The paper examines risk aggregation under mixtures of marginals, finding that more homogeneous distributions lead to larger uncertainty.
problem Investigating the impact of mixing on risk aggregation uncertainty.
method Analyzes ordering relations and inequalities for aggregation sets under distribution and quantile mixtures.
result More homogeneous marginals result in larger aggregation sets, indicating greater model uncertainty.
Solves risk minimization problem with SSD constraints.
problem Finding SSD-minimal quantile function under mixed constraints.
method Explicitly works out SSD-minimal solution and relates to Skorokhod problem.
result Explicit solution to risk minimizing problem.
We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk ma…
New insights into risk aversion for complex decision models.
problem Understanding risk aversion in non-monotone decision models.
method Characterization of probabilistic risk aversion for generalized rank-dependent functions.
result Probabilistic risk aversion is determined by the distortion function, which is convex or scaled quantile-spread mixtures.
In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be co…
Develops new algorithms for QRF to handle mixed-frequency and longitudinal data.
problem Handling mixed-frequency and longitudinal data in quantile regression.
method Mixed-Frequency Quantile Regression Forest (MIDAS-QRF) and Finite Mixture Quantile Regression Forest (FM-QRF).
result Valid and flexible models for complex empirical settings in financial risk management and climate-change impact evaluation.
Study federates measurement of demographic disparities from quantile sketches.
problem Misalignment of fairness goals with siloed data collection and privacy regulations.
method Federated auditing of demographic parity through score distributions, using Wasserstein--Frechet variance and quantile summaries.
result Proposes a one-shot, communication-efficient protocol to estimate global disparity and its decomposition.
LCMQR improves prediction intervals by adapting to local heteroscedasticity.
problem Efficient and adaptive prediction intervals for local heteroscedasticity.
method LCMQR combines multi-quantile information with kernel-based localization.
result LCMQR constructs tighter intervals than prior methods, especially in heterogeneous environments.
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.
Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is evaluated on the estimated mixture instead of the (unknown) true one, then it is impor…
In this paper we propose a model with a Dirichlet process mixture of gamma densities in the bulk part below threshold and a generalized Pareto density in the tail for extreme value estimation. The proposed model is simple and flexible allowing us posterior density estimation and posterior inference for high quantiles. …
New VAE model improves data fitting without sacrificing computational efficiency.
problem Limitation of Gaussian assumption in VAE for continuous variable fitting.
method Infinite mixture of asymmetric Laplace distribution in decoder, nonparametric M-estimator for quantile estimation.
result Model demonstrates superior data privacy adjustment and better distribution fitting.
We propose a novel exponentially-modified Gaussian (EMG) mixture residual model. The EMG mixture is well suited to model residuals that are contaminated by a distribution with positive support. This is in contrast to commonly used robust residual models, like the Huber loss or ℓ1, which assume a symmetric contami…
Paper tackles overestimation bias in continuous control, improving performance by 25%.
problem Overestimation bias in off-policy learning.
method Truncated Quantile Critics (TQC) combines distributional representation, truncation, and ensembling of critics.
result TQC outperforms state-of-the-art methods by 25% on the Humanoid environment.
The paper addresses risk sharing and variability measures among agents with general risk preferences.
problem Risk sharing and variability measures among agents with general risk preferences.
method Characterizes Pareto-optimal allocations using Gini deviation, mean-median deviation, and inter-quantile difference as variability measures.
result Optimal allocations are not comonotonic and feature a mixture of pairwise counter-monotonic structures.
A new method detects changes in mixture models quickly and accurately.
problem Detecting changes in mixture models with heavy-tailed components.
method Change-point methods based on robust and quick approach.
result The method is up to 500 times faster and more accurate than existing methods.
New method estimates SW distance using CDFs for scalable data parallelism.
problem Estimating SW distance efficiently for large datasets.
method Estimators based on CDFs of projected measures, avoiding sorting.
result Efficient estimation for large datasets and federated learning.
