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We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…
Large sample statistical analysis of threshold autoregressive (TAR) models is usually based on the assumption that the underlying driving noise is uncorrelated. In this paper, we consider a model, driven by Gaussian noise with geometric…
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…
Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type…
When observations are curves over some natural time interval, the field of functional data analysis comes into play. Functional linear processes account for temporal dependence in the data. The prediction problem for functional linear…
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their…
Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…
Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…
Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
High-frequency financial data can be collected as a sequence of curves over time; for example, as intra-day price, currently one of the topics of greatest interest in finance. The Functional Data Analysis framework provides a suitable tool…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
In this work we study two Riemannian distances between infinite-dimensional positive definite Hilbert-Schmidt operators, namely affine-invariant Riemannian and Log-Hilbert-Schmidt distances, in the context of covariance operators associated…
We propose a novel estimator of the autocorrelation function in presence of missing observations. We establish the consistency, the asymptotic normality, and we derive deviation bounds for various classes of weakly dependent stationary time…
Conventional variational autoencoders fail in modeling correlations between data points due to their use of factorized priors. Amortized Gaussian process inference through GP-VAEs has led to significant improvements in this regard, but is…
We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
It was shown in Mishura et al. (Stochastic Process. Appl. 123 (2013) 2353-2369), that any random variable can be represented as improper pathwise integral with respect to fractional Brownian motion. In this paper, we extend this result to…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…