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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 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)
- Chun-Liang Li, Kirthevasan Kandasamy, Barnabás Póczos, Jeff G. Schneider
- AISTATS
- 2016
Bayesian Optimization (BO) is commonly used to optimize blackbox objective functions which are expensive to evaluate. A common approach is based on using Gaussian Process (GP) to model the objective function. Applying GP to higher dimensional settings is generally difficult due to the curse of dimen-sionality for nonparametric regression. Existing works… (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 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)
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)
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 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)
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)
Bandit methods for black-box optimisation, such as Bayesian optimisation, are used in a variety of applications including hyper-parameter tuning and experiment design. Recently, multifidelity methods have garnered considerable attention since function evaluations have become increasingly expensive in such applications. Multifidelity methods use cheap… (More)