Related papers: Transformed Central Quantile Subspace
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…
To address the challenge posed by noise in real quantum devices, quantum error mitigation techniques play a crucial role. These techniques are resource-efficient, making them suitable for implementation in noisy intermediate-scale quantum…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
This study proposes a novel method for forecasting a scalar variable based on high-dimensional predictors that is applicable to various data distributions. In the literature, one of the popular approaches for forecasting with many…
The vector autoregression (VAR) has been widely used in system identification, econometrics, natural science, and many other areas. However, when the state dimension becomes large the parameter dimension explodes. So rank reduced modelling…
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…
We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…
Information from related source studies can often enhance the findings of a target study. However, the distribution shift between target and source studies can severely impact the efficiency of knowledge transfer. In the high-dimensional…
We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an…
Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification…
We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
We consider supervised dimension reduction problems, namely to identify a low dimensional projection of the predictors $\-x$ which can retain the statistical relationship between $\-x$ and the response variable $y$. We follow the idea of…
These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…
When facing multivariate covariates, general semiparametric regression techniques come at hand to propose flexible models that are unexposed to the curse of dimensionality. In this work a semiparametric copula-based estimator for…
The recent availability of quantum annealers as cloud-based services has enabled new ways to handle machine learning problems, and several relevant algorithms have been adapted to run on these devices. In a recent work, linear regression…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
Quadratic discriminant analysis (QDA) is a simple method to classify a subject into two populations, and was proven to perform as well as the Bayes rule when the data dimension p is fixed. The main purpose of this paper is to examine the…
Machine learning has been increasingly utilized in the field of biomedical research to accelerate the drug discovery process. In recent years, the emergence of quantum computing has been followed by extensive exploration of quantum machine…