Constructors for Gaussian priors with constraints #161

tsj5 · 2022-05-17T07:43:14Z

It's desirable to streamline the UI for specifying parameter priors, in particular those for parameters that live on a constrained domain and hence need a nontrivial Constraint().

This PR does this by adding a new constructor, ~~bounded_gaussian~~ constrained_gaussian, for ParameterizedDistribution. The unconstrained distribution is a Gaussian, with parameters (μ_u, σ_u) selected to reproduce user-required statistics in the constrained space [currently only (mean, standard deviation) are supported]. This therefore includes the lognormal and logit-normal distributions as special cases.

In the cases where the constraint interval is infinite or semi-infinite, closed-form expressions are used for (μ_u, σ_u). When the interval is finite, no closed-form solution exists, and (μ_u, σ_u) are optimized numerically via the simplex method. This is still less reliable than it should be for large |μ_u| or σ_u: for these cases the distribution becomes concentrated near one or both interval endpoints, causing instabilities for both numerical integration and optimization (since parameter changes have minimal effect on the objective function).

This PR fixes a sign error in bounded_above() which caused its Jacobian to be negative.

Tasks remaining as of this writing:

constructor for distributions given as Cartesian products of the 1D case currently implemented.
interface for using constrained_gaussian to specify priors from parameter file conventions.

tsj5 · 2022-05-17T20:36:01Z

Does anyone know how to fix the failing JuliaFormatter/format test? I've run julia .dev/climaformat.jl locally, and running it again doesn't change any files. Is the version of JuliaFormatter that's run in CI using different settings than climaformat.jl?

odunbar

Hi Tom - this looks much more along the lines of what I was looking for.
In the todo's, could you also add something to the docs to show how it works?

src/ParameterDistributions.jl

odunbar · 2022-05-24T20:21:22Z

src/ParameterDistributions.jl

+    if ~isapprox(μ_c, m_c, atol = 1e-3, rtol = 1e-2)
+        @warn "Unable to set constrained mean for `$(name)`: target = $(μ_c), got $(m_c)"
+    end
+    if ~isapprox(σ_c, s_c, atol = 1e-3, rtol = 1e-2)


If these are taken in the constrained space, perhaps they should be normalized? (or is that what rtol does?)

Sorry, I'm lost on the proper context for "normalized" -- normalization, svd. etc. are only done in CES, right?

m_c and s_c are the mean/stddev of the distribution at its final, hopefully optimized parameter values, computed as 1d numerical integrals in the physical, constrained space. The highlighted lines are a sanity check to verify that the optimization set those parameters to values that satisfy the user's requested μ_c, σ_c for the prior, to very loose tolerances. rtol is just the tolerance on the relative difference between the two values.

Sorry i was just asking about tolerances. Namely why do we need atol here? (do both tolerances needed to be satisfied?) Because the constrained space is not normalized so if your domain is on [0,1e-5] or [0, 1e5] in the first case atol is satisfied always, and in the second, one could imagine it would never be satisfied

odunbar · 2022-05-24T20:22:19Z

src/ParameterDistributions.jl

+    # optimize in log σ to avoid constraint σ>0
+    init_logσ_u = log(init_σ_u)
+
+    # Optimize parameters; could speed up with gradient info but don't bother to.


If we don't need gradients then they can be removed from the constraints?

tsj5 · 2022-05-31T20:10:58Z

Resolution of the climaformat issue mentioned above, written up here for discoverability: @odunbar mentioned that the version of JuliaFormatter had been updated to 0.22; this was in .dev/Project.toml but for some reason .dev/Manifest.toml was still using the older version (I would have thought that that would've been caught and updated when that environment was activate'ed). Deleting the Manifest and re-instantiating solved the issue.

tsj5 · 2022-06-02T21:24:13Z

bors try

bors · 2022-06-02T21:39:32Z

try

Build succeeded:

odunbar

As this is user facing - could you also provide an example snippet and some information in the docs priors page?

Otherwise, LGTM!

tsj5 · 2022-06-09T03:49:43Z

Finally added docs and examples for constrained_gaussian. See GitHub's markdown preview here -- I don't think there's any way to trigger the docs build for PRs, right?

odunbar

Sorry it's taken a while for review - this looks great. Please merge after addressing my comments.

My only real point is that now we have a "recommended" constructor, we should present this first, likewise with the simple example for it, so could you move everything for this up to the top? Then most users will only have to read the first part of this page. After we can talk about general constructors, and all the details for the constraints etc.

docs/src/parameter_distributions.md

tsj5 · 2022-06-28T02:04:43Z

Sorry it's taken a while for review - this looks great. Please merge after addressing my comments.

