Dr. Feldbacher-Escamilla & Thorn PhD (Universität Düsseldorf): Convexity of Loss Functions

Datum / Uhrzeit:
05.05.20   /  18:15 - 19:30

Institut für Theoretische Philosophie


The meta-inductive approach aims to address the problem of induction by showing that there are prediction methods (i.e., meta-inductive methods) whose predictive accuracy is demonstrably ‘access optimal’ within all logically possible prediction games. This paper surveys a number of possible limitations of the meta-inductive approach, namely, that the optimality results hold only for prediction games where: (i) there are a finite number of accessible object methods, (ii) it is possible to sensibly make predictions that are the average values of object method predictions, and (iii) the accuracy of predictions is measured by a convex loss function. Our assessment of (i) and (ii) is relatively brief: While the limitations are genuine and significant, they are not too serious. The majority of our paper is dedicated to assessing limitation (iii). Our first point is to demonstrate, using a number of new impossibility results, that the limitation is inevitable: Assuming a non-convex loss function, there are no principled prediction methods that are access optimal within all logically possible prediction games.  We then argue that the restriction to convex loss functions is not an epistemic limitation of meta-induction, by showing that non-convex loss functions fail to satisfy principles that any appropriate measure accuracy ought to satisfy. Finally, we address examples that appear to show that measuring accuracy using a non-convex loss function can be reasonable in some cases.

Christian Feldbacher-Escamilla and Paul Thorn are both post-doctoral research fellows at the Heinrich Heine University Duesseldorf, DCLPS.

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