CDF-Intervals: A Reliable Framework to Reason about Data with Uncertainty

TL;DR

This paper presents CDF-Intervals, a new framework for reasoning about uncertain data using p-box cdf-intervals, which provide tighter probabilistic bounds with minimal computational overhead.

Contribution

It introduces a novel constraint domain extending convex modeling with p-box cdfs, enabling more accurate probabilistic reasoning about uncertain data.

Findings

Provides tighter probabilistic bounds on data

Achieves full enclosure of data with minimal overhead

Employs linear computations in the probabilistic domain

Abstract

This research introduces a new constraint domain for reasoning about data with uncertainty. It extends convex modeling with the notion of p-box to gain additional quantifiable information on the data whereabouts. Unlike existing approaches, the p-box envelops an unknown probability instead of approximating its representation. The p-box bounds are uniform cumulative distribution functions (cdf) in order to employ linear computations in the probabilistic domain. The reasoning by means of p-box cdf-intervals is an interval computation which is exerted on the real domain then it is projected onto the cdf domain. This operation conveys additional knowledge represented by the obtained probabilistic bounds. Empirical evaluation shows that, with minimal overhead, the output solution set realizes a full enclosure of the data along with tighter bounds on its probabilistic distributions.