The P-Box CDF-Intervals: A Reliable Constraint Reasoning with Quantifiable Information

This paper 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. The empirical evaluation of our implementation shows that, with minimal overhead, the output solution set realizes a full enclosure of the data along with tighter bounds on its probabilistic distributions.