Related papers: Multivariate quantiles and multiple-output regress…
Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable…
Quantile regression permits describing how quantiles of a scalar response variable depend on a set of predictors. Because a unique definition of multivariate quantiles is lacking, extending quantile regression to multivariate responses is…
With the increasing availability of high-dimensional data, analysts often rely on exploratory data analysis to understand complex data sets. A key approach to exploring such data is dimensionality reduction, which embeds high-dimensional…
Among the many ways of quantifying uncertainty in a regression setting, specifying the full quantile function is attractive, as quantiles are amenable to interpretation and evaluation. A model that predicts the true conditional quantiles…
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…
We propose to smooth the entire objective function, rather than only the check function, in a linear quantile regression context. Not only does the resulting smoothed quantile regression estimator yield a lower mean squared error and a more…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
This article proposes a novel Bayesian multivariate quantile regression to forecast the tail behavior of energy commodities, where the homoskedasticity assumption is relaxed to allow for time-varying volatility. In particular, we exploit…
In this paper, we establish a uniform error rate of a Bahadur representation for local polynomial estimators of quantile regression functions. The error rate is uniform over a range of quantiles, a range of evaluation points in the…
This paper introduces a new framework for multivariate quantile regression based on the multivariate distribution function, termed multivariate quantile regression (MQR). In contrast to existing approaches--such as directional quantiles,…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
Uncertainty estimation is essential to make neural networks trustworthy in real-world applications. Extensive research efforts have been made to quantify and reduce predictive uncertainty. However, most existing works are designed for…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
Some of the most important results in prediction theory and time series analysis when finitely many values are removed from or added to its infinite past have been obtained using difficult and diverse techniques ranging from duality in…
This paper introduces a new type of regression methodology named as Convex-Area-Wise Linear Regression(CALR), which separates given datasets by disjoint convex areas and fits different linear regression models for different areas. This…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…
This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss…
We generalize the Rayleigh Quotient Iteration (RQI) to the problem of solving a nonlinear equation where the variables are divided into two subsets, one satisfying additional equality constraints and the other could be considered as…
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…