From 53dc257b51452d26244258a63519fbd1583cad82 Mon Sep 17 00:00:00 2001 From: Thomas Wutzler Date: Tue, 2 Sep 2025 10:40:01 +0200 Subject: [PATCH 1/5] recreate tutorial figures --- .../figure-commonmark/cell-11-output-1.png | Bin 94243 -> 105661 bytes .../figure-commonmark/cell-12-output-1.png | Bin 121596 -> 121144 bytes .../figure-commonmark/cell-13-output-1.png | Bin 62400 -> 65161 bytes .../figure-commonmark/cell-10-output-1.png | Bin 119485 -> 105011 bytes .../figure-commonmark/cell-11-output-1.png | Bin 147290 -> 141026 bytes .../figure-commonmark/cell-12-output-1.png | Bin 122345 -> 129946 bytes .../figure-commonmark/cell-9-output-1.png | Bin 93772 -> 91374 bytes 7 files changed, 0 insertions(+), 0 deletions(-) diff --git a/docs/src/tutorials/blocks_corr_files/figure-commonmark/cell-11-output-1.png b/docs/src/tutorials/blocks_corr_files/figure-commonmark/cell-11-output-1.png index deb0d1da8011c70306702b2aa5bfe769a6d11b77..b5f5d20ca02566b17f2cf62c34cfbc110a35f1c8 100644 GIT binary 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z#&4QCo0>GFnFJ^goWc{J3D{GkUcJzUMF*(7#j(cw(v%uqNJ2WG$)&9diU={|_l-Dg zR@94S--<~|ja%sdYiQha9k0&t-yAmTg7bexef~dvQAF8inKz~`eZ2Vo{Ezsjuk#?M J=$_-2{5Snq=>-4) From 98831cd8a68866c8939dafe3e74e2054f7836a48 Mon Sep 17 00:00:00 2001 From: Thomas Wutzler Date: Tue, 2 Sep 2025 10:41:02 +0200 Subject: [PATCH 2/5] docu strings of Lux --- .gitignore | 1 + ext/HybridVariationalInferenceLuxExt.jl | 7 +++++-- src/HybridSolver.jl | 2 ++ src/ModelApplicator.jl | 8 ++++---- src/gf.jl | 7 +++++-- 5 files changed, 17 insertions(+), 8 deletions(-) diff --git a/.gitignore b/.gitignore index 1010547..a960a8b 100644 --- a/.gitignore +++ b/.gitignore @@ -14,3 +14,4 @@ docs/src/**/*_files/libs docs/src/**/*.html docs/src/**/*.ipynb docs/src/**/*Manifest.toml +docs/src_stash/*.ipynb diff --git a/ext/HybridVariationalInferenceLuxExt.jl b/ext/HybridVariationalInferenceLuxExt.jl index 0329c1c..4c66175 100644 --- a/ext/HybridVariationalInferenceLuxExt.jl +++ b/ext/HybridVariationalInferenceLuxExt.jl @@ -7,7 +7,10 @@ using Random using StatsFuns: logistic - +# AbstractModelApplicator that stores a Lux.StatefulLuxLayer, so that +# it can be applied with given inputs and parameters +# The `int_Ï•` ComponentArrayInterpreter, attaches the correct axes to the +# supplied parameters, that do not need to keep the Axis information struct LuxApplicator{MT, IT} <: AbstractModelApplicator stateful_layer::MT int_Ï•::IT @@ -24,7 +27,7 @@ function HVI.construct_ChainsApplicator(rng::AbstractRNG, m::Chain, float_type=F end function HVI.apply_model(app::LuxApplicator, x, Ï•) - Ï•c = app.int_Ï•(Ï•) + Ï•c = app.int_Ï•(CA.getdata(Ï•)) app.stateful_layer(x, Ï•c) end diff --git a/src/HybridSolver.jl b/src/HybridSolver.jl index 87cbaf6..d88151a 100644 --- a/src/HybridSolver.jl +++ b/src/HybridSolver.jl @@ -54,6 +54,8 @@ function CommonSolve.solve(prob::AbstractHybridProblem, solver::HybridPointSolve # Zygote.gradient(Ï•0_dev -> loss_gf(Ï•0_dev, data1...)[1], Ï•0_dev) optf = Optimization.OptimizationFunction((Ï•, data) -> loss_gf(Ï•, data...)