Conformal Predictions for Longitudinal Data

The improvement in predictive performance of machine learning models over the last two decades have made them essential components of decision-making pipelines across high-stake domains such as medicine and finance. However, the point estimates yielded by these predictive models are insufficient in these critical application domains, where uncertainty estimates are of particular interest for informed decision-making (see Harries et al. (1999); Díaz-González et al. (2012); Mears et al. (2015) for uncertainty quantification in these domains). While post-hoc methods such as bootstrapping, jackknife and other ensembling procedures (see Alaa et al. (2020); van der Schaar et al. (2020); Xu & Xie (2020)) are popularly used for uncertainty estimation of a particular statistic (such as model metrics), they are only able to provide theoretical guarantees under additional assumptions on the underlying model and data distribution. This limitation, however, is addressed by the conformal prediction framework, which provides a principled way to perform model-agnostic and distribution-free uncertainty quantification of complex machine learning models. Conformal predictions are a powerful tool for constructing prediction sets or intervals that provide reliable coverage guarantees for the true value. These guarantees are typically based on the assumption of data exchangeability, which is often violated in time series data due to temporal dependencies and non-stationarity. However, accurate uncertainty quantification is crucial for time series data, which is central to applications ranging from medical diagnosis to energy demand and stock market forecasting. Consequently, there has been a growing interest in developing conformal prediction methods that can handle non-exchangeable data.