# Nikolas Kantas's research while affiliated with Imperial College London and other places

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## Publications (42)

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the...

The mirror descent algorithm is known to be effective in applications where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed optimization problems has not been previously addressed. In this paper we propose and study exact distributed mir...

A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for this gradient in terms of the solution to an appropriate Poisson equation and show that it can be approximated by...

We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can have a cost that scales exponentially with the dimension of the hidden state. Inspired by lag-approximation me...

In this paper, we consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We first establish consistency and asymptotic normality of the offline maximum likelihood estimator for the interacting particle system in the limit as the number of particles $N\rightarr...

We fitted a model of SARS-CoV-2 transmission in care homes and the community to regional surveillance data for England. Compared with other approaches, our model provides a synthesis of multiple surveillance data streams into a single coherent modelling framework allowing transmission and severity to be disentangled from features of the surveillanc...

An open problem in optimization with noisy information is the computation of an exact minimizer that is independent of the amount of noise. A standard practice in stochastic approximation algorithms is to use a decreasing step-size. This however leads to a slower convergence. A second alternative is to use a fixed step-size and run independent repl...

We fitted a model of SARS-CoV-2 transmission in care homes and the community to regional surveillance data for England. Among control measures implemented, only national lockdown brought the reproduction number below 1 consistently; introduced one week earlier it could have reduced first wave deaths from 36,700 to 15,700 (95%CrI: 8,900–26,800). Imp...

We consider the problem of parameter estimation for a class of continuous-time state space models (SSMs). In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a standard identity of the score function, we consider two particle filter based methodologies to estimat...

In this paper, we consider the problem of jointly performing online parameter estimation and optimal sensor placement for a partially observed infinite dimensional linear diffusion process. We present a novel solution to this problem in the form of a continuous-time, two-timescale stochastic gradient descent algorithm, which recursively seeks to ma...

We consider the problem of parameter estimation for a class of continuous-time state space models. In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a standard identity of the score function, we consider two particle filter based methodologies to estimate the s...

In this paper, we establish the almost sure convergence of two-timescale stochastic gradient descent algorithms in continuous time under general noise and stability conditions, extending well known results in discrete time. We analyse algorithms with both additive noise, and those with non-additive noise. In the non-additive case, our analysis is c...

An open problem in optimization with noisy information is the computation of an exact minimizer that is independent of the amount of noise. A standard practice in stochastic approximation algorithms is to use a decreasing step-size. However, to converge the step-size must decrease exponentially slow, and therefore this approach is not useful in pra...

In this paper, we consider the generalised (higher order) Langevin equation for the purpose of simulated annealing and optimisation of nonconvex functions. Our approach modifies the underdamped Langevin equation by replacing the Brownian noise with an appropriate Ornstein-Uhlenbeck process to account for memory in the system. Under reasonable condi...

We investigate how vector auto‐regressive models can be used to study the soybean crush spread. By crush spread we mean a time series marking the difference between a weighted combination of the value of soymeal and soyoil to the value of the original soybeans. Commodity industry practitioners often use fixed prescribed values for these weights, wh...

An open problem in machine learning is whether flat minima generalize better and how to compute such minima efficiently. This is a very challenging problem. As a first step towards understanding this question we formalize it as an optimization problem with weakly interacting agents. We review appropriate background material from the theory of stoch...

The multi-armed bandit (MAB) problem is a classic example of the exploration-exploitation dilemma. It is concerned with maximising the total rewards for a gambler by sequentially pulling an arm from a multi-armed slot machine where each arm is associated with a reward distribution. In static MABs, the reward distributions do not change over time, w...

We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather prediction and climate modelling, where similar models are used for unknown ocean or wind velocities. We present a...

Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigen-function and eigenvalue of a nonnegative integral kernel. Except in the finite-dimensional case, usually neither the principal eigenfunction nor the eigenvalue can be computed exactly. In this paper, we develop numerical ap...

We consider multivariate time series that exhibit reduced rank cointegration, which means a lower dimensional linear projection of the process becomes stationary. We will review recent suitable Markov Chain Monte Carlo approaches for Bayesian inference such as the Gibbs sampler of [41] and the Geodesic Hamiltonian Monte Carlo method of [3]. Then we...

In this paper we develop an analysis of multivariate time series that exhibit reduced rank cointegration, implying that a lower dimensional linear projection of the process can be obtained in which the projected process becomes stationary. Detection of the rank and basis upon which to project the process for stationarity to hold is a critical probl...

