
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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A Predictive Model using the Markov Property
Given a data set of numerical values which are sampled from some unknown...
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Active Local Learning
In this work we consider active local learning: given a query point x, a...
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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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Identity testing under label mismatch
Testing whether the observed data conforms to a purported model (probabi...
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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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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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