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https://issues.apache.org/jira/browse/SYSTEMML-510?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Mike Dusenberry updated SYSTEMML-510:
-------------------------------------
Issue Type: Bug (was: Sub-task)
Parent: (was: SYSTEMML-435)
> Generalize All Existing wdivmm Patterns
> ---------------------------------------
>
> Key: SYSTEMML-510
> URL: https://issues.apache.org/jira/browse/SYSTEMML-510
> Project: SystemML
> Issue Type: Bug
> Components: Compiler, Parser, Runtime
> Reporter: Mike Dusenberry
>
> If we look at the inner loop of Poisson nonnegative matrix factorization
> (PNMF) in general, we update the factors as
> {code}
> H = (H * (t(W) %*% (V/(W%*%H + 1e-17))))/t(colSums(W)
> W = (W * ((V/(W%*%H + 1e-17)) %*% t(H)))/t(rowSums(H))
> {code}.
> Notice the addition of the "1e-17" epsilon term in the denominators.
> Mathematically, we need this in case any cell of W%*%H evaluates to zero so
> that we can avoid dividing by zero. R needs this, but SystemML technically
> does not due to a fused operator, "wdivmm", that takes care of these
> situations (or this may be done in the general case?). This fused operator
> is currently applied to the pattern {{t(W) %*% (V / %* (W %*% H))}}, amongst
> other similar patterns. Ideally, this would easily apply to {{t(W) %*%
> (V/(W%*%H + 1e-17)}}, regardless of the unneeded epsilon term. Currently,
> the addition of the epsilon term causes the algorithm to run in non-linear
> time (quad or exponential). Initially, the behavior pointed towards the
> possibility of the optimizer avoiding the rewrite to the fused operator,
> resulting in naive computation, and non-linear growth in training time.
> Further exploration seems to show that the rewrite is indeed still being
> applied, but there seems to also be a recursive nesting of the same rewrite
> over various regions of the above statements that is not found when the
> epsilon term is removed.
> The following is the full PNMF DML script used:
> {code}
> V = read($X)
> max_iteration = $maxiter
> rank = $rank
> n = nrow(V)
> m = ncol(V)
> range = 0.01
> W = Rand(rows=n, cols=rank, min=0, max=range, pdf="uniform")
> H = Rand(rows=rank, cols=m, min=0, max=range, pdf="uniform")
> loglik0 = sum(V*log(W%*%H)) - as.scalar(colSums(W)%*%rowSums(H))
> i=0
> while(i < max_iteration) {
> # Addition of epsilon (1e-17) term causes script to run in non-linear time:
> H = (H * (t(W) %*% (V/(W%*%H + 1e-17))))/t(colSums(W))
> W = (W * ((V/(W%*%H + 1e-17)) %*% t(H)))/t(rowSums(H))
> # Removal of epsilon works correctly:
> #H = (H * (t(W) %*% (V/(W%*%H))))/t(colSums(W))
> #W = (W * ((V/(W%*%H)) %*% t(H)))/t(rowSums(H))
> i = i + 1;
> print(i + "")
> }
> loglik = sum(V*log(W%*%H+1e-17)) - as.scalar(colSums(W)%*%rowSums(H))
> print("pnmf: " + loglik0 + " -> " + loglik)
> {code}
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