Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of su…
Derives derivatives of risk measures for various types of portfolio losses.
problem Calculating precise risk measures for portfolio losses.
method Analyzes first and second order derivatives of risk measures for both continuous and discrete portfolio loss scenarios.
result Provides asymptotic results for conditional moments of heavy-tailed portfolio losses.
This paper analyzes the conflict between Hamming loss and subset accuracy in multi-label classification.
problem The conflict between Hamming loss and subset accuracy in multi-label classification.
method The paper analyzes the learning guarantees of algorithms optimizing Hamming loss and subset accuracy, providing theoretical bounds and experimental support.
result Optimizing Hamming loss with its surrogate loss can lead to good performance on subset accuracy in small label spaces, contrary to theoretical expectations.
The paper compares different risk measures for optimal portfolio strategies.
problem Finding optimal portfolio strategies with various risk measures.
method Applying the Black-Scholes model and Martingale method to solve the static optimization problem.
result Comparison of different risk measures' performances on terminal wealths and optimal strategies.
Study proposes a differentiable surrogate loss function for optimizing Fβ score in binary classification with imbalanced data.
problem Non-differentiability of Fβ score makes it unsuitable for optimization by gradient-based learning. method Investigated relationship between Fβ score and loss functions, proposed a differentiable surrogate loss function. result Gradient paths of the proposed surrogate Fβ loss function approximate the gradient paths of the Fβ score. Paper improves privacy-preserving measurement of advertising incrementality.
problem Privacy degradation in randomized lift tests for advertising measurement.
method Formulates a robust causal decision problem under signal losses, projecting clean worlds onto incrementality.
result Sharp decision frontier shows valid certification or rejection outside the frontier.
We propose a generalization of the classical notion of the V@Rλ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an appropriate family of acceptance set…
This paper introduces new risk measures for evaluating losses with varying time horizons.
problem Capturing horizon risk and cash non-additivity in risk evaluation.
method Uses BSDEs and shortfall approaches to develop h-generalized shortfall risk measures.
result Introduces hq-entropic risk measures as a new family of fully-dynamic risk measures.
Robust variable selection for high-dimensional data with missing and measurement errors.
problem Missing data and measurement errors confound data distribution.
method Exponential loss function with inverse probability weighting and additive error models.
result The Atan punishment method improves robust variable selection.
New methods evaluate data representations by complexity of low-loss predictor learning.
problem Evaluating quality of data representations for downstream tasks.
method Surplus Description Length (SDL) and ε Sample Complexity (εSC) methods.
result Methods measure the information needed to approximate optimal predictor up to specified tolerance.
Quantum machine learning uses quantum cross entropy to minimize loss, but measurement loss affects this process.
problem Quantum machine learning's loss minimization through cross entropy is affected by measurement outcomes.
method Defined quantum cross entropy, proved its lower bounds, and investigated its relation to quantum fidelity and likelihood.
result Quantum cross entropy is lower-bounded by negative log-likelihood when derived from quantum data, but measurement outcomes can cause loss.
Proposes measures for uncertainty quantification using proper scoring rules.
problem Uncertainty quantification for prediction tasks.
method Decomposes proper scoring rules into divergence and entropy components, tailoring uncertainty quantification to specific tasks.
result Flexibility in uncertainty quantification improves performance in selective prediction and active learning.
New risk measure considers horizon risk and interest rate uncertainty.
problem Dynamic risk evaluation considering horizon risk and interest rate uncertainty.
method Introduced a risk measure based on generalized Tsallis entropy.
result New q-entropic risk measure quantifies capital requirement.
We propose a max-pooling based loss function for training Long Short-Term Memory (LSTM) networks for small-footprint keyword spotting (KWS), with low CPU, memory, and latency requirements. The max-pooling loss training can be further guided by initializing with a cross-entropy loss trained network. A posterior smoothin…
Paper introduces DCoVaR for aggregate risk models, outperforming existing methods.
problem Lack of coherent risk measures for aggregate risk models.
method Proposes Dependent Conditional Value-at-Risk (DCoVaR) for a target loss dependent on another random loss.
result DCoVaR outperforms MCoVaR and CCoVaR in numerical simulations and empirical studies.
