
Almost Optimal Distributionfree Junta Testing
We consider the problem of testing whether an unknown nvariable Boolean...
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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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NearOptimal Algorithm for DistributionFree Junta Testing
In this paper, We firstly present an algorithm for the problem of distri...
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Symmetries: From Proofs To Algorithms And Back
We call an objective function or algorithm symmetric with respect to an ...
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An FDR upper bound for an adaptive oneway GBH procedure under exchangeability
There has been some numerical evidence on the conservativeness of an ada...
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Improved Bounds for Testing Forbidden Order Patterns
A sequence f{1,...,n}→R contains a permutation π of length k if there ex...
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An Upper Bound of the Bias of NadarayaWatson Kernel Regression under Lipschitz Assumptions
The NadarayaWatson kernel estimator is among the most popular nonparame...
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Strongly Sublinear Algorithms for Testing Pattern Freeness
Given a permutation π:[k] → [k], a function f:[n] →ℝ contains a πappearance if there exists 1 ≤ i_1 < i_2 < … < i_k ≤ n such that for all s,t ∈ [k], it holds that f(i_s) < f(i_t) if and only if π(s) < π(t). The function is πfree if it has no πappearances. In this paper, we investigate the problem of testing whether an input function f is πfree or whether at least ε n values in f need to be changed in order to make it πfree. This problem is a generalization of the wellstudied monotonicity testing and was first studied by Newman, Rabinovich, Rajendraprasad and Sohler (Random Structures and Algorithms 2019). We show that for all constants k ∈ℕ, ε∈ (0,1), and permutation π:[k] → [k], there is a onesided error εtesting algorithm for πfreeness of functions f:[n] →ℝ that makes Õ(n^o(1)) queries. We improve significantly upon the previous best upper bound O(n^1  1/(k1)) by BenEliezer and Canonne (SODA 2018). Our algorithm is adaptive, while the earlier best upper bound is known to be tight for nonadaptive algorithms. Hence, our results also show that adaptivity helps in testing freeness of order patterns.
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