This paper improves operational risk modeling by selecting better loss severity distributions.
problem Inconsistent regulatory capital calculations due to changing loss severity distribution families.
method Presented truncation probability estimates and a consistent quantile scoring function for selection criteria. Also, recommended collecting loss frequencies below the minimum reporting threshold.
result More stable regulatory capital calculations through better selection of loss severity distributions.
The impact of a stress scenario of default events on the loss distribution of a credit portfolio can be assessed by determining the loss distribution conditional on these events. While it is conceptually easy to estimate loss distributions conditional on default events by means of Monte Carlo simulation, it becomes imp…
We study cross-country GDP losses due to financial crises in terms of frequency (number of loss events per period) and severity (loss per occurrence). We perform the Loss Distribution Approach (LDA) to estimate a multi-country aggregate GDP loss probability density function and the percentiles associated to extreme eve…
Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach is not prescriptive regarding the class of statistical model utilised to undertake capital estimation. It has however become well accepted to utlise a Loss Distributional Approach (LDA) paradigm to model the individual OpRisk loss…
A new loss function improves neural networks' out-of-distribution detection without side effects.
problem Neural networks struggle with out-of-distribution detection due to SoftMax loss issues.
method Proposes IsoMax loss replacing SoftMax loss, maintaining high entropy and fast inferences.
result Significantly improves neural networks' out-of-distribution detection performance.
Given a task of predicting Y from X, a loss function L, and a set of probability distributions Γ on (X,Y), what is the optimal decision rule minimizing the worst-case expected loss over Γ? In this paper, we address this question by introducing a generalization of the principle of maximum entropy. Applying t…
Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for the distributions typically used in operational risk. However with modern comput…
In this work we study loss functions for learning and evaluating probability distributions over large discrete domains. Unlike classification or regression where a wide variety of loss functions are used, in the distribution learning and density estimation literature, very few losses outside the dominant log loss ar…
New approach for distributed online optimization of non-convex losses with sublinear regret.
problem Regret evaluation and consensus in distributed, multi-agent systems with non-convex losses.
method Composite regret metric and consensus-based online normalized gradient (CONGD) approach for pseudo-convex losses; offline optimization oracle for general non-convex losses.
result First sublinear regret bound for general distributed online non-convex learning.
Neural network model improves loss reserving accuracy and distribution flexibility.
problem Accurate estimation of claim variability alongside central estimates.
method Mixture Density Neural Network (MDN) with rolling-origin approach.
result MDN consistently outperforms classical models for central estimates and quantiles.
Proposes new loss functions for better handling bimodal predictive uncertainty.
problem Bimodal predictive uncertainty in machine learning models.
method Family of distribution-aware loss functions integrating normalized RMSE with Wasserstein and Cramér distances.
result Proposed loss functions reduce predictive uncertainty estimation error by 45% on complex bimodal datasets.
The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk plays an important role in protecting the Australian banking sector against insolvency. We outline the mathematical foundations of regulatory capital for credit risk, and extend the model specification of the IRB approach to a more g…
Paper tackles Byzantine resilience in distributed multi-task learning.
problem Resilience of distributed algorithms in the presence of Byzantine agents.
method Online weight assignment rule based on accumulated loss and filtering.
result Aggregation with proposed weight assignment rule improves expected regret.
New approach combines likelihood and adversarial losses for better precipitation predictions.
problem Spatially inconsistent precipitation projections from likelihood-based models.
method Fuses likelihood-based and adversarial losses for generative models.
result Improves spatial consistency in precipitation downscaling.
New methods connect low-loss points on neural network surfaces.
problem Connecting low-loss points on neural network loss surfaces.
method Macroscopic distributional assumptions and global connection models.
result Accuracy correlates with complexity and sensitivity.
To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative metho…
Paper analyzes statistical properties of log-cosh loss function.
problem No statistical analysis of log-cosh loss function in literature.
method Presented statistical properties of log-cosh loss function, compared to Cauchy distribution, and examined various statistical procedures.
result Characterized statistical properties of log-cosh loss function, including distribution, likelihood function, and Fisher information.