The paper develops robust risk measures for uncertain loss positions.
problem Risk assessment for loss positions with uncertain distributions.
method Robust optimized certainty equivalents and generalized quantiles are proposed and analyzed.
result Robust expectiles with specific penalization functions are coherent risk measures.
Regulation and risk management in banks depend on underlying risk measures. In general this is the only purpose that is seen for risk measures. In this paper we suggest that the reporting of risk measures can be used to determine the loss distribution function for a financial entity. We demonstrate that a lack of suffi…
Develops high-dimensional measurement error models for non-linear loss functions.
problem Measurement errors in ultrahigh-dimensional biomedical data.
method Lipschitz loss functions, L1 norm minimization, Lasso analog.
result Improved accuracy in classification and quantile regression problems.
The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index and we provide its dual representation for general probability spaces. However, the gain-loss ratio w…
Methodology measures financial impacts using existing credit loss infrastructure.
problem Measuring the impact of financial scenarios on expected credit losses.
method Captures scenario effects through changes in default probabilities; uses existing provisioning infrastructure.
result Methodology validated through standardized climate scenario exercise in Canada and Quebec.
Sparse model selection by structural risk minimization leads to a set of a few predictors, ideally a subset of the true predictors. This selection clearly depends on the underlying loss function L~. For linear regression with square loss, the particular (functional) Gradient Boosting variant L2−Boosting exce…
The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, s…
New bounds on neural network test loss derived from conditional information measures.
problem Estimating test loss of neural networks trained on limited data.
method Framework based on conditional information density between hypothesis and training set.
result Tail bounds on test loss decay as 1/n, improving over previous 1/sqrt{n} bounds.
Investors suffer welfare loss despite having better information.
problem Welfare loss among investors with absolute information advantages.
method Examined financial markets with heterogenous investors and objective measures of welfare.
result Investors incur welfare loss even with better information, revealing a double loss phenomenon.
New metric to measure liquidity position PNL, delta hedging algorithm for automated market makers.
problem Vulnerability of liquidity positions to price changes in underlying assets.
method Proposes a new metric for measuring PNL, delta hedging algorithm for various AMMs.
result New metric more accurately measures net value change due to price movement.
This paper develops convex surrogates for optimizing the multi-label F-measure.
problem Optimizing the F-measure for multi-label classification is computationally hard.
method Designing convex surrogate losses calibrated for the F-measure.
result The F-measure for multi-label problems has a rank of at most s2+1. We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting measure are shown to satisfy an infinit…
Submodularity is studied for convex risk measures, including Expected Shortfall.
problem Characterizing submodularity in convex risk measures.
method Analyzing submodularity properties of law-invariant coherent risk measures, including Expected Shortfall and Value-at-Risk.
result AES is submodular only when it reduces to ES, and empirical analysis shows AES violations are less frequent than VaR and ES violations.
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the su…
We introduce a scalable measure of curvature for analyzing training dynamics of large language models.
problem Analyzing the training dynamics of large language models due to high computational cost of measuring Hessian sharpness.
method We introduce critical sharpness and relative critical sharpness as computationally efficient measures capturing Hessian sharpness phenomena.
result We provide the first demonstration of sharpness phenomena at scale up to 7B parameters.
The paper decomposes probabilistic scores into reliability, uncertainty, and information loss.
problem Understanding the reliability and uncertainty of probabilistic predictions.
method Developed decomposition identities for proper losses, quantifying reliability, residual uncertainty, and information gain.
result A three-term identity for classification scores, revealing miscalibration, grouping term, and feature-level uncertainty.
Understanding and measuring model risk is important to financial practitioners. However, there lacks a non-parametric approach to model risk quantification in a dynamic setting and with path-dependent losses. We propose a complete theory generalizing the relative-entropic approach by Glasserman and Xu to the dynamic ca…
In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a distortion premium principle. Firstly, we show that how optimal reinsurance mod…
The paper explores optimal insurance contracts using various deviation measures.
problem Optimal insurance contracts with mean-deviation measures.
method Study of convex signed Choquet integrals and standard deviation as deviation measures, analyzing premium principles like expected value, Value-at-Risk, and Expected Shortfall.
result Characterization of optimal indemnities and deductibles under different premium principles.