[1], Optimization.AutoZygote()) + # use CA.getdata(Ï•0_dev), i.e. the plain vector to avoid recompiling for specific CA + # loss_gf re-attaches the axes optprob = OptimizationProblem(optf, CA.getdata(Ï•0_dev), train_loader_dev) res = Optimization.solve(optprob, solver.alg; kwargs...) Ï• = intÏ•(res.u) diff --git a/src/ModelApplicator.jl b/src/ModelApplicator.jl index 943a147..4d08fc0 100644 --- a/src/ModelApplicator.jl +++ b/src/ModelApplicator.jl @@ -11,10 +11,10 @@ a tuple with two components: - The applicator - a sample parameter vector (type depends on the used ML-framework) -Implemented are -- `construct_SimpleChainsApplicator` -- `construct_FluxApplicator` -- `construct_LuxApplicator` +Implemented overloads of `construct_ChainsApplicator` for layers of +- `SimpleChains.SimpleChain` +- `Flux.Chain` +- `Lux.Chain` """ abstract type AbstractModelApplicator end diff --git a/src/gf.jl b/src/gf.jl index 4322992..9ab728a 100644 --- a/src/gf.jl +++ b/src/gf.jl @@ -138,8 +138,9 @@ Create a loss function for given - transM: transforamtion of parameters at unconstrained space - f(θMs, θP): mechanistic model - intÏ•: interpreter attaching axis with components Ï•g and Ï•P -- intP: interpreter attaching axis to ζP = Ï•P with components used by f -- kwargs: additional keyword arguments passed to gf, such as gdev or pbm_covars +- intP: interpreter attaching axis to ζP = Ï•P with components used by f, + The default, uses `intÏ•(Ï•)` as a template +- kwargs: additional keyword arguments passed to `gf`, such as `gdev` or `pbm_covars` The loss function `loss_gf(Ï•, xM, xP, y_o, y_unc, i_sites)` takes - parameter vector Ï• @@ -147,6 +148,8 @@ The loss function `loss_gf(Ï•, xM, xP, y_o, y_unc, i_sites)` takes - xP: iteration of drivers for each site - y_o: matrix of observations, sites in columns - y_unc: vector of uncertainty information for each observation + Currently, hardcoes squared error loss of `(y_pred .- y_o) ./ σ`, + with `σ = exp.(y_unc ./ 2)`. - i_sites: index of sites in the batch and returns a NamedTuple of From 0697a443203cf00f175b7d4db1302dc1eb3739dc Mon Sep 17 00:00:00 2001 From: Thomas Wutzler Date: Tue, 2 Sep 2025 14:24:09 +0200 Subject: [PATCH 3/5] make PoiintSoilver use Problems logdensity function --- dev/doubleMM.jl | 2 +- src/HybridSolver.jl | 3 ++- src/gf.jl | 8 +++++--- src/logden_normal.jl | 2 +- test/test_HybridProblem.jl | 3 ++- test/test_doubleMM.jl | 7 ++++--- test/test_util_gpu.jl | 10 +++++----- 7 files changed, 20 insertions(+), 15 deletions(-) diff --git a/dev/doubleMM.jl b/dev/doubleMM.jl index 3f1a813..021b936 100644 --- a/dev/doubleMM.jl +++ b/dev/doubleMM.jl @@ -137,7 +137,7 @@ end () -> begin # optimized loss is indeed lower than with true parameters int_ϕθP = ComponentArrayInterpreter(CA.ComponentVector( Ï•g = 1:length(prob0.Ï•g), θP = prob0.θP)) - loss_gf = get_loss_gf(prob0.g, prob0.transM, prob0.transP, prob0.f, Float32[], int_ϕθP) + loss_gf = get_loss_gf(prob0.g, prob0.transM, prob0.transP, prob0.f, Float32[], py, int_ϕθP) loss_gf(vcat(prob3.Ï•g, prob3.θP), xM, xP, y_o, y_unc, i_sites)[1] loss_gf(vcat(prob3o.Ï•g, prob3o.