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Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
We consider the ASEP and the stochastic six vertex model started with step initial data. After a long time, $T$, it is known that the one-point height function fluctuations for these systems are of order $T^{1/3}$. We prove the KPZ…
Gradient clipping is a commonly used technique to stabilize the training process of neural networks. A growing body of studies has shown that gradient clipping is a promising technique for dealing with the heavy-tailed behavior that emerged…
An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…
This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $\beta$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the…
This paper proposes methods for Bayesian inference in time-varying parameter (TVP) quantile regression (QR) models featuring conditional heteroskedasticity. I use data augmentation schemes to render the model conditionally Gaussian and…
Transient responses in disordered systems typically show a heavy-tail relaxation behavior: the decay time constant increases as time increases, revealing a spectral distribution of time constants. The asymptotic value of such transients is…
We obtain some optimal inequalities on tail probabilities for sums of independent bounded random variables. Our main result completes an upper bound on tail probabilities due to Talagrand by giving a one-term asymptotic expansion for large…
We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…
We study generalisations of a simple, combinatorial proof of a Chernoff bound similar to the one by Impagliazzo and Kabanets (RANDOM, 2010). In particular, we prove a randomized version of the hitting property of expander random walks and…
In high-dimensions, the prior tails can have a significant effect on both posterior computation and asymptotic concentration rates. To achieve optimal rates while keeping the posterior computations relatively simple, an empirical Bayes…
The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…
The tail behavior of aggregates of heavy-tailed random vectors is known to be determined by the so-called principle of "one large jump'', be it for finite sums, random sums, or, L\'evy processes. We establish that, in fact, a more general…
Under the assumption that the distribution of a nonnegative random variable $X$ admits a bounded coupling with its size biased version, we prove simple and strong concentration bounds. In particular the upper tail probability is shown to…
A coupling method is developed for univariate extreme value theory , providing an alternative to the use of the tail empirical/quantile processes. Emphasizing the Peak-over-Threshold approach that approximates the distribution above high…
We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether…
In this paper we consider the problem of estimating the joint upper and lower tail large deviations of the edge eigenvalues of an Erd\H{o}s-R\'enyi random graph $\mathcal{G}_{n,p}$, in the regime of $p$ where the edge of the spectrum is no…
We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. We show that a combination of gradient clipping, momentum, and normalized gradient descent yields convergence…