In regression tasks, aleatoric uncertainty is commonly addressed by considering a parametric distribution of the output variable, which is based on strong assumptions such as symmetry, unimodality or by supposing a restricted shape. These assumptions are too limited in scenarios where complex shapes, strong skews or mu…
We introduce and compare new variability measures based on risk quantiles.
problem Comparing variability measures in risk management.
method Developed a framework for one-parameter families of inter-Expected Shortfall differences and inter-expectile differences.
result Characterized symmetric and comonotonic variability measures as mixtures of inter-Expected Shortfall differences.
New approach for distributed learning of Gaussian mixtures.
problem Large datasets distributed across different centers.
method Split-and-conquer approach with MM algorithm.
result New estimator is consistent and retains root-n consistency.
A framework uses a mixture of predictors for semi-supervised inference.
problem Limited labeled data, abundant unlabeled data.
method Mixture of Experts (MOE) for semi-supervised inference.
result MOE-powered inference framework achieves smallest possible variance.
A new method for estimating SW from streaming data.
problem Estimating Wasserstein distance from sample streams.
method Introducing a streaming estimator of the 1DW and applying it to all projections.
result Stream-SW achieves more accurate approximation of SW than random subsampling.
Unified framework for PDF estimation using MDL-based binning and tensor factorization.
problem Challenges in estimating PDFs for non-uniform, multimodal data.
method MDL-based binning with quantile cuts, tensor factorization (CPD).
result Effective PDF estimation on synthetic and real data.
Investigates methods to regularize quantile regression for accurate predictions.
problem Improving accuracy and fairness in quantile regression predictions.
method Various regularization techniques including expected pinball loss, monotonicity constraints, and rate constraints.
result Deep lattice networks can maintain non-crossing quantiles and improve calibration and fairness.
A new method avoids quantile crossing in time series forecasting.
problem Quantile crossing in joint quantile regressions.
method Incremental (Spline) Quantile Functions (I(S)QF) with neural network.
result Improves consistency and accuracy in time series forecasting.
New risk measures for quantiles under ambiguity improve risk sharing.
problem Risk optimization under ambiguity using quantiles.
method Introducing Choquet quantiles and Choquet Expected Shortfall.
result Optimal allocations for quantile agents under ambiguity.
Paper finds robust Λ-quantiles equal to extremal distributions.
problem Investigating robust models for Λ-quantiles with partial loss information. method Extending classical quantiles using Λ-quantiles and applying results from robust quantiles. result Robust Λ-quantiles equal to Λ-quantiles of extremal distributions. SCQRNN prevents quantile crossing and improves computational efficiency.
problem Quantile crossing issue in regression models.
method Integrates ad hoc sorting in training to prevent quantile crossing and enhance computational efficiency.
result SCQRNN achieves faster convergence and non-intersecting quantiles.
Axiomatizes Λ-quantiles, a generalization of quantiles.
problem Found an axiomatization for Λ-quantiles. method Characterized Λ-quantiles using the locality property. result Local changes in distribution do not affect Λ-quantiles. Develops a method to ensure accurate quantile forecasts across multiple levels.
problem Ensuring accurate quantile forecasts at multiple levels, even under distribution shifts.
method Multi-level quantile tracker (MultiQT) wraps around any forecaster to produce calibrated forecasts.
result Guaranteed calibration of quantile forecasts at multiple levels, even against adversarial shifts.
Proposes a method to estimate conditional quantiles using both high-fidelity and low-fidelity data.
problem Difficulty in estimating conditional quantiles with scarce high-fidelity data.
method Two-stage, model-agnostic method using local quantile link and level function estimation.
result The method yields more accurate quantile estimates and tighter prediction intervals.
Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is also known as online quantile estimation. This area is relevant to the analysis …
The paper proposes a method for predicting equity premium using penalized quantile regression.
problem Heteroscedasticity and heavy-tails in equity premium prediction.
method Penalized quantile regression with consistent variable selection across multiple quantiles.
result The proposed method outperforms benchmark methods and reveals interesting predictor relationships.
