Related papers: Kriging measure-valued data with sparse observatio…

Gaussian processes (GPs) are a ubiquitous tool for geostatistical modeling with high levels of flexibility and interpretability, and the ability to make predictions at unseen spatial locations through a process called Kriging. Estimation of…

Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve…

Kriging is a fundamental tool for spatial prediction, but its computational complexity of $O(N^3)$ becomes prohibitive for large datasets. While local kriging using $K$-nearest neighbors addresses this issue, the selection of $K$ typically…

Modelling bounded rational decision-making through information constrained processing provides a principled approach for representing departures from rationality within a reinforcement learning framework, while still treating…

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…

This work develops a multivariate extension of the Fixed Rank Kriging (FRK) framework for spatial prediction in settings where multiple spatial processes may provide complementary information. The goal is to preserve the computational…

The Maximum Likelihood (ML) and Cross Validation (CV) methods for estimating covariance hyper-parameters are compared, in the context of Kriging with a misspecified covariance structure. A two-step approach is used. First, the case of the…

Surrogate models are extensively employed for forward and inverse uncertainty quantification in complex, computation-intensive engineering problems. Nonetheless, constructing high-accuracy surrogate models for complex dynamical systems with…

Seismic fragility curves have been introduced as key components of Seismic Probabilistic Risk Assessment studies. They express the probability of failure of mechanical structures conditional to a seismic intensity measure and must take into…

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

Proactive cyber-risk assessment is gaining momentum due to the wide range of sectors that can benefit from the prevention of cyber-incidents by preserving integrity, confidentiality, and the availability of data. The rising attention to…

This paper presents a distributionally robust Q-Learning algorithm (DrQ) which leverages Wasserstein ambiguity sets to provide idealistic probabilistic out-of-sample safety guarantees during online learning. First, we follow past work by…

This article proposes a new kriging that has a rational form. It is shown that the generalized least squares estimate of the mean from rational kriging is much more well behaved than that from ordinary kriging. Parameter estimation and…

We propose a three-step divide-and-conquer strategy within the Bayesian paradigm that delivers massive scalability for any spatial process model. We partition the data into a large number of subsets, apply a readily available Bayesian…

For estimation and predictions of random fields it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for…

In this work we analyse a number of variants of the Wasserstein distance which allow to focus the classification on the prescribed parts (fragments) of classified 2D curves. These variants are based on the use of a number of discrete…

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…

Kriging (or Gaussian process regression) is a popular machine learning method for its flexibility and closed-form prediction expressions. However, one of the key challenges in applying kriging to engineering systems is that the available…