34 citations · 64 across the 22 of their papers we have counts for
28 papers
Non-asymptotic quantisation of spherically symmetric distributions
Luc Pronzato, Anatoly Zhigljavsky
Zador's celebrated theorem is a cornerstone of optimal quantisation, establishing both the weak limit of the empirical distribution of an -point optimal quantiser in and t…
Maximum mean discrepancies of Farey sequences
Toni Karvonen, Anatoly Zhigljavsky
We identify a large class of positive-semidefinite kernels for which a certain polynomial rate of convergence of maximum mean discrepancies of Farey sequences is equivalent to the…
Covering of high-dimensional sets
Anatoly Zhigljavsky, Jack Noonan
Let be a metric space and be a Borel measure on this space defined on the -algebra generated by open subsets of ; this measure defines vol…
Statistical Modelling for Improving Efficiency of Online Advertising
Irina Scherbakova, Andrey Pepelyshev, Yuri Staroselskiy +2
Real-time bidding has transformed the digital advertising landscape, allowing companies to buy website advertising space in a matter of milliseconds in the time it takes a webpage…
Improving exploration strategies in large dimensions and rate of convergence of global random search algorithms
Jack Noonan, Anatoly Zhigljavsky
We consider global optimization problems, where the feasible region $\X$ is a compact subset of with . For these problems, we demonstrate the following. F…
Quasi-uniform designs with optimal and near-optimal uniformity constant
Luc Pronzato, Anatoly Zhigljavsky
A design is a collection of distinct points in a given set , which is assumed to be a compact subset of , and the mesh-ratio of a design is the ratio of its fill distance t…
Reproducing kernel Hilbert spaces, polynomials and the classical moment problems
Holger Dette, Anatoly Zhigljavsky
We show that polynomials do not belong to the reproducing kernel Hilbert space of infinitely differentiable translation-invariant kernels whose spectral measures have moments corre…
Random and quasi-random designs in group testing
Jack Noonan, Anatoly Zhigljavsky
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random design…
Non-lattice covering and quanitization of high dimensional sets
Jack Noonan, Anatoly Zhigljavsky
The main problem considered in this paper is construction and theoretical study of efficient -point coverings of a -dimensional cube . Targeted values of are be…
Comparison of different exit scenarios from the lock-down for COVID-19 epidemic in the UK and assessing uncertainty of the predictions
Anatoly Zhigljavsky, Roger Whitaker, Ivan Fesenko +2
We model further development of the COVID-19 epidemic in the UK given the current data and assuming different scenarios of handling the epidemic. In this research, we further exten…
Generic probabilistic modelling and non-homogeneity issues for the UK epidemic of COVID-19
Anatoly Zhigljavsky, Roger Whitaker, Ivan Fesenko +10
Coronavirus COVID-19 spreads through the population mostly based on social contact. To gauge the potential for widespread contagion, to cope with associated uncertainty and to info…
Covering of high-dimensional cubes and quantization
Anatoly Zhigljavsky, Jack Noonan
As the main problem, we consider covering of a -dimensional cube by balls with reasonably large (10 or more) and reasonably small , like or . We do no…
Blind deconvolution of covariance matrix inverses for autoregressive processes
Nina Golyandina, Anatoly Zhigljavsky
Matrix can be blindly deconvoluted if there exist matrices and such that , where denotes the o…
Prediction in regression models with continuous observations
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
We consider the problem of predicting values of a random process or field satisfying a linear model , where errors are correlate…
Approximations for the boundary crossing probabilities of moving sums of random variables
Jack Noonan, Anatoly Zhigljavsky
In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal r.v. We approximate a discrete time problem with a continuous time pro…
First passage time for Slepian process with linear barrier
Jack Noonan, Anatoly Zhigljavsky
In this paper we extend results of L.A. Shepp by finding explicit formulas for the first passage probability $F_{a,b}(T\, |\, x)={\rm Pr}(S(t)<a+bt \text{ for all } t\in[0,T]\,\, |…
Approximating Shepp's constants for the Slepian process
Jack Noonan, Anatoly Zhigljavsky
Slepian process is a stationary Gaussian process with zero mean and covariance For any and , define $F_T(h ) = {\rm Pr}\lef…
Approximations for the boundary crossing probabilities of moving sums of normal random variables
Jack Noonan, Anatoly Zhigljavsky
In this paper we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem wi…
Bregman divergences based on optimal design criteria and simplicial measures of dispersion
Luc Pronzato, Henry Wynn, Anatoly Zhigljavsky
In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared v…
Bayesian quadrature and energy minimization for space-filling design
Luc Pronzato, Anatoly Zhigljavsky
A standard objective in computer experiments is to approximate the behaviour of an unknown function on a compact domain from a few evaluations inside the domain. When little is kno…
Best linear unbiased estimators in continuous time regression models
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
In this paper the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form…
Optimal designs for regression models with autoregressive errors structure
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least sq…
A new approach to optimal designs for correlated observations
Holger Dette, Maria Konstantinou, Anatoly Zhigljavsky
This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this…
Optimal designs in regression with correlated errors
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this cha…