The importance of calibrated uncertainty estimates in machine learning is growing apparent across many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

Advancing probabilistic solar forecasting methods is essential to supporting the integration of solar energy into the electricity grid. In this work, we develop a variety of state-of-the-art probabilistic models for forecasting solar irradiance. We investigate the use of post-hoc calibration techniques for ensuring well-calibrated probabilistic predictions. We train and evaluate the models using public data from seven stations in the SURFRAD network, and demonstrate that the best model, NGBoost, achieves higher performance at an intra-hourly resolution than the best benchmark solar irradiance forecasting model across all stations. Further, we show that NGBoost with CRUDE post-hoc calibration achieves comparable performance to a numerical weather prediction model on hourly-resolution forecasting.

We present Natural Gradient Boosting (NGBoost), an algorithm which brings probabilistic prediction capability to gradient boosting in a generic way. Predictive uncertainty estimation is crucial in many applications such as healthcare and weather forecasting. Probabilistic prediction, which is the approach where the model outputs a full probability distribution over the entire outcome space, is a natural way to quantify those uncertainties. Gradient Boosting Machines have been widely successful in prediction tasks on structured input data, but a simple boosting solution for probabilistic prediction of real valued outputs is yet to be made. NGBoost is a gradient boosting approach which uses the \emph{Natural Gradient} to address technical challenges that makes generic probabilistic prediction hard with existing gradient boosting methods. Our approach is modular with respect to the choice of base learner, probability distribution, and scoring rule. We show empirically on several regression datasets that NGBoost provides competitive predictive performance of both uncertainty estimates and traditional metrics.

Identifying patients who will be discharged within 24 hours can improve hospital resource management and quality of care. We studied this problem using eight years of Electronic Health Records (EHR) data from Stanford Hospital. We fit models to predict 24 hour discharge across the entire inpatient population. The best performing models achieved an area under the receiver-operator characteristic curve (AUROC) of 0.85 and an AUPRC of 0.53 on a held out test set. This model was also well calibrated. Finally, we analyzed the utility of this model in a decision theoretic framework to identify regions of ROC space in which using the model increases expected utility compared to the trivial always negative or always positive classifiers.

Personalized probabilistic forecasts of time to event (such as mortality) can be crucial in decision making, especially in the clinical setting. Inspired by ideas from the meteorology literature, we approach this problem through the paradigm of maximizing sharpness of prediction distributions, subject to calibration. In regression problems, it has been shown that optimizing the continuous ranked probability score (CRPS) instead of maximum likelihood leads to sharper prediction distributions while maintaining calibration. We introduce the Survival-CRPS, a generalization of the CRPS to the time to event setting, and present right-censored and interval-censored variants. To holistically evaluate the quality of predicted distributions over time to event, we present the Survival-AUPRC evaluation metric, an analog to area under the precision-recall curve. We apply these ideas by building a recurrent neural network for mortality prediction, using an Electronic Health Record dataset covering millions of patients. We demonstrate significant benefits in models trained by the Survival-CRPS objective instead of maximum likelihood.

Improving the quality of end-of-life care for hospitalized patients is a priority for healthcare organizations. Studies have shown that physicians tend to over-estimate prognoses, which in combination with treatment inertia results in a mismatch between patients wishes and actual care at the end of life. We describe a method to address this problem using Deep Learning and Electronic Health Record (EHR) data, which is currently being piloted, with Institutional Review Board approval, at an academic medical center. The EHR data of admitted patients are automatically evaluated by an algorithm, which brings patients who are likely to benefit from palliative care services to the attention of the Palliative Care team. The algorithm is a Deep Neural Network trained on the EHR data from previous years, to predict all-cause 3-12 month mortality of patients as a proxy for patients that could benefit from palliative care. Our predictions enable the Palliative Care team to take a proactive approach in reaching out to such patients, rather than relying on referrals from treating physicians, or conduct time consuming chart reviews of all patients. We also present a novel interpretation technique which we use to provide explanations of the model's predictions.