Github user feynmanliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/7916#discussion_r36150055
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/clustering/LDAModel.scala ---
@@ -267,32 +304,42 @@ class LocalLDAModel private[clustering] (
// by topic (columns of lambda)
val Elogbeta = LDAUtils.dirichletExpectation(lambda.t).t
- var score = documents.filter(_._2.numNonzeros > 0).map { case (id:
Long, termCounts: Vector) =>
- var docScore = 0.0D
+ // Sum bounds for each document:
+ // bounds for prob(tokens) + bounds for prob(document-topic
distribution)
+ documents.filter(_._2.numNonzeros > 0).map { case (id: Long,
termCounts: Vector) =>
+ var docBound = 0.0D
val (gammad: BDV[Double], _) =
OnlineLDAOptimizer.variationalTopicInference(
termCounts, exp(Elogbeta), brzAlpha, gammaShape, k)
val Elogthetad: BDV[Double] = LDAUtils.dirichletExpectation(gammad)
// E[log p(doc | theta, beta)]
termCounts.foreachActive { case (idx, count) =>
- docScore += count * LDAUtils.logSumExp(Elogthetad + Elogbeta(idx,
::).t)
+ docBound += count * LDAUtils.logSumExp(Elogthetad + Elogbeta(idx,
::).t)
}
- // E[log p(theta | alpha) - log q(theta | gamma)]; assumes alpha is
a vector
- docScore += sum((brzAlpha - gammad) :* Elogthetad)
- docScore += sum(lgamma(gammad) - lgamma(brzAlpha))
- docScore += lgamma(sum(brzAlpha)) - lgamma(sum(gammad))
+ // E[log p(theta | alpha) - log q(theta | gamma)]
+ docBound += sum((brzAlpha - gammad) :* Elogthetad)
+ docBound += sum(lgamma(gammad) - lgamma(brzAlpha))
+ docBound += lgamma(sum(brzAlpha)) - lgamma(sum(gammad))
- docScore
+ docBound
}.sum()
+ }
- // E[log p(beta | eta) - log q (beta | lambda)]; assumes eta is a
scalar
- score += sum((eta - lambda) :* Elogbeta)
- score += sum(lgamma(lambda) - lgamma(eta))
-
+ /**
+ * Bound for prob(topic-term distributions):
+ * E[log p(beta | eta) - log q(beta | lambda)]
--- End diff --
Is this really a bound still? E[log p(beta | eta) - log q(beta | lambda)]
~== E[log (p(beta | eta) / q(beta | lambda)] is more of a KL divergence...
"Bound" was correct earlier because we were "conditioning" out the topic
distributions by taking an expectation over q i.e. E[log p(corpus, topics |
hyperparams)] - E[log q(topics | hyperparams)] ~= E[log ( p(corpus, topics |
hyperparams) / q(topics | hyperparams) )] ~= E[ log p(corpus | hyperparams) ]
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