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We propose a general framework for the construction and analysis of minimax estimators for a wide class of functionals of discrete distributions, where the alphabet size S is unknown and may be scaling with the number of observations n. We treat the respective regions where the functional is " nonsmooth " and " smooth " separately. In the " nonsmooth "… (More)

- Yanjun Han, Qing Tao, Jue Wang
- NIPS
- 2010

In multi-instance learning, there are two kinds of prediction failure, i.e., false negative and false positive. Current research mainly focus on avoiding the former. We attempt to utilize the geometric distribution of instances inside positive bags to avoid both the former and the latter. Based on kernel principal component analysis, we define a projection… (More)

We consider the problem of estimating the KL divergence between two discrete probability measures P and Q from empirical data in a non-asymptotic and possibly large alphabet setting. We construct minimax rate-optimal estimators for D(P Q) when the likelihood ratio is upper bounded by a constant which may depend on the support size, and show that the… (More)

—Although the bag-of-visual-words (BoW) representation has received wide application, it ignores the spatial information. To tackle this problem, we propose to use 'components' as the higher-level visual elements to represent images. Then we formulate object recognition into a bi-linear model along with sparsity constraints to indicate two progressive… (More)

—The free-space optical (FSO) communications can achieve high capacity with huge unlicensed optical spectrum and low operational costs. The corresponding performance analysis of FSO systems over turbulence channels is very limited, especially when using multiple apertures at both transmitter and receiver sides. This paper aim to provide the ergodic capacity… (More)

Maximum likelihood is the most widely used statistical estimation technique. Recent work by Jiao, Venkat, Han, and Weissman [1] introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements-both in theory and in practice-over the maximum likelihood estimator (MLE), particularly in… (More)

We consider estimating the Shannon entropy of a discrete distribution P from n i. constructed approximation theoretic estimators that achieve the minimax L2 rates in estimating entropy. Their estimators are consistent given n S ln S samples, where S is the alphabet size, and it is the best possible sample complexity. In contrast, the Maximum Likelihood… (More)

The Dirichlet prior is widely used in estimating discrete distributions and functionals of discrete distributions. In terms of Shannon entropy estimation, one approach is to plug-in the Dirichlet prior smoothed distribution into the entropy functional, while the other one is to calculate the Bayes estimator for entropy under the Dirichlet prior for squared… (More)