Related papers: Autoregressive Optimal Transport Models
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
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…
Compositional data, such as regional shares of economic sectors or property transactions, are central to understanding structural change in economic systems across space and time. This paper introduces a spatiotemporal multivariate…
Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector…
In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…
Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
This study introduces a novel spatial autoregressive model in which the dependent variable is a function that may exhibit functional autocorrelation with the outcome functions of nearby units. This model can be characterized as a…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Vector autoregressive (VAR) models are widely used in practical studies, e.g., forecasting, modelling policy transmission mechanism, and measuring connection of economic agents. To better capture the dynamics, this paper introduces a new…
We introduce a new class of autoregressive models for spherical time series, where the dimension of the spheres on which the observations of the time series are situated may be finite-dimensional or infinite-dimensional as in the case of a…
Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when…