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Can someone please give me a reference where I can find more info on the method of Poisson maximum likelihood maximization with smoothing hyperparametersenter image description here

Here we want to find the parameters Ws and βs are called the smoothing hyperparameter. Does anybody know what's the name of this method?

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    $\begingroup$ This looks like a Poisson fused lasso style optimization setup. $\endgroup$
    – Greenparker
    Commented Jun 10, 2017 at 10:40

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There are some book-length treatments of penalized likelihood theory, you could have a look at :

Maximum Penalized Likelihood Estimation: Volume II: Regression and Maximum Penalized Likelihood Estimation: Volume I: Density Estimation.

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