Related papers: Likelihood theory for the Graph Ornstein-Uhlenbeck…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
In past decades, Gaussian processes has been widely applied in studying trait evolution using phylogenetic comparative analysis. In particular, two members of Gaussian processes: Brownian motion and Ornstein-Uhlenbeck process, have been…
We consider a positive stationary generalized Ornstein--Uhlenbeck process \[V_t=\mathrm{e}^{-\xi_t}\biggl(\int_0^t\mathrm{e}^{\xi_{s-}}\ ,\mathrm{d}\eta_s+V_0\biggr)\qquadfor t\geq0,\] and the increments of the integrated generalized…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
\noindent \textbf{Abstract}: We consider the parameter estimation problem for the Ornstein-Uhlenbeck process $X$ driven by a fractional Ornstein-Uhlenbeck process $V$, i.e. the pair of processes defined by the non-Markovian continuous-time…
We consider a linear stochastic differential equation with stochastic drift. We study the problem of approximating the solution of such equation through an Ornstein-Uhlenbeck type process, by using direct methods of calculus of variations.…
The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability,…
We introduce Ising-H\"usler-Reiss processes, a new class of multivariate L\'evy processes that allows for sparse modeling of the path-wise conditional independence structure between marginal stable processes with different stability…
We study the stochastic growth process in discrete time $x_{i+1} = (1 + \mu_i) x_i$ with growth rate $\mu_i = \rho e^{Z_i - \frac12 var(Z_i)}$ proportional to the exponential of an Ornstein-Uhlenbeck (O-U) process $dZ_t = - \gamma Z_t dt +…
The phenomenon of intermittency has been widely discussed in physics literature. This paper provides a model of intermittency based on L\'evy driven Ornstein-Uhlenbeck (OU) type processes. Discrete superpositions of these processes can be…
We investigate the distributional properties of two generalized Ornstein-Uhlenbeck (OU) processes whose stationary distributions are the gamma law and the bilateral gamma law, respectively. The said distributions turn out to be related to…
Exponential functionals of L\'evy processes appear as stationary distributions of generalized Ornstein-Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of the GOU process and show that it is a Feller process.…
We consider a system of interacting particles governed by the generalized Langevin equation (GLE) in the presence of external confining potentials, singular repulsive forces, as well as memory kernels. Using a Mori-Zwanzig approach, we…
Graph Networks (GNs) enable the fusion of prior knowledge and relational reasoning with flexible function approximations. In this work, a general GN-based model is proposed which takes full advantage of the relational modeling capabilities…
Autoregressive graph generators define likelihoods via a sequential construction process, but these likelihoods are only meaningful if they are consistent across all linearizations of the same graph. Segmented Eulerian Neighborhood Trails…
It is considered Ornstein-Uhlenbeck process $ x_t = x_0 e^{-\theta t} + \mu (1-e^{-\theta t}) + \sigma \int_0^t e^{-\theta (t-s)} dW_s$, where $x_0 \in R$, $\theta>0$, $ \mu \in R$ and $\sigma > 0$ are parameters. By use values $(z_k)_{k…
We study sparsity-regularized maximum likelihood estimation for the drift parameter of high-dimensional non-stationary Ornstein--Uhlenbeck processes given repeated measurements of i.i.d. paths. In particular, we show that Lasso and Slope…
In this paper, we study an approximation scheme for L\'evy processes with drift in terms of a representation that is akin to the celebrated Mehler formula for L\'evy-Ornstein-Uhlenbeck processes. The approximation scheme is based on a…
Superpositions of Ornstein-Uhlenbeck type (supOU) processes provide a rich class of stationary stochastic processes for which the marginal distribution and the dependence structure may be modeled independently. We show that they can also…