Christof Seiler

Alexander G. Reisach, Myriam Tami, Christof Seiler et al.

Additive Noise Models (ANMs) are a common model class for causal discovery from observational data and are often used to generate synthetic data for causal discovery benchmarking. Specifying an ANM requires choosing all parameters, including those not fixed by explicit assumptions. Reisach et al. (2021) show that sorting variables by increasing variance often yields an ordering close to a causal order and introduce var-sortability to quantify this alignment. Since increasing variances may be unrealistic and are scale-dependent, ANM data are often standardized in benchmarks. We show that synthetic ANM data are characterized by another pattern that is scale-invariant: the explainable fraction of a variable's variance, as captured by the coefficient of determination $R^2$, tends to increase along the causal order. The result is high $R^2$-sortability, meaning that sorting the variables by increasing $R^2$ yields an ordering close to a causal order. We propose an efficient baseline algorithm termed $R^2$-SortnRegress that exploits high $R^2$-sortability and that can match and exceed the performance of established causal discovery algorithms. We show analytically that sufficiently high edge weights lead to a relative decrease of the noise contributions along causal chains, resulting in increasingly deterministic relationships and high $R^2$. We characterize $R^2$-sortability for different simulation parameters and find high values in common settings. Our findings reveal high $R^2$-sortability as an assumption about the data generating process relevant to causal discovery and implicit in many ANM sampling schemes. It should be made explicit, as its prevalence in real-world data is unknown. For causal discovery benchmarking, we implement $R^2$-sortability, the $R^2$-SortnRegress algorithm, and ANM simulation procedures in our library CausalDisco at https://causaldisco.github.io/CausalDisco/.

Kristian van Kuijk, Mark Dirksen, Christof Seiler

UCI WorldTour races, the premier men's elite road cycling tour, are grueling events that put physical fitness and endurance of riders 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 judgement and experience of coaches, 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 estimates for each individual rider per stage instantly. In addition, we compare methods to quantify uncertainty using conformal prediction. The empirical analysis of the jackknife+, jackknife-minmax, jackknife-minmax-after-bootstrap, CV+, CV-minmax, conformalized quantile regression, and inductive conformal prediction methods in conformal prediction reveals that all methods achieve valid prediction intervals. All but minmax-based methods also produce sufficiently narrow prediction intervals for decision-making. Furthermore, methods computing prediction intervals of fixed size produce tighter intervals for low significance values. Among the methods computing intervals of varying length across the input space, inductive conformal prediction computes narrower prediction intervals at larger significance level.

Alexander G. Reisach, Christof Seiler, Sebastian Weichwald

Simulated DAG models may exhibit properties that, perhaps inadvertently, render their structure identifiable and unexpectedly affect structure learning algorithms. Here, we show that marginal variance tends to increase along the causal order for generically sampled additive noise models. We introduce varsortability as a measure of the agreement between the order of increasing marginal variance and the causal order. For commonly sampled graphs and model parameters, we show that the remarkable performance of some continuous structure learning algorithms can be explained by high varsortability and matched by a simple baseline method. Yet, this performance may not transfer to real-world data where varsortability may be moderate or dependent on the choice of measurement scales. On standardized data, the same algorithms fail to identify the ground-truth DAG or its Markov equivalence class. While standardization removes the pattern in marginal variance, we show that data generating processes that incur high varsortability also leave a distinct covariance pattern that may be exploited even after standardization. Our findings challenge the significance of generic benchmarks with independently drawn parameters. The code is available at https://github.com/Scriddie/Varsortability.