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We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions.
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Polynomial learning of distribution families
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R. Koenker and I. Mizera · 2010
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A. T. Kalai, A. Moitra, and G. Valiant · 2010
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Estimating a mixture of two product distributions
Y. Freund and Y. Mansour · 1999
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A two-round variant of EM for Gaussian mixtures
S. Dasgupta and L. Schulman · 2000
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Learning mixtures of arbitrary Gaussians
S. Arora and R. Kannan · 2001
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Combinatorial methods in density estimation
L. Devroye and G. Lugosi · 2001
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Settling the polynomial learnability of mixtures of Gaussians
A. Moitra and G. Valiant · 2010
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Learning k k -modal distributions via testing
C. Daskalakis, I. Diakonikolas, and R.A. Servedio · 2012
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Learning Poisson Binomial Distributions
C. Daskalakis, I. Diakonikolas, and R.A. Servedio · 2012
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Learning mixtures of structured distributions over discrete domains
S. Chan, I. Diakonikolas, R. Servedio, and X. Sun · 2013
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Smoothed log-concave maximum likelihood estimation with applications
Y. Chen and R. J. Samworth · 2013
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Learning Sums of Independent Integer Random Variables
C. Daskalakis, I. Diakonikolas, R. O’Donnell, R.A. Servedio, and L. Tan · 2013
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Global Rates of Convergence of the MLEs of Log-concave and s s -concave Densities
C. R. Doss and J. A. Wellner · 2013
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Modern computer algebra
J. Von Zur Gathen and J. Gerhard · 2013
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Inference for a Mixture of Symmetric Distributions under Log-Concavity
F. Balabdaoui and C. R. Doss · 2014
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Efficient density estimation via piecewise polynomial approximation
S. Chan, I. Diakonikolas, R. Servedio, and X. Sun · 2014
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Near-optimal density estimation in near-linear time using variable-width histograms
S. Chan, I. Diakonikolas, R. Servedio, and X. Sun · 2014
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Faster and sample near-optimal algorithms for proper learning mixtures of gaussians
C. Daskalakis and G. Kamath · 2014
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Nonparametric Estimation under Shape Constraints: Estimators, Algorithms and Asymptotics
P. Groeneboom and G. Jongbloed · 2014
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Global rates of convergence in log-concave density estimation
A. K. H. Kim and R. J. Samworth · 2014
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Path finding methods for linear programming: Solving linear programs in O ~ rank \widetilde{O}{\sqrt{\textrm{rank}}} iterations and faster algorithms for maximum flow
Y. T. Lee and A. Sidford · 2014
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Near-optimal-sample estimators for spherical gaussian mixtures
A. T. Suresh, A. Orlitsky, J. Acharya, and A. Jafarpour · 2014
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Fast and Near-Optimal Algorithms for Approximating Distributions by Histograms
J. Acharya, I. Diakonikolas, C. Hegde, J. Li, and L. Schmidt · 2015
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Sparse Solutions to Nonegative Linear Systems and Applications
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Sharp bounds for learning a mixture of two gaussians
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Approximation and Estimation of s s -Concave Densities via Renyi Divergences
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A Nearly Optimal and Agnostic Algorithm for Properly Learning a Mixture of k k Gaussians, for any Constant k k
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