arXiv research

Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.

Markov chain decoders improve generative models' ability to produce heavy-tailed data.

In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve according to quite general semimartingales. We show that the ruin problem corresponds to…

Study examines robust regression in high dimensions with heavy-tailed data.

Bayesian inference and superstatistics model financial volatility dynamics across different timescales.

New sampling method for heavy-tailed distributions using Langevin Algorithm.

We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation and the closed form momen…

The paper examines how heavy-tailed risks behave under Gaussian copula models.

We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation. The moment …

Ridge regression performs optimally in noisy environments with heavy-tailed distributions.

Introduces recency bias to improve time-series forecasting.

We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying tails. Rather than resorting to a concentration-based argument, the method used her…

Continuous Hidden Markov Models for Equity Returns

Study optimizes sampling to avoid extreme tail risks in unknown heavy-tailed distributions.

Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of light-tailed and heavy-tailed distributions. In the light-tailed case, we use a classical CVaR estimator based on the empirical distributi…

Improved VAE for heavy-tailed data using Student's t-distributions.

Interpolating models can have heavy-tailed risk, leading to rare but severe errors.

Nonlinear SGD achieves high-probability rates in non-convex optimization with heavy-tailed noise.

A hybrid model combines BPH and HE distributions for better heavy-tailed distribution approximation.

This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.

Paper develops sparse learning for heavy-tailed time series with locally stationary dynamics.

Paper develops robust estimators and strategies for stochastic MABs with heavy-tailed rewards.

Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size polynomially and lead to optimal sublinear rates on (strongly) convex problems. An alternative schedule, popular in nonconvex optimization, is called \emph{geometric step decay…

The paper studies quantile contributions and their relationship with order statistics in heavy-tailed distributions.

DE-SGD shows heavy-tailed behavior in decentralized settings.

New ensemble method improves model stability exponentially.

This paper analyzes ETFs with Taiwan exposure, finding heavy tails and asymmetric volatility.

Unified view of Lion and Muon as Stochastic Frank-Wolfe methods.

The paper analyzes multivariate Hawkes processes and their induced population processes.

An analysis of the stylized facts in financial time series is carried out. We find that, instead of the heavy tails in asset return distributions, the slow decay behaviour in autocorrelation functions of absolute returns is actually directly related to the degree of clustering of large fluctuations within the financial…

A new algorithm improves both computational efficiency and statistical optimality for robust low-rank matrix and tensor estimation.

We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L2, "weight decay", regularization. Our results characterize a more intricate regularization effect at the level of the unit activat…

Analyzed Bitcoin market index volatility changes over two distinct periods using anomalous diffusion and multifractal analysis.

Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.

New stability theory for Sinkhorn semigroups with explicit decay rates.

Adaptive experiment designs can dramatically improve statistical efficiency in randomized trials, but they also complicate statistical inference. For example, it is now well known that the sample mean is biased in adaptive trials. Inferential challenges are exacerbated when our parameter of interest differs from the pa…

The paper explores how score-driven models can approximate rough volatility.

Study improves ERM for heavy-tailed data with dependent inputs.

Efficiently estimates sparse linear regression with heavy-tailed and outlier-contaminated data.

Is AdamW effective under heavy-tailed noise?

Self-regulating annealing improves sampling from heavy-tailed datasets.

New diffusion models capture heavy-tailed distributions better.

Paper forecasts financial trading durations using a new point process model.

New concentration inequalities for tensors with heavy-tailed coefficients.

Robust Kalman filter for corrupted measurements.

New models explain heavy-tailed behavior in neural networks.

New PAC-Bayes bounds for heavy-tailed losses using supermartingales.

New bounds for heavy-tailed SDEs without info-theory terms.