We apply stochastic Lyapunov theory to perform stability analysis of MPC controllers for nonlinear deterministic systems where the underlying optimisation algorithm is based on Markov Chain Monte Carlo (MCMC) or other stochastic methods. We provide a set of assumptions and conditions required for employing the approximate value function obtained as...

Nonlinear non-Gaussian state-space models are ubiquitous in statistics,
econometrics, information engineering and signal processing. Particle methods,
also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical
approximations to the associated state inference problems. However, in most
applications, the state-space model of inter...

We consider the inverse problem of estimating the initial condition of a
partial differential equation, which is only observed through noisy
measurements at discrete time intervals. In particular, we focus on the case
where Eulerian measurements are obtained from the time and space evolving
vector field, whose evolution obeys the two-dimensional Na...

In this article we focus on Maximum Likelihood estimation (MLE) for the static model parameters of hidden Markov models (HMMs). We will consider the case where one cannot or does not want to compute the conditional likelihood density of the observation given the hidden state because of increased computational complexity or analytical intractability...

In the following article we consider approximate Bayesian parameter
inference for observation driven time series models. Such statistical
models appear in a wide variety of applications, including econometrics
and applied mathematics. This article considers the scenario where the
likelihood function cannot be evaluated point-wise; in such cases, on...

In this article we focus on Maximum Likelihood estimation (MLE) for the
static parameters of hidden Markov models (HMMs). We will consider the case
where one cannot or does not want to compute the conditional likelihood density
of the observation given the hidden state because of increased computational
complexity or analytical intractability. Inst...

We show that the sensor self-localization problem can be cast as a
static parameter estimation problem for Hidden Markov Models and we
implement fully decentralized versions of the Recursive Maximum
Likelihood and on-line Expectation-Maximization algorithms to localize
the sensor network simultaneously with target tracking. For linear
Gaussian mode...

Perron-Frobenius theory treats the existence of a positive eigen-vector
associated with the principal eigen-value \lambda_{\star} of a non-negative
matrix, say Q . A simple method for approximating this eigen-vector involves
computing the iterate \lambda_{\star}^{-n}Q^{(n)}, for large n. In the more
general case that Q is a non-negative integral ke...

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and is stopped or killed at the first hitting time of a known set A. Such processes occur naturally within the context of population genetics [25, 15], statistical analysis of rare events [9, 17, 23], finance [7] a...

We consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B
0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally within the context of a wide variety of applications. The associated posterior distributions are highly complex and posterior pa...

This article establishes sufficient conditions for a linear-in-time bound on
the non-asymptotic variance of particle approximations of time-homogeneous
Feynman-Kac formulae. These formulae appear in a wide variety of applications
including option pricing in finance and risk sensitive control in engineering.
In direct Monte Carlo approximation of th...

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, provide very good numerical approximations to the associated optimal state estimation problems. However, in many scenarios, the state-space model of interest also depends on...

Recursive maximum likelihood (RML) and expectation maximization (EM) are a popular methodologies for estimating unknown static parameters in state-space models. We describe how a completely decentralized version of RML and EM can be implemented in dynamic graphical models through the propagation of suitable messages that are exchanged between neigh...

We describe how a completely decentralized version of Recursive Maximum Likelihood (RML) can be implemented in dynamic graphical models through the propagation of suitable messages that are exchanged between neighbouring nodes of the graph. The resulting algorithm can be interpreted as a generalization of the celebrated belief propagation algorithm...

Recursive maximum likelihood (RML) is a popular methodology for estimating unknown static parameters in state-space models. We describe how a completely decentralized version of RML can be implemented in dynamic graphical models through the propagation of suitable messages that are exchanged between neighbouring nodes of the graph. The resulting al...

In this paper we investigate the use of Model Predic-tive control for Markov Decision Processes under weak assump-tions. We provide conditions for stability based on optimality of a specific class of cost functions. These results are useful from both a theoretical and computational perspective. When nonlinear non-Gaussian models for general state s...

## Citations

... This can be quite non-trivial to achieve and, in some scenarios such as when the target density is multimodal, rather inefficient, leading to large variances in estimation. This was partially addressed in [35] which considered an unbiased version of the Schrödinger-Föllmer sampler (SFS). The latter is a diffusion process on a bounded time domain [0, 1], that transports a degenerate distribution at 0, to the target of interest, assuming that the latter is absolutely continuous w.r.t. a d−dimensional standard Gaussian. ...

