Prediction models inform important clinical decisions, aiding in diagnosis, prognosis, and treatment planning. The predictive performance of these models is typically assessed through discrimination and calibration. However, changes in the distribution of the data impact model performance. In health-care, a typical change is a shift in case-mix: for example, for cardiovascular risk management, a general practitioner sees a different mix of patients than a specialist in a tertiary hospital. This work introduces a novel framework that differentiates the effects of case-mix shifts on discrimination and calibration based on the causal direction of the prediction task. When prediction is in the causal direction (often the case for prognosis predictions), calibration remains stable under case-mix shifts, while discrimination does not. Conversely, when predicting in the anti-causal direction (often with diagnosis predictions), discrimination remains stable, but calibration does not. A simulation study and empirical validation using cardiovascular disease prediction models demonstrate the implications of this framework. This framework provides critical insights for evaluating and deploying prediction models across different clinical settings, emphasizing the importance of understanding the causal structure of the prediction task.

The discovery of causal relationships in a set of random variables is a fundamental objective of science and has also recently been argued as being an essential component towards real machine intelligence. One class of causal discovery techniques are founded based on the argument that there are inherent structural asymmetries between the causal and anti-causal direction which could be leveraged in determining the direction of causation. To go about capturing these discrepancies between cause and effect remains to be a challenge and many current state-of-the-art algorithms propose to compare the norms of the kernel mean embeddings of the conditional distributions. In this work, we argue that such approaches based on RKHS embeddings are insufficient in capturing principal markers of cause-effect asymmetry involving higher-order structural variabilities of the conditional distributions. We propose Kernel Intrinsic Invariance Measure with Heterogeneous Transform (KIIM-HT) which introduces a novel score measure based on heterogeneous transformation of RKHS embeddings to extract relevant higher-order moments of the conditional densities for causal discovery. Inference is made via comparing the score of each hypothetical cause-effect direction. Tests and comparisons on a synthetic dataset, a two-dimensional synthetic dataset and the real-world benchmark dataset T\"ubingen Cause-Effect Pairs verify our approach. In addition, we conduct a sensitivity analysis to the regularization parameter to faithfully compare previous work to our method and an experiment with trials on varied hyperparameter values to showcase the robustness of our algorithm.

The ability to learn and act in novel situations is still a prerogative of animate intelligence, as current machine learning methods mostly fail when moving beyond the standard i.i.d. setting. What is the reason for this discrepancy? Most machine learning tasks are anti-causal, i.e., we infer causes (labels) from effects (observations). Typically, in supervised learning we build systems that try to directly invert causal mechanisms. Instead, in this paper we argue that strong generalization capabilities crucially hinge on searching and validating meaningful hypotheses, requiring access to a causal model. In such a framework, we want to find a cause that leads to the observed effect. Anti-causal models are used to drive this search, but a causal model is required for validation. We investigate the fundamental differences between causal and anti-causal tasks, discuss implications for topics ranging from adversarial attacks to disentangling factors of variation, and provide extensive evidence from the literature to substantiate our view. We advocate for incorporating causal models in supervised learning to shift the paradigm from inference only, to search and validation.

We provide theoretical and empirical evidence for a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. Assuming that the causes and the effects have the same distribution, we show that the distribution of the residuals of a linear fit in the anti-causal direction is closer to a Gaussian than the distribution of the residuals in the causal direction. This Gaussianization effect is characterized by reduction of the magnitude of the high-order cumulants and by an increment of the differential entropy of the residuals. The problem of non-linear causal inference is addressed by performing an embedding in an expanded feature space, in which the relation between causes and effects can be assumed to be linear. The effectiveness of a method to discriminate between causes and effects based on this type of asymmetry is illustrated in a variety of experiments using different measures of Gaussianity. The proposed method is shown to be competitive with state-of-the-art techniques for causal inference.