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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 >>>

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