Re: proposal : cross-column stats

From: Tomas Vondra <tv(at)fuzzy(dot)cz>
To: pgsql-hackers(at)postgresql(dot)org
Subject: Re: proposal : cross-column stats
Date: 2010-12-17 20:50:34
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I've read about 10 papers about estimation this week, and I have gained
some insight. I'm not going to describe each of the papers here, I plan
to set up a wiki page about cross column statistics

and I'll put the list of papers and some basic info there. There was a
lot of discussion in this thread, and it's difficult to follow it, so
I'll put there some details about the proposal etc.

So I'll just briefly describe the interesting things I've learned from
those papers.

---------------------- instances of the problem ----------------------

Generally, there are four quite different cases of the problem.

First, the columns may be either real-valued or discrete. And by
'discrete' I mean the value is rather a label than a value. It does not
make sense to add or subtract them, etc. So for example city names or
zip codes are discrete values (although zip codes are numbers etc).

Second, the queries are consist of equality or inequality (range)

So actually there are four instances of the problem:

| equality conditions | inequality conditions |
discrete values | A | D |
numeric values | C | B |

I think those four problems should be treated separately, although some
of the techniques may be common.

A) discrete values and inequality conditions

One of the papers (A Bayesian Approach to Estimating The Selectivity
of Conjuctive Predicates) describes a quite interesting solution to
this problem - I've already posted a description on how to apply it
to the ZIP code / city name problem - see this

B) numeric values and inequality conditions

Most of the papers dealing with this problem are based on
discretization and multi-dimensional histograms to approximate the
joint distribution. So I believe my initial proposal was not a
complete nonsense.

Once we have a working histogram-based solution, we can work on
precision and efficiency (how much space is needed to store it, how
long does it take to compute an estimate, etc.). There are two
ways to do that.

First, most of the papers offer an enhanced type of histogram
(although the histogram proposed in the paper is always evaluated as
the most efficient one, which is a bit suspicious). Anyway there are
advanced quite-promising ways to build multi-dimensional histograms.

Second, the paper "Selectivity estimation using probabilistic
models") describes a solution based on bayesian networks. That means
really really promising (actually it addresses join selectivity
estimation too).

So yeas, I'm quite confident we can solve this issue and improve the
efficiency - either by an advanced histogram or using bayesian

C) numeric values and equality conditions

OK, I'm not sure how to solve this case. But the queries against
numeric queries are range queries in most cases I guess, so maybe
that's not that big deal.

D) discrete values and inequality conditions

Basically, this can be handled just like numeric values after
discretization, i.e. using a histogram. But this is usually

E) a combination of discrete / numeric columns

I'm not sure how to deal with this. Obviously it's possible to
build multi-dimensional histogram, and estimate as many queries as


The papers describe some interesting alternative approaches, e.g. based
on SVD (singular value decomposition) or random sampling (or kernel
estimators, which an enhanced version of sampling).

But there are various issues associated with those solutions. SVD is
applicable to 2D only, so we'd be stuck with 2 columns, and random
sampling sounds a bit suspicious to me).


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