Using a Neural Network as a replacement for Fractional Log it ; Which Cost Function to Use?

03 March 2018 0 4K Report

I am working on a deep neural net model to estimate the monthly mortgage prepayment ratio for a large loan portfolio (this ratio is called SMMSMM in finance literature, all you need to know is that 0≤SMM≤10≤SMM≤1). My basic approach is to extend the methodology in (Papke- Wooldridge 1996) paper on modelling fractional outcomes. So I started by

replacing the G(z)G(z) (sigmoid function in the above paper) by a deep NN.

minimizing the negative Bernoulli log-likelihood function: argminθ(−∑iyilog[G(Xiθ)]+(1−yi)log[1−G(Xiθ)])argminθ(−∑iyilog⁡[G(Xiθ)]+(1−yi)log⁡[1−G(Xiθ)])

My question is: what is the conceptual difference between using the above cost function as opposed to the usual Mean Squared Error cost for a regular quantitative response 0≤y≤10≤y≤1?

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