Re: multivariate statistics v14

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
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