My only real point is that now we have a "recommended" constructor, we should present this first, likewise with the simple example for it, so could you move everything for this up to the top? Then most users will only have to read the first part of this page. After we can talk about general constructors, and all the details for the constraints etc.

Good idea -- I definitely agree that it'll be best for users if we put all the info pertaining to the "recommended" constructor up front.

tsj5 · 2022-06-28T05:19:43Z

Current CI failures are described by issue #175 and fixed in PR #176.

odunbar · 2022-06-28T17:40:48Z

@tsj5 Much prefer the structure now! LGTM - merge away!

PS - you have been extraordinarily unlucky with the CI failures on your PRs :(

tsj5 · 2022-06-28T19:48:24Z

bors try

bors · 2022-06-28T20:02:06Z

try

Build succeeded:

Add Optim, QuadGK as deps Add xform jacobian to Constraint struct Properly handle +/-Inf in Constraints Fix sign of bounded_above() Initial commit of bounded_gaussian Rename bounded_gaussian -> constrained_gaussian Extra tests for codecov Add optional kwargs passed to Optim.optimize Reorder sections of parameter_distributions.md doc Add docs & examples for constrained_gaussian()

tsj5 · 2022-06-29T21:06:16Z

bors try

bors · 2022-06-29T21:24:33Z

try

Build succeeded:

tsj5 · 2022-06-29T21:28:25Z

bors r+

161: Constructors for Gaussian priors with constraints r=tsj5 a=tsj5 It's desirable to streamline the UI for specifying parameter priors, in particular those for parameters that live on a constrained domain and hence need a nontrivial Constraint(). This PR does this by adding a new constructor, ~~bounded_gaussian~~ `constrained_gaussian`, for ParameterizedDistribution. The unconstrained distribution is a Gaussian, with parameters (μ_u, σ_u) selected to reproduce user-required statistics in the constrained space [currently only (mean, standard deviation) are supported]. This therefore includes the [lognormal](https://en.wikipedia.org/wiki/Log-normal_distribution) and [logit-normal](https://en.wikipedia.org/wiki/Logit-normal_distribution) distributions as special cases. In the cases where the constraint interval is infinite or semi-infinite, closed-form expressions are used for (μ_u, σ_u). When the interval is finite, no closed-form solution exists, and (μ_u, σ_u) are optimized numerically via the simplex method. This is still less reliable than it should be for large |μ_u| or σ_u: for these cases the distribution becomes concentrated near one or both interval endpoints, causing instabilities for both numerical integration and optimization (since parameter changes have minimal effect on the objective function). This PR fixes a sign error in bounded_above() which caused its Jacobian to be negative. Tasks remaining as of this writing: - constructor for distributions given as Cartesian products of the 1D case currently implemented. - interface for using `constrained_gaussian` to specify priors from parameter file conventions. Co-authored-by: Thomas Jackson <[email protected]>

bors · 2022-06-29T21:35:30Z

Build failed:

test_success

tsj5 · 2022-06-30T04:48:42Z

bors r+

bors · 2022-06-30T04:59:20Z

Build succeeded:

tsj5 mentioned this pull request May 17, 2022

[WIP] Constructors for priors with constraints #141

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tsj5 requested a review from odunbar May 17, 2022 07:44

tsj5 self-assigned this May 17, 2022

tsj5 force-pushed the tsj/prior-init-2 branch from e68eb3b to 6d804a7 Compare May 17, 2022 07:48

tsj5 force-pushed the tsj/prior-init-2 branch 2 times, most recently from 91e0b5d to dffb677 Compare May 17, 2022 21:10

odunbar reviewed May 24, 2022

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bors bot added a commit that referenced this pull request Jun 2, 2022

Try #161:

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odunbar reviewed Jun 3, 2022

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odunbar reviewed Jun 17, 2022

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tsj5 mentioned this pull request Jun 28, 2022

Make use of @test_logs less brittle #175

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bors bot added a commit that referenced this pull request Jun 28, 2022

Try #161:

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tsj5 force-pushed the tsj/prior-init-2 branch from e94bdf2 to eabc313 Compare June 29, 2022 21:05

bors bot added a commit that referenced this pull request Jun 29, 2022

Try #161:

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tsj5 changed the title ~~[WIP] Constructors for priors with constraints~~ Constructors for Gaussian priors with constraints Jun 29, 2022

bors bot merged commit 6585e00 into CliMA:main Jun 30, 2022

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Constructors for Gaussian priors with constraints #161

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