A Formal Proof of PAC Learnability for Decision Stumps

We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoretic subtleties arise when carrying it out fully formally. Our proof is structured so as to separate reasoning about deterministic properties of a learning function from proofs of measurability and analysis of probabilities.Comment: 13 pages, appeared in Certified Programs and Proofs (CPP) 202

Statistical learning theory

xxiv, 736 p. : ill. ; 25 cm

The nature of statistical learning theory

xv, 188 p. : ill. ; 21x3

Case Studies in Data-Driven Verification of Dynamical Systems

We interpret several dynamical system verification questions, e.g., region of attraction and reachability analyses, as data classification problems. We discuss some of the tradeoffs between conventional optimization-based certificate constructions with certainty in the outcomes and this new date-driven approach with quantified confidence in the outcomes. The new methodology is aligned with emerging computing paradigms and has the potential to extend systematic verification to systems that do not necessarily admit closed-form models from certain specialized families. We demonstrate its effectiveness on a collection of both conventional and unconventional case studies including model reference adaptive control systems, nonlinear aircraft models, and reinforcement learning problems.United States. Air Force Research Laboratory (FA8650-15-C-2546)United States. Office of Naval Research (N000141310778)United States. Army Research Office (W911NF- 15-1-0592)National Science Foundation (U.S.) (1550212)United States. Defense Advanced Research Projects Agency (W911NF-16-1-0001