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Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
In many practical reinforcement learning tasks, feedback is only provided at the end of a long horizon, leading to sparse and delayed rewards. Existing reward redistribution methods typically assume that per-step rewards are independent,…
Estimating the parameters of max-stable parametric models poses significant challenges, particularly when some parameters lie on the boundary of the parameter space. This situation arises when a subset of variables exhibits extreme values…
We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can…
The gamma distribution is a useful model for small area prediction of a skewed response variable. We study the use of the gamma distribution for small area prediction. We emphasize a model, called the gamma-gamma model, in which the area…
We study four different approaches to model time-dependent extremal behavior: dynamics introduced by (a) a state-space model (SSM), (b) a shot-noise-type process with GPD marginals, (c) a copula-based autoregressive model with GPD…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature.…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in $\mathbb {R}^d$. We present a…
The gapped local alignment score of two random sequences follows a Gumbel distribution. If computers could estimate the parameters of the Gumbel distribution within one second, the use of arbitrary alignment scoring schemes could increase…
In practice, there often exist unobserved variables, also termed hidden variables, associated with both the response and covariates. Existing works in the literature mostly focus on linear regression with hidden variables. However, when the…
The geometric mean method (GMM) and the eigenvector method (EM) are well-known approaches to deriving information from pairwise comparison matrices in decision making processes. However, the original algorithms of these methods are…
Observed accidents have been the main resource for road safety analysis over the past decades. Although such reliance seems quite straightforward, the rare nature of these events has made safety difficult to assess, especially for new and…
Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample…
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…
These notes were written for the mini-course "Extrema of log-correlated random variables: Principles and Examples" at the Introductory School held in January 2015 at the Centre International de Rencontres Math\'ematiques in Marseille. There…
Count time series data are frequently analyzed by modeling their conditional means and the conditional variance is often considered to be a deterministic function of the corresponding conditional mean and is not typically modeled…
Severe Ionosphere magnetic storms are feared events for integrity and continuity of navigation systems such as EGNOS, the European SBAS (Satellite-Based Augmentation System) complementing GPS and an accurate modelling of this event…