GitHub user actuaryzhang opened a pull request:
https://github.com/apache/spark/pull/16149
[SPARK-18715][ML]Fix AIC calculations in Binomial GLM
The AIC calculation in Binomial GLM seems to be off when the response or
weight is non-integer: the result is different from that in R. This issue
arises when one models rates, i.e, num of successes normalized over num of
trials, and uses num of trials as weights. In this case, the effective
likelihood is weight * label ~ binomial(weight, mu), where weight = number of
trials, and weight * label = number of successes and mu = is the success rate.
@srowen @sethah @yanboliang @HyukjinKwon @zhengruifeng
## What changes were proposed in this pull request?
I suggest changing the current aic calculation for the Binomial family from
```
-2.0 * predictions.map { case (y: Double, mu: Double, weight: Double) =>
weight * dist.Binomial(1, mu).logProbabilityOf(math.round(y).toInt)
}.sum()
```
to the following which generalizes to the case of real-valued response and
weights.
```
-2.0 * predictions.map { case (y: Double, mu: Double, weight: Double)
=>
val wt = math.round(weight).toInt
if (wt == 0){
0.0
} else {
dist.Binomial(wt, mu).logProbabilityOf(math.round(y *
weight).toInt)
}
}.sum()
```
## How was this patch tested?
I will write the unit test once the community wants to include the proposed
change. For now, the following modifies existing tests in weighted Binomial GLM
to illustrate the issue. The second label is changed from 0 to 0.5.
```
val datasetWithWeight = Seq(
(1.0, 1.0, 0.0, 5.0),
(0.5, 2.0, 1.0, 2.0),
(1.0, 3.0, 2.0, 1.0),
(0.0, 4.0, 3.0, 3.0)
).toDF("y", "w", "x1", "x2")
val formula = (new RFormula()
.setFormula("y ~ x1 + x2")
.setFeaturesCol("features")
.setLabelCol("label"))
val output =
formula.fit(datasetWithWeight).transform(datasetWithWeight).select("features",
"label", "w")
val glr = new GeneralizedLinearRegression()
.setFamily("binomial")
.setWeightCol("w")
.setFitIntercept(false)
.setRegParam(0)
val model = glr.fit(output)
model.summary.aic
```
The AIC from Spark is 17.3227, and the AIC from R is 15.66454.
You can merge this pull request into a Git repository by running:
$ git pull https://github.com/actuaryzhang/spark aic
Alternatively you can review and apply these changes as the patch at:
https://github.com/apache/spark/pull/16149.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 #16149
----
commit 7fdab860f740de558fa1281255b5e7dc35480d7d
Author: actuaryzhang <actuaryzhan...@gmail.com>
Date: 2016-12-05T18:18:07Z
Fix AIC calculations in Binomial GLM
----
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