Understanding causal relationships among the variables of a system is paramount to explain and control its behavior. For many real-world systems, however, the true causal graph is not readily available and one must resort to predictions made by algorithms or domain experts. Therefore, metrics that quantitatively assess the goodness of a causal graph provide helpful checks before using it in downstream tasks. Existing metrics provide an absolute number of inconsistencies between the graph and the observed data, and without a baseline, practitioners are left to answer the hard question of how many such inconsistencies are acceptable or expected. Here, we propose a novel consistency metric by constructing a baseline through node permutations. By comparing the number of inconsistencies with those on the baseline, we derive an interpretable metric that captures whether the graph is significantly better than random. Evaluating on both simulated and real data sets from various domains, including biology and cloud monitoring, we demonstrate that the true graph is not falsified by our metric, whereas the wrong graphs given by a hypothetical user are likely to be falsified.

When domain knowledge is limited and experimentation is restricted by ethical, financial, or time constraints, practitioners turn to observational causal discovery methods to recover the causal structure, exploiting the statistical properties of their data. Because causal discovery without further assumptions is an ill-posed problem, each algorithm comes with its own set of usually untestable assumptions, some of which are hard to meet in real datasets. Motivated by these considerations, this paper extensively benchmarks the empirical performance of recent causal discovery methods on observational _iid_ data generated under different background conditions, allowing for violations of the critical assumptions required by each selected approach. Our experimental findings show that score matching-based methods demonstrate surprising performance in the false positive and false negative rate of the inferred graph in these challenging scenarios, and we provide theoretical insights into their performance. This work is also the first effort to benchmark the stability of causal discovery algorithms with respect to the values of their hyperparameters. Finally, we hope this paper will set a new standard for the evaluation of causal discovery methods and can serve as an accessible entry point for practitioners interested in the field, highlighting the empirical implications of different algorithm choices.

Common deep neural networks (DNNs) for image classification have been shown to rely on shortcut opportunities (SO) in the form of predictive and easy-to-represent visual factors. This is known as shortcut learning and leads to impaired generalization. In this work, we show that common DNNs also suffer from shortcut learning when predicting only basic visual object factors of variation (FoV) such as shape, color, or texture. We argue that besides shortcut opportunities, generalization opportunities (GO) are also an inherent part of real-world vision data and arise from partial independence between predicted classes and FoVs. We also argue that it is necessary for DNNs to exploit GO to overcome shortcut learning. Our core contribution is to introduce the Diagnostic Vision Benchmark suite DiagViB-6, which includes datasets and metrics to study a network’s shortcut vulnerability and generalization capability for six independent FoV. In particular, DiagViB-6 allows controlling the type and degree of SO and GO in a dataset. We benchmark a wide range of popular vision architectures and show that they can exploit GO only to a limited extent.