David Fetter <david(at)fetter(dot)org> writes:
> > In the prior discussions someone posted the paper with the algorithm
> > I mentioned. That paper mentions that previous work showed poor
> > results at estimating n_distinct even with sample sizes as large as
> > 50% or more.
> Which paper? People have referenced several different ones.
Phillip B Gibbons. Distinct Sampling for Highly-Accurate Answers to Distinct
Values Queries and Event Reports. In Proceedings of the 27th VLDB Conference,
Roma, Italy, 2001.
Which says (emphasis in original as italics):
The most well-studied approach for distinct-values estimation is to
collect a uniform random sample S of the data, store S in a database, and
then use S at query time to provide fast, approximate answers to distinct
values queries [22, 23, 27, 21, 29, 5, 28, 18, 19, 9, 7]. However,
previous work [28, 18, 9, 7] has shown powerful negative results on the
quality of distinct-values estimates based on sampling (or other
techniques that examine only part of the input data), even for the simple
case of counting the number of distinct values in a column. The strongest
negative result is due to Charikar et al. , who proved that estimating
the number of distinct values in a column to within a small constant
factor (with probability > 1/2) requires that *nearly* *the* *entire*
*data* *set* *be* *sampled*. Moreover, all known sampling-based estimators
provide unsatisfactory results on data sets of interest , even for this
Using a variety of synthetic and real-world data sets, we show that
distinct sampling gives estimates for distinct values queries that are
within 0%-10%, whereas previous methods were typically 50%-250% off,
across the spectrum of data sets and queries studied.
Here "distinct sampling" is the algorithm being proposed which requires
looking at every record and keeping a sample *of the distinct values*. The
"previous methods" are methods based on sampling the records
I haven't read the citation  that proves the strong negative result for any
estimator of distinct values based on sampling. It's:
M. Charikar, S. Chaudhuri, R. Motwani, and V. Narasayya. Towards estimation
error guarantees for distinct values. In Proc. 19th ACM Symp. on Principles
of Database Systems, pages 268?279, May 2000.
> > Hopefully you're right that you don't need complete histograms.
> > Perhaps there's some statistics concept they don't teach in stats
> > 101 that would cover this need. What we're looking for is a
> > function f(a,b,x) that gives the net selectivity given a and b, the
> > selectivity of two clauses based on two columns, and x some simple
> > value that can be easily calculated by looking at the data in
> > advance.
> That would be neat :)
Doing a bit of basic searching around I think the tool we're looking for here
is called a "chi-squared test for independence".
I haven't read up on how it works so I'm unclear if i it be calculated using a
simple O(n) scan or if it would require some non-linear post-processing after
the analyze pass which would be unfortunate.
And I haven't found anything that describes how to make use of the resulting
number. Does it actually give a formula f(a,b,x) that gives a nice convenient
expected selectivity for the clause?
Oh, and incidentally, at first glance it seems like calculating it depends on
having good distinct value sampling.
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