All reports by Author Ilias Diakonikolas:

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TR16-178
| 11th November 2016
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Ilias Diakonikolas, Themis Gouleakis, John Peebles, Eric Price#### Collision-based Testers are Optimal for Uniformity and Closeness

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TR16-177
| 11th November 2016
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Ilias Diakonikolas, Daniel Kane, Alistair Stewart#### Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixtures

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TR16-074
| 9th May 2016
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Ilias Diakonikolas, Daniel Kane#### A New Approach for Testing Properties of Discrete Distributions

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TR13-172
| 1st December 2013
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Anindya De, Ilias Diakonikolas, Rocco Servedio#### Deterministic Approximate Counting for Degree-$2$ Polynomial Threshold Functions

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TR13-171
| 1st December 2013
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Anindya De, Ilias Diakonikolas, Rocco Servedio#### Deterministic Approximate Counting for Juntas of Degree-$2$ Polynomial Threshold Functions

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TR12-181
| 20th December 2012
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Anindya De, Ilias Diakonikolas, Rocco Servedio#### The Inverse Shapley Value Problem

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TR12-152
| 7th November 2012
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Anindya De, Ilias Diakonikolas, Rocco Servedio#### Inverse Problems in Approximate Uniform Generation

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TR12-072
| 5th June 2012
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Anindya De, Ilias Diakonikolas, Vitaly Feldman, Rocco Servedio#### Nearly optimal solutions for the Chow Parameters Problem and low-weight approximation of halfspaces

Ilias Diakonikolas, Themis Gouleakis, John Peebles, Eric Price

We study the fundamental problems of (i) uniformity testing of a discrete distribution,

and (ii) closeness testing between two discrete distributions with bounded $\ell_2$-norm.

These problems have been extensively studied in distribution testing

and sample-optimal estimators are known for them~\cite{Paninski:08, CDVV14, VV14, DKN:15}.

In this work, we show ... more >>>

Ilias Diakonikolas, Daniel Kane, Alistair Stewart

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 >>>

Ilias Diakonikolas, Daniel Kane

We study problems in distribution property testing:

Given sample access to one or more unknown discrete distributions,

we want to determine whether they have some global property or are $\epsilon$-far

from having the property in $\ell_1$ distance (equivalently, total variation distance, or ``statistical distance'').

In this work, we give a ...
more >>>

Anindya De, Ilias Diakonikolas, Rocco Servedio

We give a {\em deterministic} algorithm for approximately computing the fraction of Boolean assignments that satisfy a degree-$2$ polynomial threshold function. Given a degree-2 input polynomial $p(x_1,\dots,x_n)$ and a parameter $\eps > 0$, the algorithm approximates

\[

\Pr_{x \sim \{-1,1\}^n}[p(x) \geq 0]

\]

to within an additive $\pm \eps$ in ...
more >>>

Anindya De, Ilias Diakonikolas, Rocco Servedio

Let $g: \{-1,1\}^k \to \{-1,1\}$ be any Boolean function and $q_1,\dots,q_k$ be any degree-2 polynomials over $\{-1,1\}^n.$ We give a \emph{deterministic} algorithm which, given as input explicit descriptions of $g,q_1,\dots,q_k$ and an accuracy parameter $\eps>0$, approximates \[

\Pr_{x \sim \{-1,1\}^n}[g(\sign(q_1(x)),\dots,\sign(q_k(x)))=1] \]

to within an additive $\pm \eps$. For any constant ...
more >>>

Anindya De, Ilias Diakonikolas, Rocco Servedio

For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley ... more >>>

Anindya De, Ilias Diakonikolas, Rocco Servedio

We initiate the study of \emph{inverse} problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform random satisfying assignments of an unknown function $f$ belonging to a class $\C$ of Boolean functions ... more >>>

Anindya De, Ilias Diakonikolas, Vitaly Feldman, Rocco Servedio

The \emph{Chow parameters} of a Boolean function $f: \{-1,1\}^n \to \{-1,1\}$ are its $n+1$ degree-0 and degree-1 Fourier coefficients. It has been known since 1961 \cite{Chow:61, Tannenbaum:61} that the (exact values of the) Chow parameters of any linear threshold function $f$ uniquely specify $f$ within the space of all Boolean ... more >>>