We finally report the detailed comparison on real benchmarks in Figure 14 and Tables 1 and 2. 21 Figure 13: Comparison voter strength (1st column), training error (2nd column), test error (3rd

We finally report the detailed comparison on real benchmarks in Figure 14 and Tables 1 and 2. 21 Figure 13: Comparison voter strength (1st column), training error (2nd column), test error (3rd

Weaknesses: The paper is technically heavy for my expertise, so I can only raise questions about its content. Might they be naive, discussing them in the paper would help other readers to understand the scope of this work. A first concern is about the fact that the paper presents solely (Theorem 1) the PAC-Bayes bound of McAllester (1999), converging at rate sqrt(1/m). Since this pioneer work, many variations on the PAC-Bayes bounds have been proposed. Notably, Seeger (2002)'s and Catoni (2007)'s bounds are known to converge at rate 1/m when the empirical risk is zero (see also Guedj (2019) for a up-to-date overview of PAC-Bayes literature).

We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions: this allows for a closed-form and differentiable expression for the expected risk, which then turns the generalization bound into a tractable training objective. The resulting stochastic majority vote learning algorithm achieves state-of-the-art accuracy and benefits from (non-vacuous) tight generalization bounds, in a series of numerical experiments when compared to competing algorithms which also minimize PAC-Bayes objectives -- both with uninformed (data-independent) and informed (data-dependent) priors.

One recent afternoon, Tina Seeger and Diana Trujillo were showing off a few snaps from their latest trip. "I have a soft spot for rover selfies," Seeger, a twenty-seven-year-old NASA geologist, said. She was screen-sharing a shot of the Perseverance rover posing at the Jezero Crater on Mars, taken April 6th. Jezero (rhymes with "hetero") is just north of the Martian equator. "It's really special, because it used to have this ancient lake environment with rivers flowing into a delta," Seeger, who has wavy hair and was seated outside a coffee shop in Bellingham, Washington, said.