This paper explains why distributional reinforcement learning is better than vanilla RL using small-loss bounds.
problem Understanding when and why distributional reinforcement learning (DistRL) is superior to vanilla reinforcement learning (RL).
method The paper uses small-loss bounds to explain the benefits of DistRL, proposing algorithms and proving bounds for different RL settings.
result Distributional reinforcement learning (DistRL) outperforms vanilla RL when optimal costs are small, as shown by small-loss bounds.
This paper examines the Histogram Loss for regression, revealing its effectiveness without needing complex tuning.
problem Improving regression models by learning the entire distribution.
method Investigates Histogram Loss, a method that minimizes cross-entropy between a target distribution and a histogram prediction.
result The performance gain in regression models using Histogram Loss comes from optimization improvements, not extra modeling.
Using Monte Carlo simulation to calculate the Value at Risk (VaR) as a possible risk measure requires adequate techniques. One of these techniques is the application of a compound distribution for the aggregates in a portfolio. In this paper, we consider the aggregated loss of Gamma distributed severities and estimate …
New approach shapes error distribution in long-term forecasting.
problem Disparate error distributions in recent transformer models.
method Loss shaping constraints to respect upper bounds on loss at each time-step.
result Competitive average performance with shaped error distribution.
Paper proposes SinkhornDRL for distributional RL using Sinkhorn divergence and regularized Wasserstein loss.
problem Improving distributional reinforcement learning by minimizing Bellman return distribution differences.
method Introduces SinkhornDRL, a distributional RL algorithm using Sinkhorn divergence and regularized Wasserstein loss.
result SinkhornDRL consistently outperforms or matches existing algorithms on Atari games, especially in multi-dimensional reward settings.
Solves learning halfspaces with Massart noise for log-concave distributions.
problem Learning halfspaces with Massart noise in distribution-specific PAC model.
method Identifies a smooth non-convex surrogate loss and uses SGD to solve the learning problem.
result First computationally efficient algorithm for learning halfspaces with Massart noise for a broad family of distributions.
A new approach to model rejection using density ratios.
problem Improving model performance through selective prediction.
method Optimization of a loss's risk with φ-divergence regularization to find an idealized data distribution.
result Model rejection can be made by comparing the density ratio of the idealized distribution to the actual data distribution.
Paper develops a generative model using Wasserstein-2 loss.
problem Creating realistic data samples from limited data.
method Uses a distribution-dependent ODE with a gradient flow for W2 loss.
result The method converges to the true data distribution exponentially.
When optimizing against the mean loss over a distribution of predictions in the context of a regression task, then even if there is a distribution of targets the optimal prediction distribution is always a delta function at a single value. Methods of constructing generative models need to overcome this tendency. We con…
We introduce a novel loss max-pooling concept for handling imbalanced training data distributions, applicable as alternative loss layer in the context of deep neural networks for semantic image segmentation. Most real-world semantic segmentation datasets exhibit long tail distributions with few object categories compri…
Loss estimator improves model calibration and generalization.
problem Ensuring models generalize to unseen data.
method Train a loss estimator alongside the model using contrastive training.
result Improves model generalization and calibration.
We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with pair-copula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of con…
We analyze the semi-hard triplet loss using Edgeworth expansion for better understanding of its behavior.
problem Understanding the behavior of the semi-hard triplet loss function.
method Developed a higher-order asymptotic analysis using the Edgeworth expansion.
result Derived explicit Edgeworth expansions revealing first-order corrections in terms of the third cumulant.
Here we present an application of two maxentropic procedures to determine the probability density distribution of compound sums of random variables, using only a finite number of empirically determined fractional moments. The two methods are the Standard method of Maximum Entropy (SME), and the method of Maximum Entrop…
A new model calculates LGD distribution based on firm value and credit market conditions.
problem Estimating LGD distribution in credit markets.
method Uses last passage time of a linear diffusion process to model LGD distribution.
result Explicit distributions of default time and LGD are obtained under minimal assumptions.
