Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sampling Correctors   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 have sampling correctors that are
significantly more efficient than achievable by the learning approach.
  We also consider the question of whether an additional source of independent
random bits is required by sampling correctors to implement the correction
process.

15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci