Conformal Regression in Calorie Prediction for Team Jumbo-Visma

UCI WorldTour races, the premier men's elite road cycling tour, are grueling events that put riders' physical fitness and endurance to the test. The coaches of Team Jumbo-Visma have long been responsible for predicting the energy needs of each rider of the Dutch team for every race on the calendar. Those must be estimated to ensure riders have the energy and resources necessary to maintain a high level of performance throughout a race. This task, however, is both time-consuming and challenging, as it requires precise estimates of race speed and power output. Traditionally, the approach to predicting energy needs has relied on coaches' judgement and experience, but this method has its limitations and often leads to inaccurate predictions. In this paper, we propose a new, more effective approach to predicting energy needs for cycling races. By predicting the speed and power with regression models, we provide the coaches with calorie needs estimate for each individual rider per stage instantly. In addition, we compare methods to quantify uncertainty in estimating the speed and power of Team Jumbo-Visma riders for cycling races. The empirical analysis of the jackknife+, jackknife-minmax, jackknife-minmax-after-bootstrap, CV+, CV-minmax, conformalized quantile regression (CQR) and inductive conformal prediction (ICP) methods in conformal prediction reveals all methods except minmax based methods achieve valid prediction intervals while producing prediction intervals tight enough to be used for decision making. Furthermore, methods computing prediction intervals of fixed size produce significantly tighter intervals for low significance value. Among the methods computing intervals of varying length across the input space, namely the CQR and ICP methods, ICP computes tighter prediction intervals at larger significance level.

Simple Sorting Criteria Help Find the Causal Order in Additive Noise Models

Additive Noise Models (ANM) encode a popular functional assumption that enables learning causal structure from observational data. Due to a lack of real-world data meeting the assumptions, synthetic ANM data are often used to evaluate causal discovery algorithms. Reisach et al. (2021) show that, for common simulation parameters, a variable ordering by increasing variance is closely aligned with a causal order and introduce var-sortability to quantify the alignment. Here, we show that not only variance, but also the fraction of a variable's variance explained by all others, as captured by the coefficient of determination $R^2$, tends to increase along the causal order. Simple baseline algorithms can use $R^2$-sortability to match the performance of established methods. Since $R^2$-sortability is invariant under data rescaling, these algorithms perform equally well on standardized or rescaled data, addressing a key limitation of algorithms exploiting var-sortability. We characterize and empirically assess $R^2$-sortability for different simulation parameters. We show that all simulation parameters can affect $R^2$-sortability and must be chosen deliberately to control the difficulty of the causal discovery task and the real-world plausibility of the simulated data. We provide an implementation of the sortability measures and sortability-based algorithms in our library CausalDisco (https://github.com/CausalDisco/CausalDisco).

Beware of the Simulated DAG! Varsortability in Additive Noise Models

Additive noise models are a class of causal models in which each variable is defined as a function of its causes plus independent noise. In such models, the ordering of variables by marginal variances may be indicative of the causal order. We introduce varsortability as a measure of agreement between the ordering by marginal variance and the causal order. We show how varsortability dominates the performance of continuous structure learning algorithms on synthetic data. On real-world data, varsortability is an implausible and untestable assumption and we find no indication of high varsortability. We aim to raise awareness that varsortability easily occurs in simulated additive noise models. We provide a baseline method that explicitly exploits varsortability and advocate reporting varsortability in benchmarking data.