Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Max-Information, Differential Privacy, and Post-Selection Hypothesis
  Testing   In this paper, we initiate a principled study of how the generalization
properties of approximate differential privacy can be used to perform adaptive
hypothesis testing, while giving statistically valid $p$-value corrections. We
do this by observing that the guarantees of algorithms with bounded approximate
max-information are sufficient to correct the $p$-values of adaptively chosen
hypotheses, and then by proving that algorithms that satisfy
$(\epsilon,\delta)$-differential privacy have bounded approximate max
information when their inputs are drawn from a product distribution. This
substantially extends the known connection between differential privacy and
max-information, which previously was only known to hold for (pure)
$(\epsilon,0)$-differential privacy. It also extends our understanding of
max-information as a partially unifying measure controlling the generalization
properties of adaptive data analyses. We also show a lower bound, proving that
(despite the strong composition properties of max-information), when data is
drawn from a product distribution, $(\epsilon,\delta)$-differentially private
algorithms can come first in a composition with other algorithms satisfying
max-information bounds, but not necessarily second if the composition is
required to itself satisfy a nontrivial max-information bound. This, in
particular, implies that the connection between
$(\epsilon,\delta)$-differential privacy and max-information holds only for
inputs drawn from product distributions, unlike the connection between
$(\epsilon,0)$-differential privacy and max-information.

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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics