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.
Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
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.
Efficient algorithms compute lambda quantiles for robust portfolio optimization.
problem Computing lambda quantiles efficiently and robustly.
method Λ-Newton-Bis algorithm combining Newton's method and bisection, interval analysis for multiple roots.
result Demonstrated computational efficiency and practical relevance in portfolio optimization.
Researchers define quantiles on Riemannian manifolds using optimal transport.
problem Defining quantiles on nonlinear manifolds.
method Measure-transportation-based approach.
result Theoretical and empirical properties of quantile functions on manifolds.
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. This study improves hyperparameter optimization for categorical and non-normal data.
problem Bayesian hyperparameter optimization struggles with categorical hyperparameters and non-normal data.
method Integrates conformalized quantile regression to address estimation weaknesses and provides robust calibration guarantees.
result Quantile surrogate architectures and acquisition functions yield superior performance compared to existing methods.
New method learns optimal policies in presence of unmeasured confounders.
problem Optimal policy learning with unobserved confounders.
method Causal-assisted policy learning methods using instrumental variables and negative controls.
result Policies are ildeO(n−1/2) quantile-optimal under mild coverage assumptions. Neural optimal transport improves multivariate conformal prediction.
problem Multivariate quantile regression challenges and existing methods ignore joint distribution geometry.
method Combines neural optimal transport with amortized optimization for efficient training and faster inference.
result Constructs tighter and more informative predictive regions for multivariate conformal prediction.
Many investment models in discrete or continuous-time settings boil down to maximizing an objective of the quantile function of the decision variable. This quantile optimization problem is known as the quantile formulation of the original investment problem. Under certain monotonicity assumptions, several schemes to so…
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.
We propose and analyze StoROO, an algorithm for risk optimization on stochastic black-box functions derived from StoOO. Motivated by risk-averse decision making fields like agriculture, medicine, biology or finance, we do not focus on the mean payoff but on generic functionals of the return distribution. We provide a g…
New algorithm for estimating multivariate quantiles using stochastic optimal transport.
problem Estimating multivariate quantiles from data.
method Stochastic algorithm for entropic optimal transport in Banach spaces, using Fourier coefficients.
result Almost sure convergence of the stochastic algorithm in infinite-dimensional Banach spaces.
Optimal inference in distributed quantile regression without stringent scaling conditions.
problem Challenges in achieving optimal inference in distributed quantile regression due to the non-smooth nature of the QR loss function.
method Double-smoothing approach applied to local and global objective functions, with a trade-off between communication cost and statistical error.
result Established a finite-sample theoretical framework for distributed QR estimators, showing a trade-off between communication cost and statistical error.
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.
A new method for optimizing hyperparameters using conformalized quantile regression.
problem Optimizing hyperparameters with strong assumptions about noise.
method Conformalized quantile regression for more realistic modeling.
result Quicker convergence on empirical benchmarks.
New toolkit for directed distances improves flexibility of OT problems.
problem Optimal transport problems with constraints.
method Directed distances between quantile functions.
result Flexibility in solving OT problems enhanced.
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.
Optimizes quantile and semi-adversarial regret with novel root-logarithmic regularizers.
problem Minimizes regret in adversarial and semi-adversarial online learning.
method FTRL with root-logarithmic regularizers for quantile and semi-adversarial settings.
result Achieves minimax optimal regret bounds in both paradigms.
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.
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.
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile he…
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
problem Constructing minimum-volume prediction regions that satisfy conditional coverage.
method Super-level-set regression (SLS) directly optimizes geometric boundaries of conditional level sets.
result SLS optimizes regions directly, capturing complex conditional structures end-to-end.
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.
CPP solves chance constrained optimization problems with a framework that combines samples and quantile lemma.
problem Chance constrained optimization problems with constraints on random variables.
method CPP framework using samples and quantile lemma to transform into deterministic problem.
result CPP provides a posteriori guarantees on constraint satisfaction and can handle different types of chance constraints.
Study quantile multi-armed bandits for identifying the best arm with a specified quantile level.
problem Identifying the arm with the highest quantile in multi-armed bandits with private rewards.
method Proposed a (non-private) and differentially private successive elimination algorithms for best-arm identification.
result The proposed algorithms are essentially optimal for quantile bandit problems, with finite sample complexity even for distributions with infinite support-size.
Proposes a method to achieve quantile fairness in predictions.
problem Lack of research on quantile fairness in socially sensitive domains.
method Introduces a framework to learn a real-valued quantile function under Demographic Parity fairness.
result Demonstrates superior empirical performance and uncovering fairness-accuracy trade-offs.