θP), xM, xP, y_o, y_unc, i_sites)[1] # diff --git a/src/HybridSolver.jl b/src/HybridSolver.jl index d88151a..a7c9cb0 100644 --- a/src/HybridSolver.jl +++ b/src/HybridSolver.jl @@ -32,13 +32,14 @@ function CommonSolve.solve(prob::AbstractHybridProblem, solver::HybridPointSolve train_loader_dev = train_loader end f = get_hybridproblem_PBmodel(prob; scenario, use_all_sites=false) + py = get_hybridproblem_neg_logden_obs(prob; scenario) pbm_covars = get_hybridproblem_pbmpar_covars(prob; scenario) n_site, n_batch = get_hybridproblem_n_site_and_batch(prob; scenario) priors = get_hybridproblem_priors(prob; scenario) priorsP = [priors[k] for k in keys(par_templates.θP)] priorsM = [priors[k] for k in keys(par_templates.θM)] #intP = ComponentArrayInterpreter(par_templates.θP) - loss_gf = get_loss_gf(g_dev, transM, transP, f, intÏ•; + loss_gf = get_loss_gf(g_dev, transM, transP, f, py, intÏ•; cdev=infer_cdev(gdevs), pbm_covars, n_site_batch=n_batch, priorsP, priorsM,) # call loss function once l1 = is_infer ? diff --git a/src/gf.jl b/src/gf.jl index 9ab728a..30b5a76 100644 --- a/src/gf.jl +++ b/src/gf.jl @@ -137,6 +137,7 @@ Create a loss function for given - g(x, Ï•): machine learning model - transM: transforamtion of parameters at unconstrained space - f(θMs, θP): mechanistic model +- py: `function(y_pred, y_obs, y_unc)` to compute negative log-likelihood, i.e. cost - intÏ•: interpreter attaching axis with components Ï•g and Ï•P - intP: interpreter attaching axis to ζP = Ï•P with components used by f, The default, uses `intÏ•(Ï•)` as a template @@ -160,7 +161,7 @@ and returns a NamedTuple of - `neg_log_prior`: negative log-prior of `θMs` and `θP` - `neg_log_prior`: negative log-prior of `θMs` and `θP` """ -function get_loss_gf(g, transM, transP, f, +function get_loss_gf(g, transM, transP, f, py, intÏ•::AbstractComponentArrayInterpreter, intP::AbstractComponentArrayInterpreter = ComponentArrayInterpreter( intÏ•(1:length(intÏ•)).Ï•P); @@ -178,7 +179,6 @@ function get_loss_gf(g, transM, transP, f, #, intP = get_concrete(intP) #inv_transP = inverse(transP), kwargs = kwargs function loss_gf(Ï•, xM, xP, y_o, y_unc, i_sites) - σ = exp.(y_unc ./ 2) Ï•c = intÏ•(Ï•) # μ_ζP = Ï•c.Ï•P # xMP = _append_each_covars(xM, CA.getdata(μ_ζP), pbm_covar_indices) @@ -190,7 +190,9 @@ function get_loss_gf(g, transM, transP, f, y_pred, θMs_pred, θP_pred = gf( g, transMs, transP, f, xM, xP, CA.getdata(Ï•c.Ï•g), CA.getdata(Ï•c.Ï•P), pbm_covar_indices; cdev, kwargs...) - nLy = sum(abs2, (y_pred .- y_o) ./ σ) + #σ = exp.(y_unc ./ 2) + #nLy = sum(abs2, (y_pred .- y_o) ./ σ) + nLy = py( y_pred, y_o, y_unc) # logpdf is not typestable for Distribution{Univariate, Continuous} logpdf_t = (prior, θ) -> logpdf(prior, θ)::eltype(θP_pred) logpdf_tv = (prior, θ::AbstractVector) -> begin diff --git a/src/logden_normal.jl b/src/logden_normal.jl index 19b7d3a..d3cd814 100644 --- a/src/logden_normal.jl +++ b/src/logden_normal.jl @@ -1,7 +1,7 @@ """ neg_logden_indep_normal(obs, μ, logσ2s; σfac=1.0) -Compute the negative Log-density of `θM` for multiple independent normal distributions, +Compute the negative Log-density of `obs` for multiple independent normal distributions, given estimated means `μ` and estimated log of variance parameters `logσ2s`. All the arguments should be vectors of the same length. diff --git a/test/test_HybridProblem.jl b/test/test_HybridProblem.jl index ef105bf..c8b9c2b 100644 --- a/test/test_HybridProblem.jl +++ b/test/test_HybridProblem.jl @@ -141,6 +141,7 @@ test_without_flux = (scenario) -> begin train_loader = get_hybridproblem_train_dataloader(prob; scenario) (xM, xP, y_o, y_unc, i_sites) = first(train_loader) f = get_hybridproblem_PBmodel(prob; scenario, use_all_sites = false) + py = get_hybridproblem_neg_logden_obs(prob; scenario) par_templates = get_hybridproblem_par_templates(prob; scenario) #f(par_templates.