相关论文: Filtering of partially observed polynomial process…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

De Facto, signal processing is the interpolation and extrapolation of a sequence of observations viewed as a realization of a stochastic process. Its role in applied statistics ranges from scenarios in forecasting and time series analysis,…

Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…

We obtain solutions to conservation laws under any random initial conditions that are described by Gaussian stochastic processes (in some cases discretized). We analyze the generalization of Burgers' equation for a smooth flux function…

In this paper, we propose an approach to address the problems with ambiguity in tuning the process and observation noises for a discrete-time linear Kalman filter. Conventional approaches to tuning (e.g. using normalized estimation error…

A learning-based safety filter is developed for discrete-time linear time-invariant systems with unknown models subject to Gaussian noises with unknown covariance. Safety is characterized using polytopic constraints on the states and…

Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers.…

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing…

In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…

The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…

We present FlowMO: an open-source Python library for molecular property prediction with Gaussian Processes. Built upon GPflow and RDKit, FlowMO enables the user to make predictions with well-calibrated uncertainty estimates, an output…

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous…

The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A widely-used form of the filter is the Gaussian bilateral…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview…

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

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…

Although many time series are realizations from discrete processes, it is often that a continuous Gaussian model is implemented for modeling and forecasting the data, resulting in incoherent forecasts. Forecasts using a Poisson-Lindley…