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Electronic Colloquium on Computational Complexity

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All reports by Author Clement Canonne:

TR18-079 | 19th April 2018
Jayadev Acharya, Clement Canonne, Himanshu Tyagi

Distributed Simulation and Distributed Inference

Revisions: 1

Independent samples from an unknown probability distribution $\mathbf{p}$ on a domain of size $k$ are distributed across $n$ players, with each player holding one sample. Each player can communicate $\ell$ bits to a central referee in a simultaneous message passing (SMP) model of communication to help the referee infer a ... 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 >>>

TR17-029 | 18th February 2017
Clement Canonne, Tom Gur

An Adaptivity Hierarchy Theorem for Property Testing

Revisions: 1

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of \emph{adaptive} testing algorithms, wherein each query may be determined by the answers received to prior queries, and their \emph{non-adaptive} counterparts, in which all ... more >>>

TR16-168 | 2nd November 2016
Eric Blais, Clement Canonne, Tom Gur

Alice and Bob Show Distribution Testing Lower Bounds (They don't talk to each other anymore.)

Revisions: 1

We present a new methodology for proving distribution testing lower bounds, establishing a connection between distribution testing and the simultaneous message passing (SMP) communication model. Extending the framework of Blais, Brody, and Matulef [BBM12], we show a simple way to reduce (private-coin) SMP problems to distribution testing problems. This method ... more >>>

TR16-136 | 31st August 2016
Clement Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, Karl Wimmer

Testing k-Monotonicity

Revisions: 1

A Boolean $k$-monotone function defined over a finite poset domain ${\cal D}$ alternates between the values $0$ and $1$ at most $k$ times on any ascending chain in ${\cal D}$. Therefore, $k$-monotone functions are natural generalizations of the classical monotone functions, which are the $1$-monotone functions.

Motivated by the ... more >>>

TR16-105 | 13th July 2016
Eric Blais, Clement Canonne, Talya Eden, Amit Levi, Dana Ron

Tolerant Junta Testing and the Connection to Submodular Optimization and Function Isomorphism

Revisions: 1

The function $f\colon \{-1,1\}^n \to \{-1,1\}$ is a $k$-junta if it depends on at most $k$ of its variables. We consider the problem of tolerant testing of $k$-juntas, where the testing algorithm must accept any function that is $\epsilon$-close to some $k$-junta and reject any function that is $\epsilon'$-far from ... more >>>

TR15-160 | 30th September 2015
Clement Canonne

Are Few Bins Enough: Testing Histogram Distributions

Revisions: 1

A probability distribution over an ordered universe $[n]=\{1,\dots,n\}$ is said to be a $k$-histogram if it can be represented as a piecewise-constant function over at most $k$ contiguous intervals. We study the following question: given samples from an arbitrary distribution $D$ over $[n]$, one must decide whether $D$ is a ... more >>>

TR15-063 | 15th April 2015
Clement Canonne

A Survey on Distribution Testing: Your Data is Big. But is it Blue?

Revisions: 1

The field of property testing originated in work on program checking, and has evolved into an established and very active research area. In this work, we survey the developments of one of its most recent and prolific offspring, distribution testing. This subfield, at the junction of property testing and Statistics, ... more >>>

TR14-156 | 26th November 2014
Jayadev Acharya, Clement Canonne, Gautam Kamath

A Chasm Between Identity and Equivalence Testing with Conditional Queries

Revisions: 2

A recent model for property testing of probability distributions enables tremendous savings in the sample complexity of testing algorithms, by allowing them to condition the sampling on subsets of the domain.
In particular, Canonne et al. showed that, in this setting, testing identity of an unknown distribution $D$ (i.e., ... more >>>

TR14-153 | 14th November 2014
Clement Canonne, Venkatesan Guruswami, Raghu Meka, Madhu Sudan

Communication with Imperfectly Shared Randomness

Revisions: 2

The communication complexity of many fundamental problems reduces greatly
when the communicating parties share randomness that is independent of the
inputs to the communication task. Natural communication processes (say between
humans) however often involve large amounts of shared correlations among the
communicating players, but rarely allow for perfect sharing of ... more >>>

TR14-144 | 30th October 2014
Eric Blais, Clement Canonne, Igor Carboni Oliveira, Rocco Servedio, Li-Yang Tan

Learning circuits with few negations

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and ... more >>>

TR14-021 | 18th February 2014
Clement Canonne, Ronitt Rubinfeld

Testing probability distributions underlying aggregated data

In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution $D$ over $[n]$. More precisely, we define both the dual and extended ... more >>>

TR12-155 | 15th November 2012
Clement Canonne, Dana Ron, Rocco Servedio

Testing probability distributions using conditional samples

Revisions: 1

We study a new framework for property testing of probability distributions, by considering distribution testing algorithms that have access to a conditional sampling oracle. \footnote{Independently from our work, Chakraborty et al. [CFGM13] also considered this framework. We discuss their work in Subsection 1.4.} This is an oracle that takes as ... more >>>

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