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TR02-060 | 15th July 2002 00:00
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#### New Lower Bounds for Statistical Query Learning

TR02-060
Authors:

Ke Yang
Publication: 3rd November 2002 19:32

Downloads: 1979

Keywords:

**Abstract:**
We prove two lower bounds on the Statistical Query (SQ) learning

model. The first lower bound is on weak-learning. We prove that for a

concept class of SQ-dimension $d$, a running time of

$\Omega(d/\log d)$ is needed. The SQ-dimension of a concept class is

defined to be the maximum number of concepts that are ``uniformly

correlated'', in that each pair of them have nearly the same

correlation. This lower bound matches the upper bound

in~\cite{BFJ+94}, up to a logarithmic factor. We prove this lower

bound against an ``honest SQ-oracle'', which gives a stronger result

than the ones against the more frequently used ``adversarial

SQ-oracles''. The second lower bound is more general. It gives a

continuous trade-off between the ``advantage'' of an algorithm in

learning the target function and the number of queries it needs to

make, where the advantage of an algorithm is the probability it

succeeds in predicting a label minus the probability it doesn't.

Both lower bounds extend and/or strengthen previous results, and

solved an open problem left in~\cite{Y01}.

A preliminary version of this paper appeared in

the Proceedings of the Fifteenth Annual Conference on

Computational Learning Theory, 2002 (COLT 2002)