family parameter

[idiazst]

Is there a reason not to have a family ('gaussian' or 'binomial') parameter and pass it to glmnet?

[nhejazi]

Based on my (likely limited) understanding, there's no theoretical reason that requires us to hardcode the default of family = "gaussian" as we do right now. Simply a matter of adding ... to the main function. @benkeser and @osofr, please feel free to correct me if I'm missing something.

[benkeser]

I hesitated to do this for a theoretical reason, though I think in practice, it is probably fine to include a family argument.

My hesitation came from the following line of thinking: we know that any function with bounded variation norm can be represented using an indicator basis function parameterization that we use. However, it's not immediately clear to me that this remains true on the expit scale, i.e., not sure that it's true that we can write equation (1) from our paper on the expit scale. I honestly am not sure whether this is true or even relevant. Again, my hunch is that it'd be fine in practice. However, for the time being I'm more comfortable truncating predictions > 1 or < 0.

[jlstiles]

Maybe I am missing something but really we are only representing a probability function as opposed to a function that is outside 0-1 possibly. Then you just fit Y = expit(linear function) except with log-lik-loss and constraint on coeffs. Perhaps I'm being thick but don't see what the issue is. The outcome plays no role in the basis functions.

[jlstiles]

Oh nevermind, yes I have to think about that, too

[jlstiles]

log odds of the true prob function is fit at the required rate so it is just a question of the transformed one which must as well. The loss is valid of course so I think we are good

[benkeser]

Makes sense to me.

[idiazst]

Great, thank you guys. That's what I thought as well, all you need is the logit of the true probability to have bounded variation norm. This probably requires the true probability to be bounded away from 0 and 1? Iván On Sep 7, 2017 3:32 PM, David Benkeser <notifications@github.com> wrote: Makes sense to me. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub<https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_benkeser_halplus_issues_3-23issuecomment-2D327900602&d=DwMCaQ&c=lb62iw4YL4RFalcE2hQUQealT9-RXrryqt9KZX2qu2s&r=Xu0Nkc3s7mQJgyxM3aVR55z_xBA1KUt_dKcne0ehGxU&m=EavKO3g0HlWTpwnJjlgRMwO2zXjAHk_1Ry0ypVhnhZI&s=N1G9pX_b-09VicR1__EUlMVj4iq_dCKcDiPgUQCawcE&e=>, or mute the thread<https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_notifications_unsubscribe-2Dauth_AafXeM16329TleI-2D8yYecEumlGay7alpks5sgESggaJpZM4PJWjb&d=DwMCaQ&c=lb62iw4YL4RFalcE2hQUQealT9-RXrryqt9KZX2qu2s&r=Xu0Nkc3s7mQJgyxM3aVR55z_xBA1KUt_dKcne0ehGxU&m=EavKO3g0HlWTpwnJjlgRMwO2zXjAHk_1Ry0ypVhnhZI&s=_i1oSKrGtLz4RBMYyplktAAYt8USD6-CjqlN8c3SfFw&e=>.