Jan Arpe, RĂ¼diger Reischuk

Detecting the relevant attributes of an unknown target concept

is an important and well studied problem in algorithmic learning.

Simple greedy strategies have been proposed that seem to perform reasonably

well in practice if a sufficiently large random subset of examples of the target

concept is provided.

Introducing a ... more >>>

Bireswar Das, Manjish Pal, Vijay Visavaliya

In this paper, we prove that most of the boolean functions, $f : \{-1,1\}^n \rightarrow \{-1,1\}$

satisfy the Fourier Entropy Influence (FEI) Conjecture due to Friedgut and Kalai (Proc. AMS'96)\cite{FG96}. The conjecture says that the Entropy of a boolean function is at most a constant times the Influence of ...
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Swagato Sanyal

We prove that the Fourier dimension of any Boolean function with

Fourier sparsity $s$ is at most $O\left(s^{2/3}\right)$. Our proof

method yields an improved bound of $\widetilde{O}(\sqrt{s})$

assuming a conjecture of Tsang~\etal~\cite{tsang}, that for every

Boolean function of sparsity $s$ there is an affine subspace of

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Venkatesan Guruswami, Rishi Saket

A hypergraph is $k$-rainbow colorable if there exists a vertex coloring using $k$ colors such that each hyperedge has all the $k$ colors. Unlike usual hypergraph coloring, rainbow coloring becomes harder as the number of colors increases. This work studies the rainbow colorability of hypergraphs which are guaranteed to be ... more >>>

Shafi Goldwasser, Guy Rothblum, Jonathan Shafer, Amir Yehudayoff

We consider the following question: using a source of labeled data and interaction with an untrusted prover, what is the complexity of verifying that a given hypothesis is "approximately correct"? We study interactive proof systems for PAC verification, where a verifier that interacts with a prover is required to accept ... more >>>