arXiv research

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

Gradient descent implicitly follows regularization for general losses.

Boosted CVaR Classification improves tail performance in classification tasks.

Optimizes hybrid insurance contracts for heavy-tailed losses.

We provide a detailed study on the implicit bias of gradient descent when optimizing loss functions with strictly monotone tails, such as the logistic loss, over separable datasets. We look at two basic questions: (a) what are the conditions on the tail of the loss function under which gradient descent converges in the…

Paper presents a Bayesian-decision-theory framework for long-tailed classification.

Derives derivatives of risk measures for various types of portfolio losses.

We study the asymptotic behavior of the difference between the values at risk VaR(L) and VaR(L+S) for heavy tailed random variables L and S for application in sensitivity analysis of quantitative operational risk management within the framework of the advanced measurement approach of Basel II (and III). Here L describe…

Improved privacy-preserving methods for convex optimization with heavy-tailed data.

A new tail-shape index based on Value at Risk and Expected Shortfall.

We analyze systems of agents sharing light-tailed risky claims issued by different financial objects. Assuming exponentially distributed claims, we obtain that both agents' and system's losses follow generalized exponential mixture distributions. We show that this leads to qualitatively different results on individual …

Study uses spectral risk for learning with heavy-tailed data.

New bounds on neural network test loss derived from conditional information measures.

We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the s…

New algorithms avoid a dominant lower-order term in heavy-tailed loss settings.

Improved scalable machine learning under heavy-tailed data.

New method allocates capital based on tail central moments for financial risk assessment.

We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account the Pareto tails of losses and the heterogeneous dependence structures between the…

Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.

The paper examines how small positive dependence can lead to correlated tail risks.

New loss function restores importance weighting in overparameterized models.

New risk class penalizes loss deviations from mean on both sides.

Adam outperforms gradient descent on language models due to handling heavy-tailed class imbalance.

Paper improves PAC-Bayes bounds for various loss types.

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation of the tail probability of a compound distribution in the form of a rapidly conve…

We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to $η$-generalized Bayesian, MDL, and empirical risk minimization estimators. …

Mitigates anomaly score imbalance in long-tailed distributions.

Two-Tailed Averaging improves generalization by optimizing the number of leading iterates to ignore.

Optimizes privacy-preserving optimization for heavy-tailed data.

New study shows diversification can increase risk for heavy-tailed losses.

We improve generative models for heavy-tailed multivariate data using an invariant statistical loss.

New bounds link SGD's generalization to heavy tails without topological assumptions.

Study improves recognition of long-tail visual relationships.

This work extends implicit bias analysis to multiclass classification using a new loss framework.

The goal of this paper is to study organized flocking behavior and systemic risk in heterogeneous mean-field interacting diffusions. We illustrate in a number of case studies the effect of heterogeneity in the behavior of systemic risk in the system, i.e., the risk that several agents default simultaneously as a result…

The study analyzes a model for aggregate losses with dependent and overdispersed inter-losses times.

Heavy Lasso improves robustness in high-dimensional linear regression with heavy-tailed errors.

Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also undergone a large loss) as a function of the parameters of the underlying factor mod…

Work on SGDm under heavy-tailed noise, revealing its generalization properties.

New method estimates extreme outcomes in heavy-tailed data, breaking circular dependence.

Agents prefer non-diversification in markets with extreme losses.

Paper introduces a new robust method for estimating Pareto tail index from grouped data.

Paper supports robust estimation in regression with heavy-tailed errors.

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating the conditional median. To address the challenge that both the input and output c…

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

Robust biclustering method tackles heavy-tailed data issues.

Paper tackles robust matrix completion with heavy-tailed noise.

The paper explores how benign overfitting occurs in heavy-tailed input distributions.