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. New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
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.
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.
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.
We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is expanded from a set of fixed quantiles to the whole Quantile Function by a univar…
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.
Develops a new method for sampling from Bayesian credible sets using deep generative quantile learning.
problem Sampling from posterior distributions in high-dimensional spaces with intractable likelihoods.
method Uses deep neural networks to implicitly sample from Bayesian credible sets via a push-forward mapping and Monge-Kantorovich depth.
result Demonstrates improved performance and theoretical consistency of the quantile learning framework.
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…
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 …
Unified approach for estimating quantiles of potential outcomes using inverse estimating equations.
problem Estimating quantiles of potential outcomes for causal inference.
method Inverse estimating equations and moment function.
result Unified approach to estimate mean and quantiles of potential outcomes.
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.
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.
Quantum algorithm samples from SDEs using DQCs and quantile mechanics.
problem Sampling from solutions of stochastic differential equations.
method Differentiable quantum circuits (DQCs) encoding latent variables, quantile mechanics.
result Quantum algorithm generates time-series from SDEs.
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, …
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…
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…
New method for risk quantification using quantile processes and measure distortions.
problem Risk quantification and valuation in financial markets.
method Develops a novel stochastic valuation principle based on probability measure distortions induced by quantile processes.
result Introduces a system of subjective probability measures that indexes a stochastic valuation principle susceptible to probability measure distortions.
We show how to reduce the process of predicting general order statistics (and the median in particular) to solving classification. The accompanying theoretical statement shows that the regret of the classifier bounds the regret of the quantile regression under a quantile loss. We also test this reduction empirically ag…
The paper derives formulas for moments of a Student t distribution and applies them to quantify Lp-quantiles.
problem Understanding the moments and quantiles of a Student t distribution.
method Developed formulas for partial and complete moments, and derived relationships between Lp-quantiles. result For a Student t distribution, the Ln−j+1-quantile and Lj-quantile coincide at any confidence level. 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.
Causal inference using observational data is challenging, especially in the bivariate case. Through the minimum description length principle, we link the postulate of independence between the generating mechanisms of the cause and of the effect given the cause to quantile regression. Based on this theory, we develop Bi…
Deep learning improves PV generation quantile forecasting.
problem Accurate probabilistic forecasting of PV generation.
method Developed an encoder-decoder deep learning model for multi-output quantile PV forecasting.
result The model improves forecast quality and computational efficiency.
New bounds for quantile aggregation unify and clarify existing methods.
problem Analytical bounds for quantile aggregation with dependence uncertainty.
method Using inf-convolution of quantile-based risk measures, establish new analytical bounds called convolution bounds.
result Convolution bounds are the best available and provide sharp results in many cases.
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.
Deep Huber QRNs predict Huber quantiles for house prices.
problem Predicting more functionals of predictive probability distributions.
method Training a DL algorithm with the Huber quantile scoring function.
result DHQRNs provide satisfactory absolute performance in house price prediction.
TSVQR captures heterogeneous and asymmetric data using quantile regression.
problem Capturing heterogeneous and asymmetric information in modern data.
method Twin Support Vector Quantile Regression (TSVQR) with two nonparallel planes for quantile levels.
result TSVQR outperforms previous methods in capturing and learning from data.
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.
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is unknown, the database is sparse, and therefore special tail models are used. Very often…
We consider new formulations and methods for sparse quantile regression in the high-dimensional setting. Quantile regression plays an important role in many applications, including outlier-robust exploratory analysis in gene selection. In addition, the sparsity consideration in quantile regression enables the explorati…
New method solves quantile crossing problem in econometrics.
problem Quantile crossing problem in quantile regression.
method Flexible check function approach.
result Eliminates or greatly reduces quantile crossing problem.
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. Paper introduces a new robust loss function for RL.
problem Heuristic selection of threshold parameters in quantile Huber loss.
method Derived from Wasserstein distance, captures noise in quantile values.
result Enhances robustness against outliers and enables parameter adjustment.
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.
New framework forecasts ES using weighted quantiles.
problem Forecasting Expected Shortfall (ES) in financial markets.
method Two-step procedure: VaR estimation through quantile regressions, ES computation as weighted average.
result Proposed models outperform other methods in stock market indices forecasting.
Bayesian QFSTS model tackles feature selection in quantile time series analysis.
problem Quantile feature selection in correlated multivariate time series data.
method Bayesian dimension reduction methodology using QFSTS model with multivariate asymmetric Laplace distribution, spike-and-slab prior, Metropolis-Hastings algorithm, and Bayesian model averaging.
result QFSTS model outperforms in feature selection, parameter estimation, and forecasting.
Bayesian method improves extreme quantile estimation with zero coverage error.
problem Estimating extreme quantiles with zero coverage error in small samples.
method Bayesian quantile estimation using Jeffreys prior.
result Bayesian method results in zero coverage error, unlike maximum likelihood.
New algorithms improve uncertainty estimation in satellite precipitation predictions.
problem Lack of uncertainty estimates in machine learning spatial precipitation predictions from satellite data.
method Benchmarked six algorithms including LightGBM, compared using quantile scoring functions and rules.
result LightGBM outperformed other algorithms in quantile scoring rule by 11.10%.
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.
This work extends VQR to non-linear cases and provides scalable solvers.
problem Limitations of VQR in handling non-linear relationships and scalability.
method Extension to non-linear VQR, vector monotone rearrangement, fast solvers.
result Substantial improvement over linear VQR and scalable solvers.
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.
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.
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 …
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.
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.
Predicts asset return distributions using LSTM and quantile regression.
problem Predicting complex asset return distributions.
method Two-stage approach: quantile prediction using asset-specific features, market data adjustment.
result Significantly outperforms existing models (98% improvement over baseline).
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.
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.