Related papers: An autoregressive model leading to stable distribu…
Well-posedness of a reversible variant of the Gray-Scott model is shown, along with the convergence of each trajectory to one of the two spatially homogeneous steady states. The principle of linearized stability provides the local…
Contemporary time series data often feature objects connected by a social network that naturally induces temporal dependence involving connected neighbours. The network vector autoregressive model is useful for describing the influence of…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
In the setting of dominated statistical models, we provide conditions yielding strong continuity of the posterior distribution with respect to the observed data. We show some applications, with special focus on exponential models.
A new class of integer-valued autoregressive models with dynamic survival probability is proposed. The peculiarity of this class of models lies on the specification of the survival probability through a stochastic recurrence equation. The…
We address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
We develop a new methodology for the fitting of nonstationary time series that exhibit nonlinearity, asymmetry, local persistence and changes in location scale and shape of the underlying distribution. In order to achieve this goal, we…
In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
We address a distributed adaptive control methodology for nonlinear interconnected systems possibly affected by network anomalies. In the framework of adaptive approximation, the distributed controller and parameter estimator are designed…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an…
A new mixture autoregressive model based on Student's $t$-distribution is proposed. A key feature of our model is that the conditional $t$-distributions of the component models are based on autoregressions that have multivariate…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…