θP, hcat(par_templates.θM, par_templates.θM), xP[1:2]) (; transM, transP) = get_hybridproblem_transforms(prob; scenario) @@ -154,7 +155,7 @@ test_without_flux = (scenario) -> begin p = p0 = vcat(Ï•g0, par_templates.θP .* convert(eltype(Ï•g0), 0.8)) # Pass the site-data for the batches as separate vectors wrapped in a tuple - loss_gf = get_loss_gf(g, transM, transP, f, intÏ•; + loss_gf = get_loss_gf(g, transM, transP, f, py, intÏ•; pbm_covars, n_site_batch = n_batch, priorsP, priorsM) (_xM, _xP, _y_o, _y_unc, _i_sites) = first(train_loader) l1 = loss_gf(p0, _xM, _xP, _y_o, _y_unc, _i_sites) diff --git a/test/test_doubleMM.jl b/test/test_doubleMM.jl index 9f16a4b..b4d6936 100644 --- a/test/test_doubleMM.jl +++ b/test/test_doubleMM.jl @@ -199,6 +199,7 @@ end n_site, n_site_batch = get_hybridproblem_n_site_and_batch(prob; scenario) f = get_hybridproblem_PBmodel(prob; scenario, use_all_sites = false) f2 = get_hybridproblem_PBmodel(prob; scenario, use_all_sites = true) + py = get_hybridproblem_neg_logden_obs(prob; scenario) priors = get_hybridproblem_priors(prob; scenario) priorsP = [priors[k] for k in keys(par_templates.θP)] priorsM = [priors[k] for k in keys(par_templates.θM)] @@ -218,9 +219,9 @@ end pbm_covars = get_hybridproblem_pbmpar_covars(prob; scenario) #loss_gf = get_loss_gf(g, transM, f, intÏ•; gdev = identity) - loss_gf = get_loss_gf(g, transM, transP, f, intÏ•; + loss_gf = get_loss_gf(g, transM, transP, f, py, intÏ•; pbm_covars, n_site_batch = n_batch, priorsP, priorsM) - loss_gf2 = get_loss_gf(g, transM, transP, f2, intÏ•; + loss_gf_site = get_loss_gf(g, transM, transP, f2, py, intÏ•; pbm_covars, n_site_batch = n_site, priorsP, priorsM) nLjoint = @inferred first(loss_gf(p0, first(train_loader)...)) (xM_batch, xP_batch, y_o_batch, y_unc_batch, i_sites_batch) = first(train_loader) @@ -237,7 +238,7 @@ end #optprob, Adam(0.02), callback = callback_loss(100), maxiters = 5000); optprob, Adam(0.02), maxiters = 2000) - (;nLjoint_pen, y_pred, θMs_pred, θP_pred, nLy, neg_log_prior, loss_penalty) = loss_gf2( + (;nLjoint_pen, y_pred, θMs_pred, θP_pred, nLy, neg_log_prior, loss_penalty) = loss_gf_site( res.u, train_loader.data...) #(nLjoint, y_pred, θMs_pred, θP, nLy, neg_log_prior, loss_penalty) = loss_gf(p0, xM, xP, y_o, y_unc); θMs_pred = CA.ComponentArray(θMs_pred, CA.getaxes(θMs_true')) diff --git a/test/test_util_gpu.jl b/test/test_util_gpu.jl index 75162f8..04a2b8e 100644 --- a/test/test_util_gpu.jl +++ b/test/test_util_gpu.jl @@ -15,11 +15,11 @@ gdev = gpu_device() if gdev isa MLDataDevices.CUDADevice @testset "ones_similar_x" begin B = CUDA.rand(Float32, 5, 2); # GPU matrix - @test HVI.ones_similar_x(B, size(B,1)) isa CuArray - @test HVI.ones_similar_x(ComponentVector(b=B), size(B,1)) isa CuArray - @test