Hi,

On 03/22/2016 11:41 AM, Tatsuo Ishii wrote:
Hum. So without 0006 or beyond, there's not much benefit for the
PostgreSQL users, and you are not too confident about 0006 or
beyond. Then I would think it is a little bit hard to justify in
putting 000[2-5] into 9.6. I really like this feature and would
like to see in PostgreSQL someday, but I'm not sure if we should
put the patches (0002-0005) into PostgreSQL now. Please let me
know if there's some reaons we should put the patches into
PostgreSQL now.


I don't think so. While being able to combine multiple statistics
is certainly useful, I'm convinced that the initial patched add
enough

Can you please elaborate a little bit more how combining multiple
statistics is useful?

Sure.

The goal of multivariate statistics is to approximate a probability distribution on a group of columns. The larger the number of columns, the less accurate the statistics will be (with respect to individual columns), assuming fixed size of the sample in ANALYZE, and fixed statistics size.

For example, if you add a column to multivariate histogram, you'll do some "bucket splits" by this dimension, thus reducing the accuracy for the other columns. You may of course allow larger statistics (e.g. histograms with more buckets), but that also requires larger samples, and so on.

Now, let's  assume you have a query like this:

    WHERE (a=1) AND (b=2) AND (c=3) AND (d=4)

and that "a" and "b" are correlated, and "c" and "d" are correlated, but that otherwise the columns are independent. It'd be a bit silly to require building statistics on (a,b,c,d), when two statistics on each of the column pairs would be cheaper and also more accurate.

That's of course a trivial case - independent groups of correlated columns. But I'd say this is actually a pretty common case, and I do believe there's not much controversy that we should support it.

Another reason to allow multiple statistics is that columns in one group may be a good fit for MCV list (which works well for discrete values), while the other group may be a good candidate for histogram (which works well for continuous values). This can't be solved by first building a MCV and then a histogram on the group.

The question of course is what to do if the groups are not independent. The patch does that by assuming the statistics overlap, and uses conditions on the columns included in both statistics to combine them using conditional probabilities. I do believe this works quite well, but this is perhaps the part that needs further discussion. There are other ways to combine the statistics, but I do expect them to be considerably more expensive.

Is this a sufficient explanation?

Of course, there's a fair amount of additional complexity that I have not mentioned here (e.g. selecting the right combination of stats).

regards

--
Tomas Vondra                  http://www.2ndQuadrant.com
PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services


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