Supervised learning is an active research area, with numerous applications in diverse fields such as data analytics, computer vision, speech and audio processing, and image understanding. In most cases, the loss functions used in machine learning assume symmetric noise models, and seek to estimate the unknown function …
Improved conformalized quantile regression for adaptive prediction intervals.
problem Lack of adaptiveness in the conformal step of conformalized quantile regression.
method Cluster explanatory variables by permutation importance and apply k conformal steps.
result Improved prediction intervals are more adaptive to heteroscedasticity.
Proposes a deep learning method to ensure non-crossing quantiles in conditional distributions.
problem Non-crossing quantiles issue in deep learning QR models.
method Generic deep learning algorithm enforcing quantile monotonicity.
result Ensures non-crossing quantiles up to machine precision.
Smoothed SGD improves quantile estimation without crossing curves.
problem Estimating quantiles without crossing estimated curves.
method Smoothed SGD algorithm with Bahadur representation and Gaussian approximation.
result Smoothed SGD provides non-asymptotic tail probability bounds and a Gaussian approximation for quantile estimates.
Private estimation of many quantiles using differential privacy.
problem Estimating quantiles of a distribution privately.
method Two approaches: 1) Private estimation of empirical quantiles, 2) Uniform density estimation.
result There is a tradeoff between estimating quantiles at specific points and uniformly estimating the quantile function.
Bayesian method improves quantile estimation and subset selection.
problem Estimating specific percentiles of the response distribution.
method Bayesian decision analysis perspective, optimal point estimates, interpretable uncertainty quantification, scalable subset selection.
result Substantial gains in quantile estimation accuracy, inference, and variable selection over competitors.
New quantile methods improve uncertainty quantification across various models.
problem Improper quantile loss limits model flexibility and accuracy.
method Developed new quantile methods that optimize for calibration, sharpness, and centered intervals.
result Improved conditional quantiles and better uncertainty quantification across diverse models.
This paper analyzes quantiles of heavy-tailed distributions, separating projection direction and quantile threshold effects.
problem Analyzing quantiles of heavy-tailed distributions with estimated parameters.
method Introduces a Q-Q orthogonality formulation to separate projection-direction and quantile-threshold effects.
result Decomposes the difference between empirical and population quantiles into three terms.
We develop a novel approach for the construction of quantile processes governing the stochastic dynamics of quantiles in continuous time. Two classes of quantile diffusions are identified: the first, which we largely focus on, features a dynamic random quantile level and allows for direct interpretation of the resultin…
DeRegiME forecasts with regime structure, improving probabilistic predictions across various time series.
problem Probabilistic forecasting discards residual uncertainty, and distribution shifts are hard to capture.
method DeRegiME uses a sparse variational Gaussian process with a nonstationary regime-mixing kernel to separate latent uncertainty regimes.
result DeRegiME improves NLPD by 20.3% on average across benchmarks, with gains on CRPS and MSE.
ConquerNet smooths quantile regression for deep learning with minimax guarantees.
problem Optimization challenges in quantile regression for deep models.
method ConquerNet uses convolution-smoothed quantile ReLU neural networks.
result ConquerNet provides minimax guarantees and outperforms standard quantile neural networks.
Improved quantile estimation model for VaR.
problem Improving quantile estimation under distribution estimation.
method Develops a compensatory model with a penalty term to control convergence error.
result Significant improvement in VaR performance.
Paper proposes a method to estimate multiple dynamic quantiles jointly.
problem Limited joint estimation of multiple dynamic quantiles.
method Introduces a crossing penalty objective function for joint estimation.
result Validation through Monte Carlo experiments and empirical application on FTSE100 shows effectiveness.
This paper examines quantile dependence between international stock markets and evaluates its use for improving volatility forecasting. First, we analyze quantile dependence and directional predictability between the US stock market and stock markets in the UK, Germany, France and Japan. We use the cross-quantilogram, …
A new method forecasts financial tail risks by combining and weighting quantiles.
problem Reducing uncertainty in financial tail risk forecasting.
method Two-step procedure: quantile combination followed by ES computation.
result The proposed framework outperforms individual models and simple approaches.