New Bayesian models optimize quantiles and expectiles for stochastic functions.
problem Optimizing for quantiles and expectiles in stochastic functions.
method Proposed variational models and BO strategies for quantile and expectile regression.
result Proposed models and strategies outperform existing methods in heteroscedastic, non-Gaussian settings.
This paper analyzes convergence of DP-SGD with adaptive quantile clipping.
problem Empirical success of adaptive clipping methods lacks theoretical understanding.
method Comprehensive convergence analysis of SGD with quantile clipping (QC-SGD).
result Establishes theoretical guarantees for DP-QC-SGD, revealing relationships between quantile selection, step size, and convergence.
A scalable PyTorch framework for non-crossing quantile regression.
problem Non-crossing quantile regression to avoid impossible negative probability densities.
method CJQR-ALM combining Augmented Lagrangian Method, differentiable pinball loss, and L-BFGS optimization.
result Achieves near-zero crossing rates on large datasets within minutes.
Both the median-based classifier and the quantile-based classifier are useful for discriminating high-dimensional data with heavy-tailed or skewed inputs. But these methods are restricted as they assign equal weight to each variable in an unregularized way. The ensemble quantile classifier is a more flexible regularize…
QS-BO optimizes functions using only rank-based feedback.
problem Optimizing expensive functions with unreliable or unavailable metric values.
method Quantile-scaling pipeline to convert ranks into Gaussian targets.
result QS-BO consistently achieves lower objective values and is statistically significant.
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.
This paper solves robust utility maximization with unknown claim dependencies.
problem Investor optimizes utility in the presence of an intractable contingent claim.
method Quantile optimization approach, transforming dynamic problem into static concave optimization.
result Optimal payoffs depend on ambiguity attitude, market conditions, and claim characteristics.
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.
Paper presents a new probabilistic approach for high-dimensional quantile prediction.
problem High-dimensional quantile prediction challenges in robust statistical methods.
method Pseudo-Bayesian framework with scaled Student-t prior and Langevin Monte Carlo.
result Demonstrates strong theoretical guarantees and competitive performance in simulations and real-world data.
Paper introduces P-FGD for online quantile regression models.
problem Training nonparametric additive quantile regression models in online settings.
method Projected functional gradient descent algorithm (P-FGD) for pinball loss.
result P-FGD achieves minimax optimal consistency rate O(t−2s+12s). Paper proposes a joint quantile regression for VaR and ES forecasting.
problem Forecasting Value at Risk (VaR) and Expected Shortfall (ES) of multiple assets simultaneously.
method Multivariate quantile regression framework with time-varying process for VaR and ES.
result The proposed method outperforms other models in risk measure forecasts.
Proposes a non-crossing deep neural network quantile regression method.
problem Quantile crossing in nonparametric quantile regression.
method Non-crossing constraints via rectified linear unit penalty function.
result Established non-asymptotic upper bounds for excess risk.
New pricing methods for α-quantile and early-exercise options using Spitzer identities.
problem Pricing perpetual Bermudan and American options and α-quantile options. method Based on Spitzer identities for general Lévy processes and Wiener-Hopf method.
result Direct calculation of the optimal exercise barrier for early-exercise options.
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.
A new method improves quantile regression for high-dimensional data.
problem Handling heteroscedastic, multimodal, or skewed data in quantile regression.
method Dynamic prototypes-based probability density estimation with conformalized high-density quantile regression.
result Enhanced prediction regions with valid coverage guarantees and scalability to higher dimensions.
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.
This paper improves kernel quantile regression with random features for handling heavy-tailed noises.
problem Handling heavy-tailed noises in kernel quantile regression.
method Introduces a refined error decomposition and establishes a novel connection between KQR-RF and KRR-RF.
result Establishes capacity-dependent learning rates for KQR-RF under mild conditions on the number of random features, which are minimax optimal up to some logarithmic factors.
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.
RQR improves prediction intervals for skewed data.
problem Invalid prediction intervals for skewed noise.
method Relaxed Quantile Regression (RQR) for asymmetric noise.
result Improved prediction intervals with desirable qualities.
A certain spectrum, indexed by a\in[0,\infty], of upper bounds P_a(X;x) on the tail probability P(X\geq x), with P_0(X;x)=P(X\geq x) and P_\infty(X;x) being the best possible exponential upper bound on P(X\geq x), is shown to be stable and monotonic in a, x, and X, where x is a real number and X is a random variable. T…