相关论文: High-frequency sampling and kernel estimation for …
The question of existence and properties of stationary solutions to Langevin equations driven by noise processes with stationary increments is discussed, with particular focus on noise processes of pseudo-moving-average type. On account of…
Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…
Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…
We derive a Dickman approximation for the small jumps of a large class of multivariate L\'evy processes. We then apply this approximation to develop a simulation method for the class of general multivariate gamma distributions (GMGD). A…
The family of Mat\'ern kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
In the study of complex physical and biological systems represented by multivariate stochastic processes, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. While methods to assess the…
Kernel-based machine learning approaches are gaining increasing interest for exploring and modeling large dataset in recent years. Gaussian process (GP) is one example of such kernel-based approaches, which can provide very good performance…
The focus of this work is the convergence of non-stationary and deep Gaussian process regression. More precisely, we follow a Bayesian approach to regression or interpolation, where the prior placed on the unknown function $f$ is a…
We provide a new method to approximate a (possibly discontinuous) function using Christoffel-Darboux kernels. Our knowledge about the unknown multivariate function is in terms of finitely many moments of the Young measure supported on the…
This is a method for discrete event simulation specified by survival analysis. It presents a sequence of steps. First, hazard rates from survival analysis specify the rates of a set of counting processes. Second, those counting processes…
Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this…
We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory…
Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
In this article, we focus on the sampling of the configurational Gibbs-Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a molecular $N$-body system modelled at constant temperature. We…
We develop a fast algorithm for Kalman Filter applied to the random walk forecast model. The key idea is an efficient representation of the estimate covariance matrix at each time-step as a weighted sum of two contributions - the process…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
We propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge…
In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…