form the foundation for human understanding and interactive data exploration, probabilistic query planning and optimization, and fast approximate query processing in probabilistic database systems. In this paper, we introduce definitions and algorithms for building histogram- and wavelet-based synopses on probabilistic data. The core problem is to choose a set of histogram bucket boundaries or wavelet coefficients to optimize the accuracy of the approximate representation of a collection of probabilistic tuples under a given error metric. For a variety of different error metrics, we devise efficient algorithms that construct optimal or near optimal B-term histogram and wavelet synopses. This requires careful analysis of the structure of the probability distributions, and novel extensions of known dynamic-programming-based techniques for the deterministic domain. Our experiments show that this approach clearly outperforms simple ideas, such as building summaries for samples drawn from the data distribution, while taking equal or less time.