Kernel conditional quantile estimation via reduction revisited

Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian Processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches.

Errors-in-Variables Modeling of Personalized Treatment-Response Trajectories

Estimating the impact of a treatment on a given response is needed in many biomedical applications. However, methodology is lacking for the case when the response is a continuous temporal curve, treatment covariates suffer extensively from measurement error, and even the exact timing of the treatments is unknown. We introduce a novel method for this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information across individuals, and a sparse Gaussian process for the baseline trend. Importantly, our model accounts for errors not only in treatment covariates, but also in treatment timings, a problem arising in practice for example when data on treatments are based on user self-reporting. We validate our model with simulated and real patient data, and show that in a challenging application of estimating the impact of diet on continuous blood glucose measurements, accounting for measurement error significantly improves estimation and prediction accuracy.Peer reviewe