Related papers: Estimation and Applications of Quantiles in Deep B…

In a classical regression model, it is usually assumed that the explanatory variables are independent of each other and error terms are normally distributed. But when these assumptions are not met, situations like the error terms are not…

Uncertainty quantification is an important and challenging problem in deep learning. Previous methods rely on dropout layers which are not present in modern deep architectures or batch normalization which is sensitive to batch sizes. In…

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

Linear quantile regression models aim at providing a detailed and robust picture of the (conditional) response distribution as function of a set of observed covariates. Longitudinal data represent an interesting field of application of such…

Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian…

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…

Quantification is a supervised learning task that consists in predicting, given a set of classes C and a set D of unlabelled items, the prevalence (or relative frequency) p(c|D) of each class c in C. Quantification can in principle be…

Despite impressive state-of-the-art performance on a wide variety of machine learning tasks, deep learning methods can produce over-confident predictions, particularly with limited training data. Therefore, quantifying uncertainty is…

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

Measurement of uncertainty of predictions from machine learning methods is important across scientific domains and applications. We present, to our knowledge, the first such technique that quantifies the uncertainty of predictions from a…

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…

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…

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques…

Uncertainty quantification of deep neural networks has become an active field of research and plays a crucial role in various downstream tasks such as active learning. Recent advances in evidential deep learning shed light on the direct…

We propose a novel framework for fitting additive quantile regression models, which provides well calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing parameters, for model structures as…

Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile…

Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb{R}^{d}$ with an optimal number of samples. We generalize this problem to the case of spatial signals,…

Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient; we also need estimates of predictive uncertainty.…