
Distributionfree Junta Testing
We study the problem of testing whether an unknown nvariable Boolean fu...
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Almost Optimal Distributionfree Junta Testing
We consider the problem of testing whether an unknown nvariable Boolean...
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The Power of Many Samples in Query Complexity
The randomized query complexity R(f) of a boolean function f{0,1}^n→{0,1...
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An Optimal Tester for kLinear
A Boolean function f:{0,1}^n→{0,1} is klinear if it returns the sum (ov...
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Is your function lowdimensional?
We study the problem of testing if a function depends on a small number ...
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Hard properties with (very) short PCPPs and their applications
We show that there exist properties that are maximally hard for testing,...
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Learning Sparse Additive Models with Interactions in High Dimensions
A function f: R^d →R is referred to as a Sparse Additive Model (SPAM), i...
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DistributionFree Testing of Linear Functions on R^n
We study the problem of testing whether a function f:R^n>R is linear (i.e., both additive and homogeneous) in the distributionfree property testing model, where the distance between functions is measured with respect to an unknown probability distribution over R. We show that, given query access to f, sampling access to the unknown distribution as well as the standard Gaussian, and eps>0, we can distinguish additive functions from functions that are epsfar from additive functions with O((1/eps)log(1/eps)) queries, independent of n. Furthermore, under the assumption that f is a continuous function, the additivity tester can be extended to a distributionfree tester for linearity using the same number of queries. On the other hand, we show that if we are only allowed to get values of f on sampled points, then any distributionfree tester requires Omega(n) samples, even if the underlying distribution is the standard Gaussian.
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