Dan Li

As scientists start to adopt machine learning (ML) as one research tool, the security of ML and the knowledge generated become a concern. In this paper, I explain how supervised ML can be improved with better data ontology, or the way we make categories and turn information into data. More specifically, we should design data ontology in such a way that is consistent with the knowledge that we have about the target phenomenon so that such ontology can help us make the inductive leap. I do so by thinking through a thought experiment, Goodman’s New Riddle of Induction (Fact, fiction, and forecast, Harvard University Press, 1955). Goodman’s riddle helps flesh out three problems of induction: (1) the problem of equal goodies, that there are often too many equally good inductive results given the same data; (2) the problem of diverging performance, that these equally good results can give opposite predictions in the future; and (3) the problem of mediocrity, that when averaged across all equally possible datasets and tasks, no inductive algorithm outperforms any other. I show that all these three problems are manifested as real obstacles in ML practice, namely, the Rashomon effect (Breiman in Stat Sci 16(3):199–231, 2001), the problem of underspecification (D’Amour et al. in J Mach Learn Res, 2020, https://doi.org/10.48550/arXiv.2011.03395 ), and the No Free Lunch theorem (Wolpert in Neural Comput 8(7):1341–90, 1996, https://doi.org/10.1162/neco.1996.8.7.1341 ). Lastly, I argue that proper data ontology can help mitigate these problems and I demonstrate how using concrete examples from climate science. This research highlights the links between philosophers’ discussions of induction and implications in ML practice.

Lisciandra poses a challenge for robustness analysis as applied to economic models. She argues that substituting tractability assumptions risks altering the main mathematical structure of the model, thereby preventing the possibility of meaningfully evaluating the same model under different assumptions. In such cases RA is argued to be inapplicable. However, Lisciandra is mistaken to take the goal of RA as keeping the mathematical properties of tractability assumptions intact. Instead, RA really aims to keep the modeling component while varying the corresponding mathematical formulation. Thus, her argument concerning whether the associated mathematical properties of certain assumptions can be kept intact is irrelevant to the success of RA. Furthermore, we explicate and develop Lloyd’s account of “model robustness” to provide solutions to Lisciandra’s challenges. Our solutions are, namely, error analysis and independent empirical support. We conclude that although complex economic models do face potential dangers, there are solutions and robustness analysis need not be given up..