Add write up for negative binomial family GLM dispersion estimation using Maximum Likelihood method

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h2. Summary

We implemented the negative binomial regression with dispersion parameter estimation using Maximum Likelihood method.  Regularization is not supported when using dispersion parameter estimation using maximum likelihood. To use it, set the {{dispersion_parameter_method="ml"}} in the GLM constructor.

h2. Implementation details

The coefficients (betas) are estimated using IRLSM and the dispersion parameter theta is estimated after each IRLSM iteration. After first beta update, initial theta estimate is made using method of moments as a starting point, then in each iteration theta is updated using maximum likelihood.

While not converged

Estimate coefficients (betas)

Estimate dispersion (theta)

If first iteration

Theta <- Moment Method estimate

Else

Theta <- Maximum Likelihood estimate using Newton’s method with learning rate estimated using Golden section search 

If anything is not clear, please feel free to contact me ([~accountid:5e43370f5a495e0c91a74ebe] ). Also, I’m not sure if we should mention it but R’s negative binomial GLM (from MASS package) uses also parameter named {{theta}} for dispersion but their theta is inverse of h2o’s theta {{(theta_r = 1/theta_h2o)}}

[wendycwong]

Completed

[h2o-ops]

JIRA Issue Details

Jira Issue: PUBDEV-8981
Assignee: hannah.tillman
Reporter: Tomas Fryda
State: Resolved
Fix Version: 3.40.0.1
Attachments: N/A
Development PRs: Available

[h2o-ops]

Linked PRs from JIRA

#6483