921 citations · 1.7k across the 59 of their papers we have counts for
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Minimax Estimation of Discrete Distributions under Loss
Yanjun Han, Jiantao Jiao, Tsachy Weissman
We analyze the problem of discrete distribution estimation under loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (…
Beyond Maximum Likelihood: from Theory to Practice
Jiantao Jiao, Kartik Venkat, Yanjun Han +1
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for func…
Maximum Likelihood Estimation of Functionals of Discrete Distributions
Jiantao Jiao, Kartik Venkat, Yanjun Han +1
We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimator…
Minimax Estimation of Functionals of Discrete Distributions
Jiantao Jiao, Kartik Venkat, Yanjun Han +1
We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case…
An Extremal Inequality for Long Markov Chains
Thomas Courtade, Jiantao Jiao
Let be jointly Gaussian vectors, and consider random variables that satisfy the Markov constraint . We prove an extremal inequality relating the mutual informa…
Relations between Information and Estimation in Discrete-Time Lévy Channels
Jiantao Jiao, Kartik Venkat, Tsachy Weissman
Fundamental relations between information and estimation have been established in the literature for the discrete-time Gaussian and Poisson channels. In this work, we demonstrate t…
Information Measures: the Curious Case of the Binary Alphabet
Jiantao Jiao, Thomas Courtade, Albert No +2
Four problems related to information divergence measures defined on finite alphabets are considered. In three of the cases we consider, we illustrate a contrast which arises betwee…
Justification of Logarithmic Loss via the Benefit of Side Information
Jiantao Jiao, Thomas Courtade, Kartik Venkat +1
We consider a natural measure of relevance: the reduction in optimal prediction risk in the presence of side information. For any given loss function, this relevance measure captur…