Study inverse problems with measure samples, improving estimator calibration and recovery.
problem Inverse problems with unknown potentials observed through measure samples.
method Introduced convex empirical objectives and sharpened Fenchel--Young losses for finite-dimensional potential classes.
result High-probability parameter recovery bounds for inverse entropic unbalanced optimal transport and inverse JKO learning.
The paper argues that uncertainty quantification in ML is application-specific and proposes a flexible family of measures.
problem The need for proper uncertainty quantification in machine learning for safety-critical applications.
method A flexible family of uncertainty measures tailored to specific applications, using proper scoring rules to control characteristics.
result Different uncertainty measures are more suitable for different tasks (e.g., selective prediction, out-of-distribution detection, active learning).
Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissi…
Consider a financial market in which an agent trades with utility-induced restrictions on wealth. For a utility function which satisfies the condition of reasonable asymptotic elasticity at −∞ we prove that the utility-based super-replication price of an unbounded (but sufficiently integrable) contingent claim i…
Model calculates capital requirements for multi-line insurance companies.
problem Measuring and capitalizing on incurred claims risk for multi-line property and casualty insurers.
method Stochastic model integrating accident semester, development lag effects, autocorrelation, and hierarchical copula.
result Model accurately reproduces empirical loss ratio dynamics and quantifies overall portfolio risk.
New loss functions based on f-divergences improve language model performance.
problem Improving multiclass classification and language modeling performance.
method Constructing new convex loss functions using f-divergences and deriving an operator for computation.
result The α-divergence loss function with α=1.5 performs well across various tasks. Boosting with tempered exponential measures improves AdaBoost's convergence rate.
problem Improving the convergence rate of AdaBoost.
method Introducing tempered exponential measures (TEMs) to generalize AdaBoost's approach.
result t-AdaBoost achieves an improved convergence rate compared to AdaBoost, especially for t∈[0,1). Paper introduces a new G⋆ regret measure for online convex optimization with smooth losses.
problem Online convex optimization with smooth losses.
method Introduces a new G⋆ regret measure that depends on the cumulative squared gradient norm. result The G⋆ regret can be arbitrarily sharper than existing measures when losses have vanishing curvature. This work examines uncertainty sampling in binary classification using equivalent loss.
problem Lack of consensus on proper uncertainty definition and theoretical guarantees for active learning.
method Systematically examines uncertainty sampling via equivalent loss, proving its optimality.
result Established that uncertainty sampling optimizes against equivalent loss, providing theoretical guarantees.
Unified framework for risk evaluation under uncertainty.
problem Risk assessment under multiple economic scenarios.
method Axiomatic framework for generalized risk measures.
result Characterization of worst-case, coherent, and robust risk measures.
Motivated by liquidity risk in mathematical finance, D. Lacker introduced concentration inequalities for risk measures, i.e. upper bounds on the \emph{liquidity risk profile} of a financial loss. We derive these inequalities in the case of time-consistent dynamic risk measures when the filtration is assumed to carry a …
Neural networks' weights don't converge to stationary points but training loss stabilizes.
problem The disconnect between theoretical analyses and neural network training practice.
method An invariant measure perspective inspired by ergodic theory of dynamical systems.
result The distribution of weights converges to an approximate invariant measure, explaining loss stabilization.
Linear NDCG is used for measuring the performance of the Web content quality assessment in ECML/PKDD Discovery Challenge 2010. In this paper, we will prove that the DCG error equals a new pair-wise loss.
New binary loss functions improve density ratio estimation accuracy.
problem Improving accuracy of density ratio estimators using binary classifiers.
method Characterized loss functions based on prescribed error measures in Bregman divergences.
result Novel loss functions prioritize accurate estimation of large density ratio values.