Related papers: M-estimation for Gaussian processes with time-inho…
The integration of physical relationships into stochastic models is of major interest e.g. in data assimilation. Here, a multivariate Gaussian random field formulation is introduced, which represents the differential relations of the…
We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variational Fourier…
The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…
In this article, we study a robust estimation method for a general class of integer-valued time series models. The conditional distribution of the process belongs to a broad class of distribution and unlike classical autoregressive…
We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…
The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. A kernel-type estimators are used for estimation of the quadratic variation of the derivative of the limit of…
Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and…
In this paper, an estimator of $m$ instants ($m$ is known) of abrupt changes of the parameter of long-range dependence or self-similarity is proved to satisfy a limit theorem with an explicit convergence rate for a sample of a Gaussian…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
In the present work, we consider a stable one-dimensional gaussian autoregressive model in continous time. Using the limit theorems with logarithmic averaging obtained for continous local martingales, we construct then an estimator of the…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing…
Extrinsic Gaussian process regression methods, such as wrapped Gaussian process, have been developed to analyze manifold data. However, there is a lack of intrinsic Gaussian process methods for studying complex data with manifold-valued…
Online anomaly detection of time-series data is an important and challenging task in machine learning. Gaussian processes (GPs) are powerful and flexible models for modeling time-series data. However, the high time complexity of GPs limits…
In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
We characterize the complete joint posterior distribution over spatially-varying basal traction and and ice softness parameters of an ice sheet model from observations of surface speed by using stochastic variational inference combined with…