相关论文: Estimation of Kramers-Moyal coefficients at low sa…

We present an optimization-based method for the joint estimation of system parameters and noise covariances of linear time-variant systems. Given measured data, this method maximizes the likelihood of the parameters. We solve the…

The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method…

Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and…

We introduce the bivariate jump-diffusion process, comprising two-dimensional diffusion and two-dimensional jumps, that can be coupled to one another. We present a data-driven, non-parametric estimation procedure of higher-order (up to 8)…

Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible…

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…

Obtaining sharp estimates for quantities involved in a given model is an integral part of the modeling process. For dynamical systems whose orbits display a complicated, perhaps chaotic, behaviour, the aim is usually to estimate time or…

Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have…

Using an operatorial formalism, we study the Kramers equation and its applications to numerical simulations. We obtain classes of algorithms which may be made precise at every desired order in the time step $\epsilon$ and with a set of free…

We study time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent…

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal…

Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of…

In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance…

Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary,…

We introduce a linear-scaling stochastic method to compute real-space maps of any positive local spectral operator in a tight-binding model. By employing positive-definite estimators, the sampling error at each site can be rigorously…

We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…

The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…