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https://issues.apache.org/jira/browse/SPARK-33678?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17245338#comment-17245338
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Richard Penney commented on SPARK-33678:
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Thanks [~srowen] - I agree that there are definitely use-cases where operating
directly in log-space is the right thing to do (obviously working with
log-likelihoods is very common in the Bayesian world). Equally, there are
clearly situations where log1p and expm1 are the right solutions when one
knows, _a priori_, that one is dealing with arguments close to 1 and 0
respectively.
My main argument is that there are common probabilistic use-cases where one
incurs quite a lot of verbosity that might involve combinations of log1p,
expm1, adding a small offset to avoid log(0), etc., when a simple "product"
aggregation would be clearer and less likely to rely on delicate calculation of
higher-order terms in exp(log(x)) when one neglects to re-express this as
exp(log1p(x-1)).
Anyway, for the probabilistic use case, which is the one that I frequently deal
with, I'd expect the situation where some of the probabilities are exactly zero
is quite common. A use-case involving negative quantities might be constructing
Lagrangian interpolation functions when modelling time-series. I'd admit that
this isn't a going to be used by everyone, but having a product() aggregation
seems like a very general-purpose tool.
> Numerical product aggregation
> -----------------------------
>
> Key: SPARK-33678
> URL: https://issues.apache.org/jira/browse/SPARK-33678
> Project: Spark
> Issue Type: Improvement
> Components: SQL
> Affects Versions: 2.4.7, 3.0.0, 3.1.0
> Reporter: Richard Penney
> Priority: Minor
>
> There is currently no facility in {{spark.sql.functions}} to allow
> computation of the product of all numbers in a grouping expression. Such a
> facility would likely be useful when computing statistical quantities such as
> the combined probability of a set of independent events, or in financial
> applications when calculating a cumulative interest rate.
> Although it is certainly possible to emulate this by an expression of the
> form {{exp(sum(log(column)))}}, this has a number of significant drawbacks:
> * It involves computationally costly functions (exp, log)
> * It is more verbose than something like {{product(column)}}
> * It is more prone to numerical inaccuracies when handling quantities that
> are close to one than by directly multiplying a set of numbers
> * It will not handle zeros or negative numbers cleanly
> I am currently developing an addition to {{sql.functions}}, which involves [a
> new Catalyst aggregation
> expression|https://github.com/rwpenney/spark/blob/feature/agg-product/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/aggregate/Product.scala].
> This needs some additional testing, and I hope to issue a pull-request soon.
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