Abstract
In this chapter, we study a particular type of neural networks that are designed for providing a representation of the input with a reduced dimensionality. These networks contains a hidden layer, called bottleneck, that contains a few nodes compared to the previous layers. The output signals of neurons in the bottleneck carry a summarized information that aggregates input signals in a non-linear way. Bottleneck networks offer an interesting alternative to principal component analysis (PCA) or non-linear PCA. In actuarial sciences, these networks can be used for understanding the evolution of longevity during the last century. We also introduce in this chapter a genetic algorithm for calibrating the neural networks. This method combined with a gradient descent speeds up the calibration.
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Notes
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- 2.
Notice that in the LC model, the log-mortality rates are Normally distributed: their skewness and kurtosis are then respectively equal to 0 and 3. Skewness and kurtosis reported in Table 4.8 are not exactly equal to these figures because they are computed with simulated log-forces of mortality.
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Denuit, M., Hainaut, D., Trufin, J. (2019). Dimension-Reduction with Forward Neural Nets Applied to Mortality. In: Effective Statistical Learning Methods for Actuaries III. Springer Actuarial(). Springer, Cham. https://doi.org/10.1007/978-3-030-25827-6_4
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