Estimating Range Queries using Aggregate Data with Integrity Constraints: a Probabilistic Approach

TL;DR

This paper presents a probabilistic method for estimating range queries over multidimensional data using only aggregate summaries, without needing access to the original data, ensuring data integrity and privacy.

Contribution

It introduces a novel probabilistic framework for accurately estimating range queries solely from aggregate data, avoiding assumptions about the original dataset.

Findings

Provides a theoretical model for query estimation

Achieves accurate estimates using only aggregate summaries

Ensures data integrity constraints are maintained

Abstract

The problem of recovering (count and sum) range queries over multidimensional data only on the basis of aggregate information on such data is addressed. This problem can be formalized as follows. Suppose that a transformation T producing a summary from a multidimensional data set is used. Now, given a data set D, a summary S=T(D) and a range query r on D, the problem consists of studying r by modelling it as a random variable defined over the sample space of all the data sets D' such that T(D) = S. The study of such a random variable, done by the definition of its probability distribution and the computation of its mean value and variance, represents a well-founded, theoretical probabilistic approach for estimating the query only on the basis of the available information (that is the summary S) without assumptions on original data.