Privatization of Probability Distributions by the Wavelet Integral approach

TL;DR

This paper introduces a wavelet-based privatization method for probability distributions, ensuring the perturbed distribution remains valid, which can enhance data privacy and fitting techniques in AI and machine learning.

Contribution

It proposes a novel wavelet integral approach for privatizing probability distributions, maintaining their validity after perturbation.

Findings

Perturbed distribution functions remain valid probability distributions.

The method allows for controlled data privatization.

Applicable to data fitting in AI and machine learning.

Abstract

A naive theory of additive perturbations on a continuous probability distribution is presented. We propose a new privatization mechanism based on a naive theory of a perturbation on a probability using wavelets, such as a noise perturbs the signal of a digital image sensor. The cumulative wavelet integral function is defined and builds up the perturbations with the help of this function. We show that an arbitrary distribution function additively perturbed is still a distribution function, which can be seen as a privatized distribution, with the privatization mechanism being a wavelet function. It is shown that an arbitrary cumulative distribution function added to such an additive perturbation is still a cumulative distribution function. Thus, we offer a mathematical method for choosing a suitable probability distribution to data by starting from some guessed initial distribution. The areas of artificial intelligence and machine learning are constantly in need of data fitting techniques, closely related to sensors. The proposed privatization mechanism is therefore a contribution to increasing the scope of existing techniques.