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We consider the problem of sparsity-constrained $M$-estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the $k$-sparse, high-dimensional regime…
A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure…
The modeling of risk situations that occur in a space-time framework can be done using max-stable random fields on lattices. Although the summary coefficients for the spatial and temporal behaviour do not characterize the finite-dimensional…
We introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this…
Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…
This paper focuses on a class of variational inequalities (VIs), where the map defining the VI is given by the component-wise conditional value-at-risk (CVaR) of a random function. We focus on solving the VI using sample average…
We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a…
Survival regression is widely used to model time-to-events data, to explore how covariates may influence the occurrence of events. Modern datasets often encompass a vast number of covariates across many subjects, with only a subset of the…
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…
In this work, it has been indicated that the key features requisite for preserving causality and stability of the popularly existing relativistic hydrodynamic theories, can be translated into each other. It has been shown here, that a…
We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…
Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…
The hazard ratio is one of the most commonly reported measures of treatment effect in randomised trials, yet the source of much misinterpretation. This point was made clear by (Hernan, 2010) in commentary, which emphasised that the hazard…
This paper develops a dynamic factor model in which common level and volatility factors evolve jointly, allowing conditional means and variances to interact endogenously within a large-information setting. The joint evolution of these…
A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results for linear and quadratic functionals of…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
Under losses which are potentially heavy-tailed, we consider the task of minimizing sums of the loss mean and standard deviation, without trying to accurately estimate the variance. By modifying a technique for variance-free robust mean…
We present a theory and accompanying importance sampling method for computing rate constants in spatially inhomogenious systems. Using the relationship between rate constants and path space partition functions, we illustrate that the…