Personalized activity recognition improves performance for diverse users.
problem Poor performance of impersonal algorithms for individual users.
method Personalized activity recognition using deep embeddings from a fully convolutional neural network with triplet loss.
result Novel subject triplet loss provides the best performance overall.
Typically, operational risk losses are reported above a threshold. Fitting data reported above a constant threshold is a well known and studied problem. However, in practice, the losses are scaled for business and other factors before the fitting and thus the threshold is varying across the scaled data sample. A report…
A non-parametric method for evaluation of the aggregate loss distribution (ALD) by combining and numerically inverting the empirical characteristic functions (CFs) is presented and illustrated. This approach to evaluate ALD is based on purely non-parametric considerations, i.e., based on the empirical CFs of frequency …
EX-DRL improves extreme quantile prediction for financial risk management.
problem Inaccurate estimation of extreme quantiles in loss distributions.
method EX-DRL uses Generalized Pareto Distribution (GPD) to model the tail of the loss distribution and Quantile Regression (QR) to improve extreme quantile prediction.
result EX-DRL provides more precise estimates of extreme quantiles, improving risk metrics reliability.
We improve generative models for heavy-tailed multivariate data using an invariant statistical loss.
problem Traditional generative models struggle with heavy-tailed and multivariate data, leading to unstable training and mode dropping.
method We extend the invariant statistical loss method to handle heavy-tailed and multivariate data using a Pareto-ISL generator trained with input noise from a generalised Pareto distribution.
result Pareto-ISL accurately models the tails of heavy-tailed distributions while capturing central characteristics.
Improved sampling via learned diffusions using variational losses.
problem Sampling from target distributions without direct access to samples.
method Generalized Schrödinger bridge problem, variational formulation, gradient-based optimization.
result Proposed log-variance loss leads to improved performance.
New method samples triplets from data distributions for training Triplet networks.
problem Training robust Triplet networks with discriminative triplets.
method Bayesian updating of multivariate normal distributions for dynamic class embedding sampling.
result Experimental validation on MNIST and histopathology CRC datasets shows effectiveness of the proposed method.
Bayes-consistent disagreement discrepancy loss improves model robustness.
problem Distribution shift in real-world neural network deployment.
method Introducing a novel disagreement loss that is Bayes consistent.
result Proves existing surrogates for disagreement discrepancy are not Bayes consistent.
Significant advances have been made recently on training neural networks, where the main challenge is in solving an optimization problem with abundant critical points. However, existing approaches to address this issue crucially rely on a restrictive assumption: the training data is drawn from a Gaussian distribution. …
In this paper we study a class of insurance products where the policy holder has the option to insure k of its annual Operational Risk losses in a horizon of T years. This involves a choice of k out of T years in which to apply the insurance policy coverage by making claims against losses in the given year. The…
Study post-hoc Learning to Defer using density-ratio losses.
problem Optimizing decision-making between models and experts.
method Density-ratio losses for post-hoc L2D scorers, derived from class-probability estimation.
result The approach recovers known results and introduces new connections to expert comparison and anomaly detection.
Bayesian analysis reveals asymmetry in financial data.
problem Quantifying asymmetry in financial time series data.
method Bayesian approach, t-Test generalization, two data distribution models, sensitivity analysis.
result Statistical significance of gain/loss asymmetry amounts.
New method ensures generated data statistics match real data distributions.
problem Ensuring generated data statistics match real data distributions in GANs.
method Added a new loss term to the generator loss function using f-divergences and kernel density estimation.
result Improved performance on synthetic and real-world datasets.
We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the condition…
Mitigates anomaly score imbalance in long-tailed distributions.
problem Class imbalance in normal data leads to skewed anomaly detection performance.
method Proposes an importance-weighted loss function to balance anomaly scores.
result Improves anomaly detection performance by 0.043 on real-world datasets.
In modern large-scale machine learning applications, the training data are often partitioned and stored on multiple machines. It is customary to employ the "data parallelism" approach, where the aggregated training loss is minimized without moving data across machines. In this paper, we introduce a novel distributed du…