Communication-Efficient Distributed Quantile Regression with Optimal Statistical Guarantees

• URL: http://arxiv.org/abs/2110.13113v1
• Date: Mon, 25 Oct 2021 17:09:59 GMT
• Title: Communication-Efficient Distributed Quantile Regression with Optimal Statistical Guarantees
• Authors: Heather Battey, Kean Ming Tan, and Wen-Xin Zhou
• Abstract summary: We address the problem of how to achieve optimal inference in distributed quantile regression without stringent scaling conditions. The difficulties are resolved through a double-smoothing approach that is applied to the local (at each data source) and global objective functions. Despite the reliance on a delicate combination of local and global smoothing parameters, the quantile regression model is fully parametric.
• Score: 2.064612766965483
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the problem of how to achieve optimal inference in distributed quantile regression without stringent scaling conditions. This is challenging due to the non-smooth nature of the quantile regression loss function, which invalidates the use of existing methodology. The difficulties are resolved through a double-smoothing approach that is applied to the local (at each data source) and global objective functions. Despite the reliance on a delicate combination of local and global smoothing parameters, the quantile regression model is fully parametric, thereby facilitating interpretation. In the low-dimensional regime, we discuss and compare several alternative confidence set constructions, based on inversion of Wald and score-type tests and resam-pling techniques, detailing an improvement that is effective for more extreme quantile coefficients. In high dimensions, a sparse framework is adopted, where the proposed doubly-smoothed objective function is complemented with an $\ell_1$-penalty. A thorough simulation study further elucidates our findings. Finally, we provide estimation theory and numerical studies for sparse quantile regression in the high-dimensional setting.

Related papers

• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• Semiparametric conformal prediction [79.6147286161434]
  Risk-sensitive applications require well-calibrated prediction sets over multiple, potentially correlated target variables. We treat the scores as random vectors and aim to construct the prediction set accounting for their joint correlation structure. We report desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• Federated Smoothing Proximal Gradient for Quantile Regression with Non-Convex Penalties [3.269165283595478]
  Distributed sensors in the internet-of-things (IoT) generate vast amounts of sparse data. We propose a federated smoothing proximal gradient (G) algorithm that integrates a smoothing mechanism with the view, thereby both precision and computational speed.
  arXiv  Detail & Related papers  (2024-08-10T21:50:19Z)
• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate. We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• Uncertainty estimation in satellite precipitation spatial prediction by combining distributional regression algorithms [3.8623569699070353]
  We introduce the concept of distributional regression for the engineering task of creating precipitation datasets through data merging. We propose new ensemble learning methods that can be valuable not only for spatial prediction but also for prediction problems in general.
  arXiv  Detail & Related papers  (2024-06-29T05:58:00Z)
• Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise [51.87307904567702]
  Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the distribution of outputs. We propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint. We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities.
  arXiv  Detail & Related papers  (2024-06-05T13:36:38Z)
• Distributed High-Dimensional Quantile Regression: Estimation Efficiency and Support Recovery [0.0]
  We focus on distributed estimation and support recovery for high-dimensional linear quantile regression. We transform the original quantile regression into the least-squares optimization. An efficient algorithm is developed, which enjoys high computation and communication efficiency.
  arXiv  Detail & Related papers  (2024-05-13T08:32:22Z)
• Bayesian Quantile Regression with Subset Selection: A Decision Analysis Perspective [0.0]
  Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods estimate conditional quantiles separately for each quantile of interest or estimate the entire conditional distribution using semi- or non-parametric models. We pose the fundamental problems of linear quantile estimation, uncertainty quantification, and subset selection from a Bayesian decision analysis perspective.
  arXiv  Detail & Related papers  (2023-11-03T17:19:31Z)
• Structured Radial Basis Function Network: Modelling Diversity for Multiple Hypotheses Prediction [51.82628081279621]
  Multi-modal regression is important in forecasting nonstationary processes or with a complex mixture of distributions. A Structured Radial Basis Function Network is presented as an ensemble of multiple hypotheses predictors for regression problems. It is proved that this structured model can efficiently interpolate this tessellation and approximate the multiple hypotheses target distribution.
  arXiv  Detail & Related papers  (2023-09-02T01:27:53Z)
• Errors-in-variables Fr\'echet Regression with Low-rank Covariate Approximation [2.1756081703276]
  Fr'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. Our proposed framework combines the concepts of global Fr'echet regression and principal component regression, aiming to improve the efficiency and accuracy of the regression estimator.
  arXiv  Detail & Related papers  (2023-05-16T08:37:54Z)
• Flexible Model Aggregation for Quantile Regression [92.63075261170302]
  Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions. We investigate methods for aggregating any number of conditional quantile models. All of the models we consider in this paper can be fit using modern deep learning toolkits.
  arXiv  Detail & Related papers  (2021-02-26T23:21:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.