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We consider nonparametric estimation of L 2 , Rényi-α and Tsallis-α divergences between continuous distributions. Our approach is to construct estimators for particular integral function-als of two densities and translate them into divergence estimators. For the integral function-als, our estimators are based on corrections of a preliminary plug-in… (More)

Bayesian Optimisation (BO) is a technique used in optimising a D-dimensional function which is typically expensive to evaluate. While there have been many successes for BO in low dimensions , scaling it to high dimensions has been notoriously difficult. Existing literature on the topic are under very restrictive settings. In this paper, we identify two key… (More)

We propose and analyse estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are derived from the von Mises expansion and are based on the theory of influence functions, which appear in the semiparametric statistics literature. We show that estimators based either on data-splitting or a… (More)

We give a comprehensive theoretical characterization of a nonparametric estimator for the L 2 2 divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is √ n-consistent provided the densities are sufficiently smooth. In this smooth regime, we then show that our estimator is asymptotically… (More)

We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics literature. We show that estimators based either on data-splitting or a leave-one-out technique enjoy fast rates of… (More)

- Kirthevasan Kandasamy, Yaoliang Yu
- ICML
- 2016

High dimensional nonparametric regression is an inherently difficult problem with known lower bounds depending exponentially in dimension. A popular strategy to alleviate this curse of dimensionality has been to use additive models of first order, which model the regression function as a sum of independent functions on each dimension. Though useful in… (More)

We study a variant of the classical stochastic K-armed bandit where observing the outcome of each arm is expensive, but cheap approximations to this outcome are available. For example, in online advertising the performance of an ad can be approximated by displaying it for shorter time periods or to narrower audiences. We formalise this task as a… (More)

In many scientific and engineering applications, we are tasked with the optimisation of an expensive to evaluate black box function f. Traditional methods for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can… (More)

- Kirthevasan Kandasamy, Ranga Rodrigo
- 2010 Fifth International Conference on…
- 2010

The bag of visual words model has seen immense success in addressing the problem of image classification. Algorithms using this model generate the codebook of visual words by vector quantizing the features (such as SIFT) of the images to be classified. However, a codebook so formed tends to get biased by the nature of the dataset. In this paper we propose… (More)

This paper studies active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior… (More)