Related papers: MM Algorithms for Statistical Estimation in Quanti…
Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…
Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
Modern machine learning (ML) methods typically fail to adequately capture causal information. Consequently, such models do not handle data distributional shifts, are vulnerable to adversarial examples, and often learn spurious correlations.…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
MM (majorization--minimization) algorithms are an increasingly popular tool for solving optimization problems in machine learning and statistical estimation. This article introduces the MM algorithm framework in general and via three…
Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum…
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…
Quantile regression is a powerful tool capable of offering a richer view of the data as compared to least-squares regression. Quantile regression is typically performed individually on a few quantiles or a grid of quantiles without…
Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…
This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…
In a context of malicious software detection, machine learning (ML) is widely used to generalize to new malware. However, it has been demonstrated that ML models can be fooled or may have generalization problems on malware that has never…
We propose a M-quantile regression model for the analysis of multivariate, continuous, longitudinal data. M-quantile regression represents an appealing alternative to standard regression models, as it combines the robustness of quantile and…
We report on an empirical study of the main strategies for quantile regression in the context of stochastic computer experiments. To ensure adequate diversity, six metamodels are presented, divided into three categories based on order…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…
The Random Forest model is one of the popular models of Machine learning. We present a quantum algorithm for testing (forecasting) process of the Random Forest machine learning model for the Regression problem. The presented algorithm is…
It is known that the estimating equations for quantile regression (QR) can be solved using an EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…
As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $\tau$, major difficulties of semiparametric…