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We develop a non-parametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is a…
We study different pointwise recurrence notions for linear dynamical systems from the Ergodic Theory point of view. We show that from any reiteratively recurrent vector $x_0$, for an adjoint operator $T$ on a separable dual Banach space…
We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…
The goal of this research is to derive an approach to assess uncertainty in an arbitrary volume conditioned by sampling data, without using geostatistical simulation. We have accomplished this goal by deriving an numerical tool suitable for…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
The computation of Gaussian orthant probabilities has been extensively studied for low-dimensional vectors. Here, we focus on the high-dimensional case and we present a two-step procedure relying on both deterministic and stochastic…
Accurately estimating latent velocity vector fields of atmospheric winds is crucial for understanding weather phenomena. Direct measurement of atmospheric winds is costly, especially in the upper atmosphere, so researchers attempt to…
Most of existing embedding based recommendation models use embeddings (vectors) corresponding to a single fixed point in low-dimensional space, to represent users and items. Such embeddings fail to precisely represent the users/items with…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
Accurate reconstruction of environmental scalar fields from sparse onboard observations is essential for autonomous vehicles engaged in aquatic monitoring. Beyond point estimates, principled uncertainty quantification is critical for active…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
We present a computational method for measuring financial risk by estimating the Value at Risk and Expected Shortfall from financial series. We have made two assumptions: First, that the predictive distributions of the values of an asset…
We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…
In this contribution we describe an approach to evolve composite covariance functions for Gaussian processes using genetic programming. A critical aspect of Gaussian processes and similar kernel-based models such as SVM is, that the…
The task of monitoring for a change in the mean of a sequence of Bernoulli random variables has been widely studied. However most existing approaches make at least one of the following assumptions, which may be violated in many real-world…
Experimental design techniques such as active search and Bayesian optimization are widely used in the natural sciences for data collection and discovery. However, existing techniques tend to favor exploitation over exploration of the search…
We consider invariant transports of stationary random measures on $\mathbb{R}^d$ and establish natural mixing criteria that guarantee persistence of asymptotic variances. To check our mixing assumptions, which are based on two-point Palm…
For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…
To validate the safety of automated vehicles (AV), scenario-based testing aims to systematically describe driving scenarios an AV might encounter. In this process, continuous inputs such as velocities result in an infinite number of…
In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to…