[SPARK-22449] Add BIC for GLM

• Type: Improvement
• Status: Resolved
• Priority: Minor
• Resolution: Later
• Affects Version/s: 2.2.0
• Component/s: ML
• Assignee: Unassigned
• Reporter: Teng Peng
• Created: 05/Nov/17 05:56
• Updated: 21/Nov/17 00:21
• Resolved: 21/Nov/17 00:21

Description

Currently, we only have AIC for GLM. BIC is another "similar" criterion widely used and implemented in all major statical tools.

Postive reasons:
1. Completeness.
2. Useful for some users.

Negative reasons:
1. Not sure how many users would actually use BIC.

Possible Implementation:
1. Duplicate AIC's methods. Calculate penalty term independently. Pros: safe & consistent. Cons: duplication.
2. Let AIC & BIC share the log likelihood by a same method. Calculate penalty term independently.
Pros: similar to scikit learn. No duplication. Cons: less safe & consistent.

Reference:
1. https://stats.stackexchange.com/questions/577/is-there-any-reason-to-prefer-the-aic-or-bic-over-the-other
2.http://users.stat.umn.edu/~yangx374/papers/Pre-Print_2003-10_Biometrika.pdf

Thoughts?