Prediction Metrics: New module

[orhankislal]

JIRA: MADLIB-907

A collection of summary statistics to gauge model accuracy
based on predicted values vs. ground-truth values.

[iyerr3]

I would use "evaluating" instead of "ensuring"

[iyerr3]

General comments:

• The distance functions (mean_*_error) all have the same structure except the distance metric. I suggest refactoring the table creation and the grouping statements into a single function that takes a parameter for the distance.
• Avoid using __ within python. It leads to name mangling, that doesn't really help in this situation.
• There seems to be considerable overlap between the grouping and non-grouping SQL in r2, adjusted_r2 and auc functions. Maybe we can combine them?
• I'll bump the suggestion by @decibel in the previous PR. It might be helpful to have 2 versions: 1 that creates the output table and the other returns the rows directly.

[iyerr3]

I have made some changes and added validation and online help functions (in my private fork branch).

I have not implemented the SRF versions as discussed earlier. We can make those functions as a separate work.

@orhankislal could you please pull in the 3 commits on that branch and update your branch to update this PR. Once we've discussed the changes here, I can merge the commits to master.

[iyerr3]

Let's add a ::int inside the sum. That way we can also support obs_col as a boolean (which would be nice considering this is binary classification).

[iyerr3]

Along with casting the columns to int in binary classification, we also need to change docs/online-help/tests to reflect that boolean columns allowed for observation columns.

[mktal]

Why not

SELECT 
     {grp_out_str}
     1 - avg(({pred_col} - {obs_col})^2)/var_pop({obs_col}) AS r2_score
FROM {table_in} {grp_by_str}

It is simpler, faster (2-3 times in my quick experiments) and numerically stable (avoid large sum)

[orhankislal]

Thank you very much for your comments @iyerr3 and @mktal. I have pushed 2 new commits to incorporate your suggestions. Please let me know if you have any other suggestions.