Abstract
The learning of large neural networks is an ill-posed problem and there is generally a continuum of possible set of admissible weights. In this case, we cannot rely anymore on asymptotic properties of maximum likelihood estimators to approximate confidence intervals. Applying the Bayesian learning paradigm to neural networks or to generalized linear models results in a powerful framework that can be used for estimating the density of predictors. Within this approach, the uncertainty about parameters is expressed and measured by probabilities. This formulation allows for a probabilistic treatment of our a priori knowledge about parameters based on Markov Chain Monte Carlo methods. In order to explain those methods that are based on simulations, we need to review the main features of Markov chains.
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Notes
- 1.
\(\mathcal {B}(\mathcal {X})\) is the sigma algebra defined on \(\mathcal {X}\).
- 2.
g.c.d. : greatest common divisor.
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Denuit, M., Hainaut, D., Trufin, J. (2019). Bayesian Neural Networks and GLM. In: Effective Statistical Learning Methods for Actuaries III. Springer Actuarial(). Springer, Cham. https://doi.org/10.1007/978-3-030-25827-6_2
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DOI: https://doi.org/10.1007/978-3-030-25827-6_2
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