Thank you so much for the comment! I'll fix it.

Fix is done

There was a discussion on this in the LOF PR. It was decided to keep decision_function on new samples as a private method. You can access the decision function values on the training data by considering the opposite of the negative_outlier_factor_. cc @ngoix @amueller

Both decision function and predict methods are private and accessible through _decision_function() and _predict() methods. It was decided so because these two methods somehow extend the use of LOF prediction to "new data". LOF originally performs both training and testing on the same dataset, ie only performs fit_predict(X).
The main problem of making these methods public is that then fit_predict(X) would be different than fit(X).predict(X).

i agree with @ngoix

fit_predict(X) different than fit(X).predict(X) is bad.

Thanks for the comments! I understand it and am sorry that I could not care such matters. The decision_function should not be merged so I would close this pull request.
Thank you.

Should we make it explicit somewhere (in the code or documentation) that predict is private because fit_predict(X) would be different than fit(X).predict(X), And that decision_function was made private because predict was made private ?

I think it could be good for people investigating the code (as I did when looking at this PR) to know why.

Thanks @albertcthomas for the advice. Comment regarding to keeping the method private was inserted to the code.

The reason that decision_function is not published is now added. Please let me know if the explanation is wrong.

These two lines have been included in PR #9015. This PR can be closed.