Related papers: Tail Annealing for Heavy-Tailed Flow Matching
Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…
We introduce L\'evy-Flows, a class of normalizing flow models that replace the standard Gaussian base distribution with L\'evy process-based distributions, specifically Variance Gamma (VG) and Normal-Inverse Gaussian (NIG). These…
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…
We develop two new estimators for a general class of stationary GARCH models with possibly heavy tailed asymmetrically distributed errors, covering processes with symmetric and asymmetric feedback like GARCH, Asymmetric GARCH, VGARCH and…
Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process (DP). The first contribution of this paper focuses on characterizing the tails…
We propose a semiparametric method for fitting the tail of a heavy-tailed population given a relatively small sample from that population and a larger sample from a related background population. We model the tail of the small sample as an…
The fine-tuning paradigm in addressing long-tail learning tasks has sparked significant interest since the emergence of foundation models. Nonetheless, how fine-tuning impacts performance in long-tail learning was not explicitly quantified.…
The fine-tuning paradigm has emerged as a prominent approach for addressing long-tail learning tasks in the era of foundation models. However, the impact of fine-tuning strategies on long-tail learning performance remains unexplored. In…
I present a parametric, bijective transformation to generate heavy tail versions Y of arbitrary RVs X ~ F. The tail behavior of the so-called 'heavy tail Lambert W x F' RV Y depends on a tail parameter delta >= 0: for delta = 0, Y = X, for…
We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace…
The real-world data distribution is essentially long-tailed, which poses great challenge to the deep model. In this work, we propose a new method, Gradual Balanced Loss and Adaptive Feature Generator (GLAG) to alleviate imbalance. GLAG…
We suggest a simple Gaussian mixture model for data generation that complies with Feldman's long tail theory (2020). We demonstrate that a linear classifier cannot decrease the generalization error below a certain level in the proposed…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
While adaptive gradient methods are the workhorse of modern machine learning, sign-based optimization algorithms such as Lion and Muon have recently demonstrated superior empirical performance over AdamW in training large language models…
Variational inference with {\alpha}-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using {\alpha}-divergences (with positive {\alpha} values) is…
In the study of heavy tail data, several models have been introduced. If the interest is in the tail of the distribution, block maxima or excess over thresholds are the typical approaches, wasting relevant information in the bulk of the…
We develop new flexible univariate models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the generalized Pareto (GP) limit for threshold exceedances. These models can accommodate departure from…
Traditional implicit generative models are capable of learning highly complex data distributions. However, their training involves distinguishing real data from synthetically generated data using adversarial discriminators, which can lead…
We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…
The presence of non-Gaussian tails is a prevalent characteristic in many financial modeling scenarios, necessitating the use of complex non-Gaussian distributions such as the generalized beta of the second kind (GB2) and the skewed…