Related papers: Extreme-value statistics of dimensions determining…
Extreme values modeling has attracting the attention of researchers in diverse areas such as the environment, engineering, or finance. Multivariate extreme value distributions are particularly suitable to model the tails of multidimensional…
Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning…
This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…
Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a…
We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
Let $n>m$, and let $A$ be an $(m\times n)$-matrix of full rank. Then obviously the estimate $\|Ax\|\leq\|A\|\|x\|$ holds for the euclidean norm of $x$ and $Ax$ and the spectral norm as the assigned matrix norm. We study the sets of all $x$…
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data…
We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
Inspired by the importance of inhibitory and excitatory couplings in the brain, we analyze the largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of a network,…
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…
We place ourselves in the setting of high-dimensional statistical inference where the number of variables $p$ in a dataset of interest is of the same order of magnitude as the number of observations $n$. We consider the spectrum of certain…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…
Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on…