804,840 research outputs found
Statistical Learning of Arbitrary Computable Classifiers
Statistical learning theory chiefly studies restricted hypothesis classes,
particularly those with finite Vapnik-Chervonenkis (VC) dimension. The
fundamental quantity of interest is the sample complexity: the number of
samples required to learn to a specified level of accuracy. Here we consider
learning over the set of all computable labeling functions. Since the
VC-dimension is infinite and a priori (uniform) bounds on the number of samples
are impossible, we let the learning algorithm decide when it has seen
sufficient samples to have learned. We first show that learning in this setting
is indeed possible, and develop a learning algorithm. We then show, however,
that bounding sample complexity independently of the distribution is
impossible. Notably, this impossibility is entirely due to the requirement that
the learning algorithm be computable, and not due to the statistical nature of
the problem.Comment: Expanded the section on prior work and added reference
Statistical learnability of nuclear masses
After more than 80 years from the seminal work of Weizs\"acker and the liquid
drop model of the atomic nucleus, deviations from experiments of mass models
( MeV) are orders of magnitude larger than experimental errors
( keV). Predicting the mass of atomic nuclei with precision is
extremely challenging. This is due to the non--trivial many--body interplay of
protons and neutrons in nuclei, and the complex nature of the nuclear strong
force. Statistical theory of learning will be used to provide bounds to the
prediction errors of model trained with a finite data set. These bounds are
validated with neural network calculations, and compared with state of the art
mass models. Therefore, it will be argued that the nuclear structure models
investigating ground state properties explore a system on the limit of the
knowledgeable, as defined by the statistical theory of learning
The Impact of Real Options on Willingness to Pay for Investments in Road Safety
Abstract: Public investments are dynamic in nature, and decision making must account for the uncertainty, irreversibility and potential for future learning. In this paper we adapt the theory for investment under uncertainty for a public referendum setting and perform the first empirical test to show that estimates of the value of safety (VSL) from stated preference surveys are highly dependent on the inclusion of the option value. Our results indicate an option value of a major economic magnitude. This implies that previously reported VSL estimates are exaggerated.Value of a Statistical Life; Real Options; Contingent Valuation; Road Safety
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