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We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...
Aims. We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey. Methods. By analysing 1000 Euclid-like light cones, ...
Understanding the diffusion patterns of sequences of interdependent events is a central question for a variety of disciplines. Temporal point processes are a class of elegant and powerful models of such sequences; these processes have become popular across ...
Random binning features, introduced in the seminal paper of Rahimi and Recht '07, are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way to approximate the ...
This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...
Poor decisions and selfish behaviors give rise to seemingly intractable global problems, such as the lack of transparency in democratic processes, the spread of conspiracy theories, and the rise in greenhouse gas emissions. However, people are more predict ...
Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...
Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loeve expansion. These operators may themselves be subject to variation, for instance in contexts wh ...
We derive a covariance formula for the class of 'topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example, (i) crossing events for level or excursion sets, (ii ...
The chapter presents an approach for the interactive definition of curves and motion paths based on Gaussian mixture model (GMM) and optimal control. The input of our method is a mixture of multivariate Gaussians defined by the user, whose centers define a ...
