Skip metric regularization if adapt window=0

[nhuurre]

Submission Checklist

• Run unit tests: ./runTests.py src/test/unit
• Run cpplint: make cpplint
• Declare copyright holder and open-source license: see below

Summary

This came up in #3027 (comment)

CmdStan accepts window=0 as a valid argument even though it means the adaptation cannot possibly estimate the inverse metric. The intended effect appears to be adapt only stepsize and leave the metric at its initial value, either the default identity or a user specified value. That works but only if you also set init_buffer=0. If init_buffer>0 the sampler tries to update the metric anyway and messes it up.

The metric update code is

stan/src/stan/mcmc/var_adaptation.hpp

Lines 24 to 28 in 35a15c8

	estimator_.sample_variance(var);
	double n = static_cast<double>(estimator_.num_samples());
	var = (n / (n + 5.0)) * var
	+ 1e-3 * (5.0 / (n + 5.0)) * Eigen::VectorXd::Ones(var.size());

The Welford estimator's sample_variance() is a no-op if there are not enough samples so that part's fine.
The problem is the subsequent regularization which in case of zero samples just discards the (unchanged) metric.
The fix is to simply skip the regularization when sample_variance() didn't do anything.

Intended Effect

Setting window=0 always keeps the initial metric.

How to Verify

Run the examples/bernoulli model with adapt init_buffer=10 window=0 and look for the mass matrix in output.csv.
On develop it says

# Diagonal elements of inverse mass matrix:
# 0.001

On this branch

# Diagonal elements of inverse mass matrix:
# 1

Side Effects

Documentation

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company): Niko Huurre

By submitting this pull request, the copyright holder is agreeing to license the submitted work under the following licenses:

• Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
• Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	3.36	3.43	0.98	-2.09% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.96	-4.56% slower
eight_schools/eight_schools.stan	0.12	0.12	0.97	-2.87% slower
gp_regr/gp_regr.stan	0.16	0.16	0.99	-0.69% slower
irt_2pl/irt_2pl.stan	6.09	5.99	1.02	1.52% faster
performance.compilation	92.0	88.87	1.04	3.4% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.66	8.64	1.0	0.23% faster
pkpd/one_comp_mm_elim_abs.stan	29.3	29.42	1.0	-0.42% slower
sir/sir.stan	130.24	119.52	1.09	8.23% faster
gp_regr/gen_gp_data.stan	0.03	0.03	0.99	-0.81% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.01	3.02	1.0	-0.35% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.41	0.39	1.05	4.51% faster
arK/arK.stan	1.88	1.84	1.02	2.01% faster
arma/arma.stan	0.76	0.86	0.88	-13.04% slower
garch/garch.stan	0.56	0.57	0.99	-1.38% slower
Mean result: 0.997801547886

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Jenkins Console Log
Blue Ocean
Commit hash: 3830f6f

---

Machine information

ProductName: Mac OS X ProductVersion: 10.11.6 BuildVersion: 15G22010

CPU:
Intel(R) Xeon(R) CPU E5-1680 v2 @ 3.00GHz

G++:
Configured with: --prefix=/Applications/Xcode.app/Contents/Developer/usr --with-gxx-include-dir=/usr/include/c++/4.2.1
Apple LLVM version 7.0.2 (clang-700.1.81)
Target: x86_64-apple-darwin15.6.0
Thread model: posix

Clang:
Apple LLVM version 7.0.2 (clang-700.1.81)
Target: x86_64-apple-darwin15.6.0
Thread model: posix

[betanalpha]

Although I largely agree with the update technically inverse metric updating is skipped for both adapt_window = 0 and adapt_window = 1. I'll change the pull name before merging.

[betanalpha]

Because this behavior probably won't be obvious I think we need to wire a message to the logger. Both here and in var_adaptation can you add a std::string& msg argument which passes the message "Warning: inverse metric is not updated for window sizes less than 2". Then we can pass that to the logger in all of the transition implementations.

[betanalpha]

Corresponding test in var_adaptation_test.cpp?

[betanalpha]

If changes are made according to #3027 (comment) then no warning message would be needed for the base_window = 0 case, in which case messages wouldn't have to be passed, but if inverse metric updating is also disabled for base_window = 1 then I think we still need the message.