Falsificationism and Statistical Learning Theory: Comparing the Popper and Vapnik-Chervonenkis Dimensions

Abstract

We compare Karl Popper's ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory. Popper's notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper's work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.

The explanation game: a formal framework for interpretable machine learning

“…5.3. Some philosophers have argued that statistical learning provides a rigorous foundation for all inductive reasoning (Corfield et al 2009;Harman and Kulkarni 2007). Although we are sympathetic to this position, none of the proceeding analysis depends upon this thesis.…”

“…Popper's "degree of falsifiability" arguably anticipates the VC dimension. For a discussion, seeCorfield et al (2009).2 The completeness of the do-calculus relies on the causal Markov and faithfulness conditions, which together state (roughly) that statistical independence implies graphical independence and vice versa. Neither assumption has gone unchallenged.…”

The Nuclear Techniques and the Selection of Model Parameters in Big Data

“…In 1986, completed the general learning machine structure after the research to the spread of technology. In the meantime, also produce the statistical learning theory [5] and has large development, produced the empirical risk minimization principle theory and algorithm complexity thoughts.…”

Falsification and Future Performance

“…Related work. The connection between Popper's ideas on falsifiability and statistical learning theory was pointed out in [5,7,14]. However, these works focus on VC-dimension, which does not relate to falsification as directly as VC-entropy and Rademacher complexity which we consider here.…”