GitHub user actuaryzhang opened a pull request:
https://github.com/apache/spark/pull/16344
[SPARK-18929][ML] Add Tweedie distribution in GLM
## What changes were proposed in this pull request?
I propose to add the full Tweedie family into the
GeneralizedLinearRegression model. The Tweedie family is characterized by a
power variance function. Currently supported distributions such as Gaussian,
Poisson and Gamma families are a special case of the Tweedie
https://en.wikipedia.org/wiki/Tweedie_distribution.
@yanboliang @srowen @sethah
I propose to add support for the other distributions:
- compound Poisson: 1 < variancePower < 2. This one is widely used to model
zero-inflated continuous distributions, e.g., in insurance, finance, ecology,
meteorology, advertising etc.
- positive stable: variancePower > 2 and variancePower != 3. Used to model
extreme values.
- inverse Gaussian: variancePower = 3.
The Tweedie family is supported in most statistical packages such as R
(statmod), SAS, h2o etc.
Changes made:
- Allow `tweedie` in family. Only `identity` and `log` links are allowed
for now.
- Add `variancePower` to `GeneralizedLinearRegressionBase`, which takes
values in (1, 2) and [3, infty). Also set default value to 1.5 and add getter
method.
- `Family.fromName` has a second argument `variancePower`
- Add `Tweedie` object
- Add tests for tweedie GLM
Note:
- In computing deviance, use `math.max(y, 0.1)` to avoid taking inverse of
0. This is the same as in R: `tweedie()$dev.res`
- `aic` is not supported in this PR because the evaluation of the [Tweedie
density](http://www.statsci.org/smyth/pubs/tweediepdf-series-preprint.pdf) in
these cases are non-trivial. I will implement the density approximation method
in a future PR. R returns `null` (see `tweedie()$aic`).
You can merge this pull request into a Git repository by running:
$ git pull https://github.com/actuaryzhang/spark tweedie
Alternatively you can review and apply these changes as the patch at:
https://github.com/apache/spark/pull/16344.patch
To close this pull request, make a commit to your master/trunk branch
with (at least) the following in the commit message:
This closes #16344
----
commit 952887e485fb0d5fa669b3b4c9289b8069ee7769
Author: actuaryzhang <[email protected]>
Date: 2016-12-16T00:50:51Z
Add Tweedie family to GLM
commit 4f184ec458f5ed7d70bc5b8165481425f911d2a3
Author: actuaryzhang <[email protected]>
Date: 2016-12-19T22:50:02Z
Fix calculation in dev resid; Add test for different var power
commit 7fe39106332663d3671b94a8ffac48ca61c48470
Author: actuaryzhang <[email protected]>
Date: 2016-12-19T23:14:37Z
Merge test into GLR
----
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