Adding support for poisson regression.

[sharatsc]

Adding support for Possion regression. Does not support --invariant mode yet. Haven't figured out the closed form for the update. Currently works with --normalized as well as --bfgs

Usage documented in a python notebook:
https://github.com/sharatsc/vowpal_wabbit/blob/c1e95f98038c628d0ff3995fb3d85bf7c35eefa3/python/poisson_regression.ipynb

[coveralls]

Coverage decreased (-0.1%) to 69.59% when pulling c1e95f9 on sharatsc:poisson into 68c22d9 on JohnLangford:master.

[coveralls]

Coverage decreased (-0.003%) to 69.705% when pulling 6f88a55 on sharatsc:poisson into 68c22d9 on JohnLangford:master.

[sharatsc]

Coverage is off by rounding error: -0.003%

Appveyor is failing on the same location as an unrelated pull request
#1000

This could be a cs code issue (or CLR version difference b/w Travis and the CS wrapper). Can @eisber somebody take a look?

[JohnLangford]

This seems good except that getUpdate is not safe. In particular, a very large learning rate/importance weight will result in the update going crazy. Have you considered designing a safe update along the lines of this paper: http://arxiv.org/abs/1011.1576 ? This has been a clear win experimentally.

[sharatsc]

Table 1 does list a closed form solution for Poisson. I'll try to work it out. In the mean time, it does work with --normalized and --bfgs.

[JohnLangford]

Nikos says he has it worked out.

[n17s]

Hi folks,

Yes the paper does not list Poisson regression but it can be derived by solving the ODE. Then you have to translate between paper and VW which I believe can be summarized in the following changes:

• VW computes -s() and the table lists s()
• VW replaces (learning rate * importance) by update_scale
• VW replaces norm(x)^2 by pred_per_update

With these in mind and some help from alpha
https://www.wolframalpha.com/input/?i=solve+y%27(t)%3Da*(exp(b-y(t)*c)-d),+y(0)%3D0
my recommendation is

float getUpdate(float prediction, float label, float update_scale, float pred_per_update) {
    if (label > 0) {
      return label * update_scale - log1p(exp(prediction)*expm1(label * update_scale * pred_per_update)/label)/pred_per_update;
    }
    else {
       return - log1p(exp(prediction) * update_scale * pred_per_update)/pred_per_update;
    }
  }

I believe I have done this carefully enough but I have not tested it. Sharat can you verify that this update is at least on par with yours?

[JohnLangford]

Sharat have you had a chance to look at Nikos's update?

[sharatsc]

Looking at it now.

[eisber]

You need to use # Test 133: and not # Train 133:

[sharatsc]

Nikos,
I was able to derive the same. Derivation outlined here: https://dl.dropboxusercontent.com/u/1897767/Implementing%20poisson%20loss%20in%20VW.pdf

The expression in notation used in the original paper (http://bit.ly/1Us0oVe) vs. your derivation (http://bit.ly/25ZG6Gp)

[JohnLangford]

Can you implement today? I want to drop a new version soon.

[coveralls]

Coverage decreased (-0.0002%) to 70.123% when pulling 8761d06 on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[sharatsc]

safe update changes incorporated along fixing with @eisber's comments. The windows build seems to be broken (also on master)

Windows build failing with unrelated error
Assert.AreEqual failed.
Expected:<--no_stdin --max_prediction 1 --bit_precision 18 --cb_adf --cb_type ips --rank_all --csoaa_ldf multiline --interact ud --csoaa_rank>.
Actual:<--no_stdin --max_prediction 1 --bit_precision 18 --cb_adf --cb_type ips --rank_all --csoaa_ldf multiline --csoaa_rank --interact ud>.

[eisber]

My PR has fixes for this… essentially replace the expected with the actual string in TestArguments.cs

[coveralls]

Coverage decreased (-0.0002%) to 70.123% when pulling 5b0d86c on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[coveralls]

Coverage increased (+0.04%) to 70.158% when pulling 960f2a5e6195838410b84a8a4c4b1cc5f358128a on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[coveralls]

Coverage increased (+0.04%) to 70.158% when pulling cf57a61ddb45ad980a70acf523d695c425b3ec76 on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[coveralls]

Coverage increased (+0.04%) to 70.158% when pulling b0bb984 on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[sharatsc]

Windows build has gotten quite flaky. We should consider spinning off cs wrapper as a separate project that consumes the vw nuget? Build time is taken up with cs and cs-tests

[coveralls]

Coverage increased (+0.04%) to 70.158% when pulling 22fa41a on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[coveralls]

Coverage increased (+0.04%) to 70.158% when pulling 18cf9a720930ce8482fd2efaa927a9a32299c103 on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[JohnLangford]

This looks good to go to me. Not sure you should worry about the windows-side tests as @eisber is working on that.

[coveralls]

Coverage increased (+0.04%) to 70.158% when pulling 56418c898105a5a7a587d29e283bc93bca5ef462 on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[coveralls]

Coverage increased (+0.04%) to 70.158% when pulling ae3b4d0 on sharatsc:poisson into 8e0fd1c on JohnLangford:master.

[sharatsc]

@JohnLangford this is ready to go. Fixed windows errors as well.

[JohnLangford]

This is merged in, thanks. All, we now have Poisson loss working thanks
to Sharat and Nikos.

@eisber there are some minor changes to make the windows test work.

-John

On Wed, Jun 15, 2016 at 10:33 AM, Sharat Chikkerur <notifications@github.com

wrote:

@JohnLangford https://github.com/JohnLangford this is ready to go.
Fixed windows errors as well.

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[trufanov-nok]

Hello,
Does poisson loss supposed to support negative labels? Like {-1,1}.
According to poisson_loss::getUpdate() it does as it has a special case for negative labels.
But poisson_loss::getLoss() returns 0 for -1 labels and I'm getting no weights update. Looks like bcs logf(label + 1e-6) is NaN here. So it doesn't support labels that is < 0 ...

[n17s]

It should not support labels <0 as the prediction is exp(w*x). The
assumption is that labels are >=0 so the else part is to avoid division by
0.

Nikos
On Jun 20, 2016 6:36 AM, "Alexander Trufanov" notifications@github.com
wrote:

Hello,
Does poisson loss supposed to support negative labels? Like {-1,1}.
According to poisson_loss::getUpdate() it does as it has
https://github.com/JohnLangford/vowpal_wabbit/blob/master/vowpalwabbit/loss_functions.cc#L306
a special case for negative labels.
But poisson_loss::getLoss() returns 0 for -1 labels and I'm getting no
weights update. Looks like bcs logf(label + 1e-6) is NaN here
https://github.com/JohnLangford/vowpal_wabbit/blob/master/vowpalwabbit/loss_functions.cc#L300.
So it doesn't support labels that is < 0 ...

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[trufanov-nok]

Ok, then it may have sense to put a label check and a warning in its getLoss() as it's done for logloss...