Related papers: Characterization of positively correlated squared …
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently,…
Linear filtering problem for infinite-dimensional Gaussian processes is studied, the observation process being finite-dimensional. Integral equations for the filter and for covariance of the error are derived. General results are applied to…
We prove that the set of thick points of the log-correlated Gaussian field contains an unbounded path in sufficiently high dimensions. This contrasts with the two-dimensional case, where Aru, Papon, and Powell (2023) showed that the set of…
We propose deep convolutional Gaussian processes, a deep Gaussian process architecture with convolutional structure. The model is a principled Bayesian framework for detecting hierarchical combinations of local features for image…
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…
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 consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
We demonstrate the parallel between the properties of Gaussian vectors and the Euclidean geometry. In particular we study the Markov property and give various equivalent Euclidean and probabilistic characterizations. We also give a simple…
This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.
We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of $m$ vs $n$…
This Dissertation collects my results on the interpretation, characterization, quantification and application of bipartite and multipartite entanglement in Gaussian states of continuous variable systems.
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean Gaussian process. We show that its autocorrelation and power spectrum exist for most regular processes, and we find a…
We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of…
The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…
We aim to link random fields and marked point processes and therefore introduce a new class of stochastic processes which are defined on a random set in R^d. Unlike for random fields, the mark covariance function of a marked random set is…
The seminal papers of Pickands [1,2] paved the way for a systematic study of high exceedance probabilities of both stationary and non-stationary Gaussian processes. Yet, in the vector-valued setting, due to the lack of key tools including…
We give a dimension-independent sparsification result for suprema of centered Gaussian processes: Let $T$ be any (possibly infinite) bounded set of vectors in $\mathbb{R}^n$, and let $\{\boldsymbol{X}_t := t \cdot \boldsymbol{g} \}_{t\in…