Les Private Genius to Optimal student Learning
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Learning problems form an important category of
computational tasks that generalizes many of the computations researchers apply
to large real-life data sets. We ask: what concept classes can be learned
privately, namely, by an algorithm whose output does not depend too heavily on
any one input or specific training example? More precisely, we investigate
learning algorithms that satisfy differential privacy, a notion that provides
strong confidentiality guarantees in contexts where aggregate information is
released about a database containing sensitive information about individuals.
We demonstrate that, ignoring computational constraints, it is possible to
privately agnostically learn any concept class using a sample size
approximately logarithmic in the cardinality of the concept class. Therefore,
almost anything learnable is learnable privately: specifically, if a concept
class is learnable by a (non-private) algorithm with polynomial sample
complexity and output size, then it can be learned privately using a polynomial
number of samples. We also present a computationally efficient private PAC
learner for the class of parity functions. Local (or randomized response)
algorithms are a practical class of private algorithms that have received
extensive investigation. We provide a precise characterization of local private
learning algorithms. We show that a concept class is learnable by a local
algorithm if and only if it is learnable in the statistical query (SQ) model.
Finally, we present a separation between the power of interactive and
noninteractive local learning algorithms.
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Comments:
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35 pages, 2 figures
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Subjects:
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Learning (cs.LG); Computational
Complexity (cs.CC); Cryptography and Security (cs.CR); Databases (cs.DB)
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Journal reference:
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SIAM Journal of Computing 40(3)
(2011) 793-826
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Cite as:
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arXiv:0803.0924 [cs.LG]
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(or arXiv:0803.0924v3
[cs.LG] for this version)
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Referent from http://arxiv.org/abs/0803.0924
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