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The term ``sequential Monte Carlo methods'' or, equivalently, ``particle filters,'' refers to a general class of iterative algorithms that performs Monte Carlo approximations of a given sequence of distributions of interest (\pi_t). We…
Conformal prediction is a simple and powerful tool that can quantify uncertainty without any distributional assumptions. Many existing methods only address the average coverage guarantee, which is not ideal compared to the stronger…
Hierarchical clustering and community detection are important problems in machine learning and complex network analysis. A common approach to identify clusters is to simply cut dendrograms at some threshold. However, single-level cuts are…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper…
We apply the Adaptive Multilevel Splitting method to the Ceq -> Cax transition of alanine dipeptide in vacuum. Some properties of the algorithm are numerically illustrated, such as the unbiasedness of the probability estimator and the…
The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the…
We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
Sequential Monte Carlo (SMC) methods represent a classical set of techniques to simulate a sequence of probability measures through a simple selection/mutation mechanism. However, the associated selection functions and mutation kernels…
We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$…
Bayesian mixture models are widely applied for unsupervised learning and exploratory data analysis. Markov chain Monte Carlo based on Gibbs sampling and split-merge moves are widely used for inference in these models. However, both methods…
A framework is introduced for actively and adaptively solving a sequence of machine learning problems, which are changing in bounded manner from one time step to the next. An algorithm is developed that actively queries the labels of the…
The efficient approximation of quantity of interest derived from PDEs with lognormal diffusivity is a central challenge in uncertainty quantification. In this study, we propose a multilevel quasi-Monte Carlo framework to approximate…
In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Levy processes that is based on the Wiener-Hopf decomposition. We pursue this idea further by combining their technique with the recently…
Reaction networks in the bulk and on surfaces are widespread in physical, chemical and biological systems. In macroscopic systems, which include large populations of reactive species, stochastic fluctuations are negligible and the reaction…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many…