... Statistical modeling of spatio-temporal data has been extensively investigated in physical science, engineering, and environment, e.g., the modeling of temperature fields (Guinness and Stein, 2013;Kuusela and Stein, 2018;Vandeskog et al., 2013), polutant propagation (Huang and Hsu, 2004;Schliep et al., 2020;Fioravanti et al., 2022), wildfires, precipitation and extreme weather events (Cooley et al., 2007;Heaton et al., 2011;Kleiber et al., 2012;Liu et al., 2018;Bopp et al., 2021;Wei et al., 2022), biomedical and remotesensing images (Kang et al., 2011;Katzfuss and Cressie, 2011;Hefley et al., 2017;Reich et al., 2018;Castruccio et al., 2018;Zammit-Mangion et al., 2021), sensor placement and spatial design (Zimmerman, 2006;Zimmerman and Buckland, 2019;Sharrock and Kantas, 2022) etc. In particular, for spatio-temporal data arising from advection-diffusion processes, a class of physics-informed statistical modeling approach has been proposed which represents the spatial process by its (truncated) Fourier series and let the governing physics (usually Partial Differential Equations (PDE)) determine the stochastic temporal dynamics of the spectral coefficients (Cressie and Wikle, 2011;Sigrist et al., 2015;Kutz et al., 2016;Liu et al., 2021). ...

... To estimate these parameters we focus on maximum likelihood inference and stochastic gradient methods that are performed in an online manner. Mainly, we follow a recursive maximum likelihood (RML) method, which has been proposed originally in [1], in [29] for finite spaces, and in [3,15,35] in the context of sequential Monte Carlo (SMC) approximations. Let ...

... In populations naive for SARS-CoV-2, age is the major epidemiological risk factor for hospitalization or death from pneumonia, with the risk doubling every 5 yr of age, from childhood onward (O'Driscoll et al., 2021). The pediatric population is, therefore, generally considered "safe," with an IFR of ∼0.001%, and a frequency of critical pneumonia thought to be on the order of 0.01%, but which remains to be estimated accurately (Knock et al., 2021;Le Vu et al., 2021). The risks of comorbidities and auto-Abs against type I IFNs both increase with age (Bastard et al., 2021a;Manry et al., 2022), whereas the levels of tonic type I IFN immunity in the respiratory tract decrease with age (Loske et al., 2021), and the production of type I IFN by pDCs is stronger in children than in adults (Splunter et al., 2019). ...

... Those who have moved to the clinical infectious group then leave it with rate γ C (1/ 4 [6]). Of them, an age-dependent fraction h 1,i subsequently require hospitalization, and a fraction h 2,i of that compartment will progress further to ICU [34]. We assume that transmission from hospitalized individuals is negligible as they are isolated. ...

... It is well known that this non-reversible diffusion converges faster to π β , and admits a lower asymptotic variance, than its reversible counterpart (Hwang et al., 2005;Duncan et al., 2016). One can also consider a system of diffusions, interacting via a matrix A, which also exhibit improved convergence properties (Borovykh et al., 2021). Given these results, it is natural to ask whether is it possible to determine an optimal perturbation, or an optimal interaction matrix. ...

... There is very limited study on nonlinear stochastic model predictive control. The stability of nonlinear SMPC using Markov chain Monte Carlo optimization is discussed in [32]. The nonlinear systems with Markov switching properties is investigated in [33]. ...

... In this paper, we formulate the adaptive channel hoping problem in TSCH-networks as a Dynamic Multi-Armed Bernoulli Bandit (Dynamic MABB) process [22] which is one of the many non-stationary variants [23] of the classical MAB specifically tailored for MABs with Bernoulli rewards/penalties. In the context of our problem, the sequence of rewards/penalties gained from each arm (channel) indeed forms a Bernoulli process (corresponding to successful/unsuccessful packet transmissions) with an unknown distribution. ...

... For example, Gibbs Sampling: BVAR (see,Karlsson (2012)) and DFM (see,Blake and Mumtaz (2012)); Metropolis-Hastings algorithm: DSGE (see,Herbst and Schorfheide (2016)); Hamiltonian Monte Carlo: Cointegrated BVAR (see,Marowka, Peters, Kantas and Bagnarosa (2017)); No-U-Turn Sampling: SVMA (see, Plagborg-Moller (2016)); Sequential Monte Carlo: DSGE (see,Herbst and Schorfheide (2015)) and ABM (see,Lux (2018)).5 We treat variance of prior for each coefficient and degrees of freedom for t-Student distribution as hyperparameters. ...

... The addition of mutation steps has been shown to be, in many cases, critical, both in theoretical and experimental works, see e.g. Beskos et al. (2014); Ruzayqat et al. (2021) and Llopis et al. (2018); van Leeuwen et al. (2021), respectively. In Section 3.2.4, ...