Corelab Seminar
2015-2016
Themis Gouleakis
Sampling Correctors
Abstract.
In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this talk will 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 consider the question of whether an additional source of independent random bits is required by sampling correctors to implement the correction process.