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Optimal Testing for Properties of Distributions
TLDR
This work provides a general approach via which sample-optimal and computationally efficient testers for discrete log-concave and monotone hazard rate distributions are obtained. Expand
A Unified Maximum Likelihood Approach for Estimating Symmetric Properties of Discrete Distributions
TLDR
It is shown that a single, simple, plug-in estimator—profile maximum likelihood (PML)– is sample competitive for all symmetric properties, and in particular is asymptotically sampleoptimal for all the above properties. Expand
Multilevel thresholding for image segmentation through a fast statistical recursive algorithm
TLDR
A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance, making use of the fact that a number of distributions tend towards Dirac delta function, peaking at the mean, in the limiting condition of vanishing variance. Expand
Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communication
TLDR
Hadamard Response (HR) is proposed, a local privatization scheme that requires no shared randomness and is symmetric with respect to the users, and which runs about 100x faster than Randomized Response, RAPPOR, and subset-selection mechanisms. Expand
Near-Optimal-Sample Estimators for Spherical Gaussian Mixtures
TLDR
The first sample-efficient polynomial-time estimator for high-dimensional spherical Gaussian mixtures is derived, and it is shown that any estimator requires Ω(dk/e2) samples, hence the algorithm's sample complexity is nearly optimal in the dimension. Expand
Sample-Optimal Density Estimation in Nearly-Linear Time
TLDR
The work resolves the sample and computational complexities of a broad class of inference tasks via a single "meta-algorithm" that yields (nearly) sample-optimal and nearly-linear time estimators for a wide range of structured distribution families over both continuous and discrete domains in a unified way. Expand
Testing Poisson Binomial Distributions
TLDR
The sample complexity of this algorithm improves quadratically upon that of the naive "learn followed by tolerant-test" approach, while instance optimal identity testing [VV14] is not applicable since it is looking to simultaneously test against a whole family of distributions. Expand
Estimating Renyi Entropy of Discrete Distributions
TLDR
Developing on a recently established connection between polynomial approximation and estimation of additive functions of the form, the lower bounds provide explicit constructions of distributions with different Rényi entropies that are hard to distinguish. Expand
Differentially Private Testing of Identity and Closeness of Discrete Distributions
TLDR
The fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over $k$ elements, under differential privacy are studied, and Le Cam's two point theorem is used to provide a general mechanism for proving lower bounds. Expand
INSPECTRE: Privately Estimating the Unseen
TLDR
Almost-tight bounds on the sample size required for this problem for several functionals of interest, including support size, support coverage, and entropy are proved. Expand
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