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.
PCA-Guided Quantile Sampling preserves data structure in large datasets.
problem Preserving data structure in large-scale subsampling.
method PCA QS uses leading principal components to guide stratified sampling.
result PCA QS maintains statistical and geometric structure without distorting semantics.
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, …
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.
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.
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…
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.
In mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density functions are not available. The simulation of any distribution is greatly facilitated by a knowledge of the quantile function, by which uniforml…
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.
Paper introduces DQPOPE for estimating return distributions in reinforcement learning.
problem Estimating the entire return distribution from off-policy data.
method Deep quantile process regression for distributional off-policy evaluation.
result DQPOPE achieves statistical advantages by estimating full return distribution with same sample size.
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…
Bayesian method for estimating quantile sets efficiently.
problem Estimating quantile sets of expensive-to-evaluate functions.
method Bayesian active learning with Gaussian process modeling and Expected Estimator Modification (EEM).
result Efficient estimation of small quantile sets.
The paper studies quantile contributions and their relationship with order statistics in heavy-tailed distributions.
problem Challenges of classical statistical models in heavy-tailed distributions.
method Theoretical study of quantile contribution statistic and its relationship with order statistics. Derivation of closed-form expression for joint CDF of order statistics and quantile contributions.
result Established asymptotic normality of quantile contributions and characterized their limiting distribution.
Bayesian method learns from aggregated quantile data.
problem Limited access to sensitive personal data.
method Bayesian quantile matching estimation based on order statistics.
result Correctly reflects uncertainty of empirical quantiles.
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.
Study quantile reward identification with 1-bit feedback constraints.
problem Best arm identification with quantile reward and 1-bit communication.
method Proposes an algorithm using noisy binary search for quantile reward estimation.
result Derives upper and lower bounds on sample complexity for 1-bit feedback.
We propose confidence sequences -- sequences of confidence intervals which are valid uniformly over time -- for quantiles of any distribution over a complete, fully-ordered set, based on a stream of i.i.d. observations. We give methods both for tracking a fixed quantile and for tracking all quantiles simultaneously. Sp…
CQNPs enhance predictive performance and distribution modeling using quantile regression.
problem Limited predictive likelihood of Gaussian models for complex distributions.
method Introducing Conditional Quantile Neural Processes (CQNPs) that focus on estimating informative quantiles.
result Significant improvements in predictive performance and better modeling of multimodal distributions.
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…
GCQRF predicts survival quantiles without linearity assumptions.
problem Survival analysis with right censoring and nonlinearity.
method Global Censored Quantile Random Forest (GCQRF) for complex relationships.
result GCQRF outperforms existing methods in predictive accuracy.
We introduce autoregressive implicit quantile networks (AIQN), a fundamentally different approach to generative modeling than those commonly used, that implicitly captures the distribution using quantile regression. AIQN is able to achieve superior perceptual quality and improvements in evaluation metrics, without incu…
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.
Flexible framework for bounding high-loss predictions using quantiles.
problem Need for rigorous guarantees in risk-sensitive applications.
method Order statistics of loss values, flexible quantile-based metrics.
result Ability to rigorously control loss quantiles on real-world datasets.
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.
Improves random forest quantile estimation and prediction intervals.
problem Excessive bias in quantile estimates from random forests.
method Minimizes quantile coverage loss (QCL) by adjusting RF parameters.
result QCL-tuned RFs produce more accurate and narrower prediction intervals.
NQE uses quantile regression for fast SBI with cubic Hermite splines.
problem Efficient Bayesian inference for complex models with limited data.
method Neural Quantile Estimation (NQE) learns quantiles autoregressively and interpolates them using cubic Hermite splines.
result NQE achieves state-of-the-art performance on various benchmark problems.
The paper provides rigorous guarantees for m-out-of-n bootstrap estimators of sample quantiles.
problem Lack of parameter-free guarantees for robust inference with heavy-tailed data.
method Central limit theorem and Edgeworth expansion for m-out-of-n bootstrap estimators of sample quantiles.
result Established rigorous guarantees for the soundness of m-out-of-n bootstrap estimators of sample quantiles.
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after normalisation, they follow the same target distribution for each sample. Choosing a "g…
Proposes a deep model for Bayesian quantile regression without Gaussian assumptions.
problem Uncertainty quantification from single forward-pass models is computationally expensive and restrictive.
method Deep evidential learning for Bayesian quantile regression.
result Achieves calibrated uncertainties on non-Gaussian distributions.
Quantile regression is a tool for learning conditional distributions. In this paper we study quantile regression in the setting where a protected attribute is unavailable when fitting the model. This can lead to "unfair'' quantile estimators for which the effective quantiles are very different for the subpopulations de…
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.
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.
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 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.
Quantile regression undercovers true uncertainty, revealing a bias in high dimensions.
problem Under-coverage bias in uncertainty estimation by quantile regression.
method Theoretical study on coverage of uncertainty estimation algorithms in learning quantiles.
result Quantile regression undercovers true uncertainty, revealing a bias in high dimensions.
A new model captures financial asset returns' tail behaviors and outperforms GARCH family.
problem Capturing the dynamic tail behaviors of financial asset returns.
method Combines LSTM with a novel parametric quantile function.
result Out-of-sample forecasts of conditional quantiles or VaR outperform GARCH family.
QFIL improves offline RL by filtering data to reduce bias and variance.
problem Improving offline reinforcement learning policies with limited data.
method QFIL uses a filtered dataset to improve policies, trading off bias and variance through quantile selection.
result QFIL provides a safe policy improvement step with function approximation and effectively balances bias and variance.
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.
A new approach to VAEs tackles variance shrinkage using quantile regression.
problem Variance shrinkage in VAEs leads to underestimation of uncertainty.
method Using quantile regression to estimate mean and variance, avoiding shrinkage.
result Our approach effectively detects anomalies and improves lesion detection.
HS-BQR extends horseshoe prior for Bayesian quantile regression.
problem Estimating quantiles in high-dimensional data with bias and error.
method Horseshoe prior for Bayesian quantile regression with a fast sampling algorithm.
result HS-BQR outperforms other shrinkage priors in coefficient bias and forecast error.
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.
Study minimax linear regression under quantile risk, improving existing bounds and providing new results.
problem Designing minimax procedures in linear regression under quantile risk.
method Analyzes realizable setting with Gaussian noise, extends to all p-th power error functions, develops new lower and upper bounds.
result Proves minimaxity of a variant of the min-max regression procedure for all p-th power error functions.
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 develops a new method to model treatment effects that are heterogeneous across different quantiles.
problem Modeling treatment effects that vary across different quantiles of the outcome distribution.
method The paper combines quantile classification with local polynomial estimation to build a decision tree and forest.
result The proposed QLPRT and QLPRF methods provide a new way to estimate and infer heterogeneous treatment effects.
Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of symbolic data analysis, we develop a time-series model for forecasting quantile-function-valued (…