Related papers: Transformed Central Quantile Subspace
We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the…
To make inferences about the shape of a population distribution, the widely popular mean regression model, for example, is inadequate if the distribution is not approximately Gaussian (or symmetric). Compared to conventional mean regression…
Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied,…
We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…
This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale…
In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme…
Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
This paper advances a variable screening approach to enhance conditional quantile forecasts using high-dimensional predictors. We have refined and augmented the quantile partial correlation (QPC)-based variable screening proposed by Ma et…
The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…
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…
In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension…
The quantile residual lifetime (QRL) regression is an attractive tool for assessing covariate effects on the distribution of residual life expectancy, which is often of interest in clinical studies. When the study subjects are exposed to…
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…
Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge…