Explore the intersection of invariance, causality, and novel robustness in this 44-minute lecture by Peter Bühlmann from ETH Zürich. Delve into robust and high-dimensional statistics, covering topics such as robust statistics, causality, and modern applications. Examine the role of mediators in heterogeneous data and prediction problems. Investigate the concept of robustness and its relationship to causality, including the definition of causality and shift perturbations. Learn about practical applications using random forests and the challenges posed by heterogeneity in data analysis.