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.
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.
Paper proposes differentially private quantile regression for high-dimensional data.
problem Privacy concerns in big data with heterogeneous sensitive personal information.
method Newton-type transformation for reformulating quantile regression into an OLS problem; iterative updates for estimation; debiased estimator for inference; communication-efficient bootstrap.
result Near-optimal statistical accuracy and formal privacy guarantees achieved.
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.
Paper proposes a federated learning method for quantile inference with local differential privacy.
problem Federated learning of quantile inference under local differential privacy constraints.
method Local stochastic gradient descent with randomized mechanism for privacy and efficiency.
result Asymptotic normality and functional central limit theorem for the proposed estimator.
Parametric quantile regressions are a useful tool for creating probabilistic energy forecasts. Nonetheless, since classical quantile regressions are trained using a non-differentiable cost function, their creation using complex data mining techniques (e.g., artificial neural networks) may be complicated. This article p…
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…
Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is however piece-wise constant (the sorting permutation of a vector does not change if th…
We develop a method for quantile-based sensitivity analysis in models with discontinuities.
problem Uncertainty in interpreting discontinuous models using traditional derivatives.
method Quantile-based derivatives for discontinuous models with discrete inputs.
result Derivatives of quantile-based outputs are well-defined and provide meaningful insights.
Efficiently estimates quantiles and maximum in unbounded datasets with differential privacy.
problem Efficiently estimating quantiles and maximum in unbounded datasets with differential privacy.
method Simple invocation of a subroutine called AboveThreshold, iteratively called in Sparse Vector Technique.
result Improved estimates on highest quantiles with robustness and accuracy.
New analysis improves SGD for robust and quantile regression with sub-quadratic convergence.
problem Improving SGD for robust and quantile regression with sub-quadratic convergence.
method Piecewise Lyapunov function for first-order differentiable functions.
result First geometrical convergence result for sub-quadratic SGD.
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.
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.
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 …
Novel method for efficient optimization of noisy, expensive hybrid models.
problem Efficient optimization of hybrid models with noisy observations and constraints.
method Constrained Upper Quantile Bound (CUQB) method exploiting composite structure.
result Significantly improved sampling efficiency and theoretical guarantees.
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.
Enhances XGBoost for better uncertainty quantification in ML predictions.
problem Uncertainty in ML predictions, especially for XGBoost.
method Quantile Extreme Gradient Boosting (QXGBoost) using Huber norm in quantile regression.
result QXGBoost produces more accurate 90% prediction intervals.
MQF2 forecasts multivariate quantiles globally.
problem Forecasting multi-horizon dependencies with error accumulation.
method Multivariate quantile function using input-convex neural networks.
result MQF2 avoids quantile crossing and captures time dependency. New neural networks learn distribution functions using quantiles and moments.
problem Approximating functions of distributions in probability spaces.
method Quantile and moment neural networks, mixing quantile and moment features.
result Moment neural network outperforms others for bivariate distributions.
Study on risk contributions of portfolios using lambda quantile risk measures.
problem No known allocation rule for non-positively homogeneous risk measures.
method Defined lambda quantiles on portfolio compositions, derived derivatives, and introduced generalized Euler contributions.
result Explicit formulae for the derivatives of lambda quantiles, showing their homogeneity properties.
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.
Investor maximizes utility from an unknown claim using robust optimization.
problem Maximizing utility from an unknown contingent claim.
method Robust optimization with quantile formulation and variational inequalities.
result Optimal trading strategy and utility indifference price determined.
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…
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.
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…
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.
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.
The risk premium of a policy is the sum of the pure premium and the risk loading. In the classification ratemaking process, generalized linear models are usually used to calculate pure premiums, and various premium principles are applied to derive the risk loadings. No matter which premium principle is used, some risk …
Quantile regression with ReLU networks achieves minimax rates for various function types.
problem Estimating quantiles from covariates with neural networks.
method Quantile regression with rectified linear unit (ReLU) neural networks.
result ReLU networks achieve minimax rates for broad collections of function types.
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.
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). Locally private online quantile regression method addresses privacy constraints.
problem Estimating and inferring quantile regression under local differential privacy constraints.
method Developed a finite-alphabet channel where users compute local contributions, apply randomized response, and send reports. A public decoder corrects distortion and reconstructs inputs for averaging.
result Established local privacy, decoder unbiasedness, consistency, asymptotic normality, and inference for scalar contrasts.
Paper converts quantiles to cumulative distribution functions to simplify risk measures.
problem Technical assumptions in risk measure calculations.
method Invention of converting integrated quantiles to integrated cumulative distribution functions.
result Avoids the need for probability density function existence.
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…
In this paper, we propose a novel asymmetric ε-insensitive pinball loss function for quantile estimation. There exists some pinball loss functions which attempt to incorporate the ε-insensitive zone approach in it but, they fail to extend the ε-insensitive approach for quantile estimation in true sense. The propo…
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.
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 …
We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S\&P 500 stocks from the New York Stock Exchange. After establishing an empirical overview we compare the quantile-based correlation function to…
Paper studies continuous prediction with experts' advice using differential equations.
problem Continuous prediction with experts' advice in online learning.
method Continuous-time stochastic calculus and differential equations.
result Improved guarantees for quantile regret with continuous-time algorithm.
A new method for modeling insurance claim frequencies using random proportions.
problem Inaccurate fitting of classical distributions to insurance claim frequency data.
method Modeling claim frequencies using random proportions of insurance contracts and applying goodness-of-fit tests.
result A new statistical approach for better modeling insurance claim frequencies.
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 analyzes statistical properties of log-cosh loss function.
problem No statistical analysis of log-cosh loss function in literature.
method Presented statistical properties of log-cosh loss function, compared to Cauchy distribution, and examined various statistical procedures.
result Characterized statistical properties of log-cosh loss function, including distribution, likelihood function, and Fisher information.
One-shot federated learning method for prediction sets.
problem Constructing prediction sets in a one-shot federated learning setting.
method Quantile-of-quantiles estimator for one-shot federated learning with privacy.
result Achieves desired coverage and length similar to centralized setting.
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.
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.
The study improves VaR forecast accuracy by modeling conditional quantile dynamics.
problem Improving the accuracy of Value-at-Risk (VaR) forecasts for time-varying quantiles.
method Time-varying modeling of VaR, evaluation via simulation, asymmetric Mean Absolute Deviation loss function.
result Substantial improvements in forecasting conditional quantiles by maintaining predicted quantile unchanged.
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…