Related papers: On Optimization over Tail Distributions
We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
We address the problem of prediction for extreme observations by proposing an extremal linear prediction method. We construct an inner product space of nonnegative random variables derived from transformed-linear combinations of independent…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…
Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…
We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply…
One potential solution to combat the scarcity of tail observations in extreme value analysis is to integrate information from multiple datasets sharing similar tail properties, for instance, a common extreme value index. In other words, for…
``Localization'' has proven to be a valuable tool in the Statistical Learning literature as it allows sharp risk bounds in terms of the problem geometry. Localized bounds seem to be much less exploited in the Stochastic Optimization…
Tail Averaging improves on Polyak averaging's non-asymptotic behaviour by excluding a number of leading iterates of stochastic optimization from its calculations. In practice, with a finite number of optimization steps and a learning rate…
Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
We present a new method, called Analysis-of-marginal-Tail-Means (ATM), for effective robust optimization of discrete black-box problems. ATM has important applications to many real-world engineering problems (e.g., manufacturing…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…
We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive measures…
We introduce the \textsc{Tailed-Uniform} proposal distribution for generating training simulations in simulation-based inference. Instead of sampling parameters uniformly within bounded regions, we extend the distribution beyond prior…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale and martingale transform by means of martingale differences in the terms of moments and tails of distributions…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…