Related papers: Spline Quantile Regression
The standard asymmetric Laplace framework for Bayesian quantile regression (BQR) suffers from a fundamental decision-theoretic misalignment, yielding biased finite-sample estimates, and precludes gradient-based computation due to…
We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and…
Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…
We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide…
Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency…
Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple…
Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response $Y$ given covariates $X$, without making distributional assumptions. However, existing constructions of CQR can be…
We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…
Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each…
We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least squares optimisation. Opposed to related previous contributions suffering from the problem of reading out the optimal…
A collection of quantile curves provides a complete picture of conditional distributions. Properly centered and scaled versions of estimated curves at various quantile levels give rise to the so-called quantile regression process (QRP). In…
In this paper, we propose an invariant quantile regression (IQR) framework specifically designed for multi-environment datasets, which captures the invariance across different environments. This framework is closely related to transfer…
Ridge regression (RR) is an important machine learning technique which introduces a regularization hyperparameter $\alpha$ to ordinary multiple linear regression for analyzing data suffering from multicollinearity. In this paper, we present…
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…
In this paper we propose the adaptive lasso for predictive quantile regression (ALQR). Reflecting empirical findings, we allow predictors to have various degrees of persistence and exhibit different signal strengths. The number of…
The studies of large-scale, high-dimensional data in fields such as genomics and neuroscience have injected new insights into science. Yet, despite advances, they are confronting several challenges, often simultaneously: lack of…
Spatial dependent data frequently occur in many fields such as spatial econometrics and epidemiology. To deal with the dependence of variables and estimate quantile-specific effects by covariates, spatial quantile autoregressive models…
In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (QRCM), is to model quantile regression coefficients as…
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 (QR) loss function, which…
Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…