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Directed polymers in heavy-tail random environment [PDF]
Annals of Probability, 2018 We study the directed polymer model in dimension ${1+1}$ when the environment is heavy-tailed, with a decay exponent $\alpha\in(0,2)$. We give all possible scaling limits of the model in the weak-coupling regime, i.e., when the inverse temperature ...
Quentin Berger, Niccolò Torri
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IEEE Transactions on Information Theory, 2012 The stochastic multiarmed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper, we examine the bandit problem under the weaker assumption that the distributions have moments of order 1 + ε, for some ε ∈ (0,1 ...
Sébastien Bubeck +2 more
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Heavy Tailed Horseshoe Priors [PDF]
, 2019 Locally adaptive shrinkage in the Bayesian framework is achieved through the use of local-global prior distributions that model both the global level of sparsity as well as individual shrinkage parameters for mean structure parameters. The most popular of these models is the Horseshoe prior and its variants due to their spike and slab behavior ...
Andrew Womack, Zikun Yang
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Airborne methane remote measurements reveal heavy-tail flux distribution in Four Corners region. [PDF]
Proc Natl Acad Sci U S A, 2016 Frankenberg C +14 more
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Understanding Heavy Tails in a Bounded World or, is a Truncated Heavy Tail Heavy or Not? [PDF]
Stochastic Models, 2010 We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft truncation regime
A. Chakrabarty, G. Samorodnitsky
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Heavy-Tail Phenomenon in Decentralized SGD [PDF]
IISE Transactions, 2022 Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to ‘multiplicative noise’, even under surprisingly simple settings, such as linear regression with Gaussian data.
Mert Gurbuzbalaban +4 more
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Nonlinear gradient mappings and stochastic optimization: A general framework with applications to heavy-tail noise [PDF]
SIAM Journal on Optimization, 2022 We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized, signed or ...
D. Jakovetić +5 more
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Propagation of chaos for the Cucker-Smale systems under heavy tail communication [PDF]
Communications in Partial Differential Equations, 2021 In this work, we study propagation of chaos for solutions of the Liouville equation derived from the classical discrete Cucker-Smale system. Assuming that the communication kernel satisfies the heavy tail condition – known to be necessary to induce ...
V. Nguyen, R. Shvydkoy
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Distribution and moment characteristics of a quotient of heavy-tailed random variables
Lietuvos Matematikos Rinkinys, 2023 Let us deal with positive i.i.d. random variables X1, . . ., Xm having a tail index α. Calculating a quotient of two biggest members in the set, we obtain a new random variable and investigate its distribution and moment properties.
Kęstutis Gadeikis
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Event and Catchment Controls of Heavy Tail Behavior of Floods
Water Resources Research, 2022 In some catchments, the distribution of annual maximum streamflow shows heavy tail behavior, meaning the occurrence probability of extreme events is higher than if the upper tail decayed exponentially.
Elena Macdonald +7 more
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