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.
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.
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.
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.
It has long been agreed by academics that the inversion method is the method of choice for generating random variates, given the availability of the quantile function. However for several probability distributions arising in practice a satisfactory method of approximating these functions is not available. The main focu…
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.
Random forests are powerful non-parametric regression method but are severely limited in their usage in the presence of randomly censored observations, and naively applied can exhibit poor predictive performance due to the incurred biases. Based on a local adaptive representation of random forests, we develop its regre…
We offer a simplified proof for Expected Shortfall's dual representation.
problem The dual representation of Expected Shortfall.
method Basic properties of quantile functions.
result New proof of Expected Shortfall's subadditivity.
Random forests are powerful non-parametric regression method but are severely limited in their usage in the presence of randomly censored observations, and naively applied can exhibit poor predictive performance due to the incurred biases. Based on a local adaptive representation of random forests, we develop its regre…
Proposes QQE for transforming and embedding data distributions.
problem Transforming and embedding data distributions for better representation or visualization.
method Quantile-Quantile Embedding (QQE) using quantile-quantile plot concept.
result QQE allows for better discrimination of classes in some cases.
The expectile can be considered as a generalization of quantile. While expected shortfall is a quantile based risk measure, we study its counterpart -- the expectile based expected shortfall -- where expectile takes the place of quantile. We provide its dual representation in terms of Bochner integral. Among other prop…
Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully. The theory of debiased estimators can be developed in the context of quantile regression models for a fixed quantile value…
This paper improves reinforcement learning by estimating return distributions using quantiles.
problem Improving reinforcement learning by estimating return distributions.
method Quantile-based distributional reinforcement learning, using quantile-projected distributional Bellman equations.
result The quantile-based approach achieves optimal sample efficiency and asymptotic efficiency.
This paper improves reinforcement learning by estimating return distributions using quantiles.
problem Improving reinforcement learning by estimating return distributions.
method The paper uses quantile-based distributional reinforcement learning to characterize return distributions.
result The quantile-based approach achieves optimal sample efficiency and asymptotic efficiency.
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.
SEMF predicts prediction intervals for ML models using latent variables.
problem Uncertainty quantification in ML models, especially for diverse data distributions.
method Supervised Expectation-Maximization Framework (SEMF) extending EM algorithm for latent variable modeling.
result SEMF produces narrower prediction intervals with desired coverage probability.
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.
New KQEs improve probability metrics without mean function constraints.
problem Improving probability metrics without relying on mean function representations.
method Kernel quantile embeddings (KQEs) to construct new distances.
result KQEs offer a competitive alternative to MMD with near-linear cost.
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…
New formula for implied volatility from Black-Scholes model.
problem Computing implied volatility from Black-Scholes model.
method Analytical solution using inverse Gaussian distribution.
result Explicit formulas for implied volatility with high precision.
Introduces generalized Orlicz premia for broader applicability.
problem Developing a flexible framework for insurance premium calculation.
method Introduces a generalized Orlicz premium definition using non-convex loss functions.
result Generalized Orlicz premia encompass various specific cases and maintain key properties.
Hybrid model combines risk measures for better portfolio allocation.
problem Optimizing portfolios with various risk measures.
method Mean-variance hybrid model combining spectral risk measure and quantile optimization.
result Hybrid model outperforms classical mean-variance model in risk allocation.
New method learns interaction-aware orderbook representation for better intraday electricity price forecasting.
problem Challenges in probabilistic intraday electricity price forecasting due to dynamic orderbook microstructure.
method OrderFusion: an end-to-end and parameter-efficient probabilistic forecasting model that learns interaction-aware representation of buy-sell dynamics.
result Consistent improvements over conventional baselines in probabilistic forecasting of CID price indices.
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.
Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.
problem Understanding max- and min-stability in stochastic dominance.
method Representation theorem for functionals satisfying max-stability, combining max- and min-stability to define Lambda-quantiles.
result New characterizations of functionals, including Lambda-quantiles, in finance and political science.
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.
Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts. To be robust to outliers and differences in scale across features, a matrix factorization step is usually preceded by ad-hoc feature normalization steps…
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.
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.
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…
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.
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…
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.
IQ-BART models conditional quantiles using a non-parametric Bayesian approach.
problem Capturing multimodal predictive distributions in time series forecasting.
method Implicit Quantile BART (IQ-BART) augments data with quantile values for non-parametric quantile function estimation.
result IQ-BART provides flexible distribution-free regression with theoretical guarantees.
The paper introduces a new method for forecasting financial risk using quantile-based modeling.
problem Forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) for financial returns.
method Semiparametric approach using restricted quantile regression to model the conditional scale of financial returns.
result The method provides robust, distribution-free estimates of extreme losses and captures risk dynamics.
Paper introduces arctan pinball loss for XGBoost quantile regression.
problem Efficiently predicting multiple quantiles with XGBoost.
method Smooth approximation of pinball loss for XGBoost, using arctan pinball loss.
result Arctan pinball loss reduces quantile crossings and improves efficiency.