Sampling Correctors

Abstract

In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported to have, in order to allow one to make "on-the-fly" corrections to samples drawn from probability distributions. These algorithms then act as filters between the noisy data and the end user. We show connections between sampling correctors, distribution learning algorithms, and distribution property testing algorithms. We show that these connections can be utilized to expand the applicability of known distribution learning and property testing algorithms as well as to achieve improved algorithms for those tasks. As a first step, we show how to design sampling correctors using proper learning algorithms. We then focus on the question of whether algorithms for sampling correctors can be more efficient in terms of sample complexity than learning algorithms for the analogous families of distributions. When correcting monotonicity, we show that this is indeed the case when also granted query access to the cumulative distribution function. We also obtain sampling correctors for monotonicity without this stronger type of access, provided that the distribution be originally very close to monotone (namely, at a distance O(1/ log 2 n)). In addition to that, we consider a restricted error model that aims at capturing "missing data" corruptions. In this model, we show that distributions that are close to monotone

GANplifying event samples

“…An interesting application is computer games, where the network traffic limits the available information and a powerful computer still generates realistic images or videos. This practical question leads to more formal question of sampling correctors [44]. Alternatively, it can be linked to a classification problem to derive scaling laws for networks fooling a given hypothesis test [43,45].…”

Certified Computation from Unreliable Datasets

“…For example, using local queries, [ACCL08] correct datasets to ensure monotonicity and other structural properties. [CGR16] solve similar local correction tasks for noisy probability distributions.…”