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Electronic Colloquium on Computational Complexity

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All reports by Author Alistair Stewart:

TR17-132 | 7th September 2017
Ilias Diakonikolas, Daniel Kane, Alistair Stewart

Sharp Bounds for Generalized Uniformity Testing

We study the problem of {\em generalized uniformity testing}~\cite{BC17} of a discrete probability distribution: Given samples from a probability distribution $p$ over an {\em unknown} discrete domain $\mathbf{\Omega}$, we want to distinguish, with probability at least $2/3$, between the case that $p$ is uniform on some {\em subset} of $\mathbf{\Omega}$ ... more >>>

TR17-075 | 29th April 2017
Clement Canonne, Ilias Diakonikolas, Alistair Stewart

Fourier-Based Testing for Families of Distributions

Revisions: 1

We study the general problem of testing whether an unknown discrete distribution belongs to a given family of distributions. More specifically, given a class of distributions $\mathcal{P}$ and sample access to an unknown distribution $\mathbf{P}$, we want to distinguish (with high probability) between the case that $\mathbf{P} \in \mathcal{P}$ and ... more >>>

TR16-177 | 11th November 2016
Ilias Diakonikolas, Daniel Kane, Alistair Stewart

Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixtures

Revisions: 1

We prove the first {\em Statistical Query lower bounds} for two fundamental high-dimensional learning problems involving Gaussian distributions: (1) learning Gaussian mixture models (GMMs), and (2) robust (agnostic) learning of a single unknown mean Gaussian. In particular, we show a {\em super-polynomial gap} between the (information-theoretic) sample complexity and the ... more >>>

TR13-069 | 1st May 2013
Kousha Etessami, Alistair Stewart, Mihalis Yannakakis

A note on the complexity of comparing succinctly represented integers, with an application to maximum probability parsing

The following two decision problems capture the complexity of
comparing integers or rationals that are succinctly represented in
product-of-exponentials notation, or equivalently, via arithmetic
circuits using only multiplication and division gates, and integer

Input instance: four lists of positive integers:

$a_1, \ldots , a_n; \ b_1, \ldots ,b_n; \ ... more >>>

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