Related papers: Smoothing in linear multicompartment biological pr…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has…

The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…

The small noise cut-off phenomenon in continuous time and space has been studied in the recent literature for the linear and non-linear stable Langevin dynamics with additive L\'evy drivers - understood as abrupt thermalization of the…

Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…

In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of…

Waves and oscillations are commonly observed in the dynamics of self-driven agents such as pedestrians or vehicles. Interestingly, many factors may perturb the stability of space homogeneous streaming, leading to the spontaneous formation…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

Investigation of protein self-assembly processes is important for the understanding of the growth processes of functional proteins as well as disease-causing amyloids. Inside cells, intrinsic molecular fluctuations are so high that they…

This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…

This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

Several integrate-to-threshold models with differing temporal integration mechanisms have been proposed to describe the accumulation of sensory evidence to a prescribed level prior to motor response in perceptual decision-making tasks. An…

Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…

We present embedding procedures for the non-Markovian stochastic Schr\"{o}dinger equations, arising from studies of quantum systems coupled with bath environments. By introducing auxiliary wave functions, it is demonstrated that the…

The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…

Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…

Recursive Bayesian filters have been widely deployed in structural system identification where output-only filters are of higher practicality. Unfortunately, the estimation obtained by instantaneous system inversion via filters can be…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…