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In this paper we focus on the development of new methods suitable for efficient and reliable coarse-graining of {\it non-equilibrium} molecular systems. In this context, we propose error estimation and controlled-fidelity model reduction…
With the growing computational power available for high-resolution ensemble simulations in scientific fields such as cosmology and oceanology, storage and computational demands present significant challenges. Current surrogate models fall…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
Online joint estimation of unknown parameters and states in a dynamical system with uncertainty quantification is crucial in many applications. For example, digital twins dynamically update their knowledge of model parameters and states to…
The study of statistical estimation without distributional assumptions on data values, but with knowledge of data collection methods was recently introduced by Chen, Valiant and Valiant (NeurIPS 2020). In this framework, the goal is to…
A new approach for feature extraction from time series is proposed in this paper. This approach consists of a specific regression model incorporating a discrete hidden logistic process. The model parameters are estimated by the maximum…
This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…
This paper presents parallel-in-time state estimation methods for systems with Slow-Rate inTegrated Measurements (SRTM). Integrated measurements are common in various applications, and they appear in analysis of data resulting from…
In this paper, the parameter estimation of ARMA(p,q) model is given by approximate Bayesian computation algorithm. In order to improve the sampling efficiency of the algorithm, approximate Bayesian computation should select as many…
The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…
A great deal of research has been conducted in the consideration of meta-heuristic optimisation methods that are able to find global optima in settings that gradient based optimisers have traditionally struggled. Of these, so-called…
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model…
Fredholm integral equations of the first kind are the prototypical example of ill-posed linear inverse problems. They model, among other things, reconstruction of distorted noisy observations and indirect density estimation and also appear…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
We develop a fast and scalable computational framework to solve large-scale and high-dimensional Bayesian optimal experimental design problems. In particular, we consider the problem of optimal observation sensor placement for Bayesian…
Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…
A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a…
Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve…
The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a…
We introduce a new method for online parameter estimation in stochastic interacting particle systems, based on continuous observation of a small number of particles from the system. Our method recursively updates the model parameters using…