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Electronic Colloquium on Computational Complexity

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All reports by Author Daniel Kane:

TR24-031 | 22nd February 2024
Daniel Kane, Anthony Ostuni, Kewen Wu

Locality Bounds for Sampling Hamming Slices

Revisions: 1

Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the complexity of computing functions.

We build upon and make explicit earlier implicit results of ... more >>>

TR22-178 | 8th December 2022
Ilias Diakonikolas, Christos Tzamos, Daniel Kane

A Strongly Polynomial Algorithm for Approximate Forster Transforms and its Application to Halfspace Learning

The Forster transform is a method of regularizing a dataset
by placing it in {\em radial isotropic position}
while maintaining some of its essential properties.
Forster transforms have played a key role in a diverse range of settings
spanning computer science and functional analysis. Prior work had given
{\em ... more >>>

TR20-140 | 14th September 2020
Ilias Diakonikolas, Themis Gouleakis, Daniel Kane, John Peebles, Eric Price

Optimal Testing of Discrete Distributions with High Probability

We study the problem of testing discrete distributions with a focus on the high probability regime.
Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and
parameters $0< \epsilon, \delta <1$, we want to distinguish {\em with probability at least $1-\delta$}
whether these distributions satisfy $\mathcal{P}$ ... more >>>

TR18-189 | 8th November 2018
Ilias Diakonikolas, Daniel Kane

Degree-$d$ Chow Parameters Robustly Determine Degree-$d$ PTFs (and Algorithmic Applications)

The degree-$d$ Chow parameters of a Boolean function $f: \bn \to \R$ are its degree at most $d$ Fourier coefficients.
It is well-known that degree-$d$ Chow parameters uniquely characterize degree-$d$ polynomial threshold functions
within the space of all bounded functions. In this paper, we prove a robust ... more >>>

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