HVI.ones_similar_x(B', size(B,1)) isa CuArray - @test HVI.ones_similar_x(@view(B[:,2]), size(B,1)) isa CuArray - @test HVI.ones_similar_x(ComponentVector(b=B)[:,1], size(B,1)) isa CuArray + @test HVI.ones_similar_x(B, size(B,1)) isa CUDA.CuArray + @test HVI.ones_similar_x(ComponentVector(b=B), size(B,1)) isa CUDA.CuArray + @test HVI.ones_similar_x(B', size(B,1)) isa CUDA.CuArray + @test HVI.ones_similar_x(@view(B[:,2]), size(B,1)) isa CUDA.CuArray + @test HVI.ones_similar_x(ComponentVector(b=B)[:,1], size(B,1)) isa CUDA.CuArray end end From f2f34a5df1ed3457af4ca5429825a1e85af5efb3 Mon Sep 17 00:00:00 2001 From: Thomas Wutzler Date: Tue, 2 Sep 2025 14:34:04 +0200 Subject: [PATCH 4/5] howto custom Likelihood --- docs/make.jl | 1 + docs/src/tutorials/logden_user.md | 225 +++++++++++++++++ docs/src/tutorials/logden_user.qmd | 231 ++++++++++++++++++ .../figure-commonmark/cell-10-output-1.png | Bin 0 -> 96146 bytes .../figure-commonmark/cell-11-output-1.png | Bin 0 -> 111405 bytes .../figure-commonmark/cell-12-output-1.png | Bin 0 -> 140883 bytes .../figure-commonmark/cell-8-output-1.png | Bin 0 -> 33215 bytes .../figure-commonmark/cell-9-output-1.png | Bin 0 -> 30951 bytes 8 files changed, 457 insertions(+) create mode 100644 docs/src/tutorials/logden_user.md create mode 100644 docs/src/tutorials/logden_user.qmd create mode 100644 docs/src/tutorials/logden_user_files/figure-commonmark/cell-10-output-1.png create mode 100644 docs/src/tutorials/logden_user_files/figure-commonmark/cell-11-output-1.png create mode 100644 docs/src/tutorials/logden_user_files/figure-commonmark/cell-12-output-1.png create mode 100644 docs/src/tutorials/logden_user_files/figure-commonmark/cell-8-output-1.png create mode 100644 docs/src/tutorials/logden_user_files/figure-commonmark/cell-9-output-1.png diff --git a/docs/make.jl b/docs/make.jl index 93bf49c..9ff370c 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -24,6 +24,7 @@ makedocs(; ], "How to" => [ ".. use GPU" => "tutorials/lux_gpu.md", + ".. specify log-Likelihood" => "tutorials/logden_user.md", ".. model independent parameters" => "tutorials/blocks_corr.md", ".. model site-global corr" => "tutorials/corr_site_global.md", ], diff --git a/docs/src/tutorials/logden_user.md b/docs/src/tutorials/logden_user.md new file mode 100644 index 0000000..9e60941 --- /dev/null +++ b/docs/src/tutorials/logden_user.md @@ -0,0 +1,225 @@ +# How to specify a custom LogLikelihood of the observations + + +``` @meta +CurrentModule = HybridVariationalInference +``` + +This guide shows how the user can specify a customized log-density function. + +## Motivation + +The loglikelihood function assigns a cost to the mismatch between predictions and +observations. This often needs to be customized to the specific inversion. + +This guide walks through he specification of such a function and inspects +differences among two log-likelihood functions. +Specifically, it will assume observation errors to be independently distributed +according to a LogNormal distribution with a specified fixed relative error, +compared to an inversion assuming observation error to be distributed independently normal. + +First load necessary packages. + +``` julia +using HybridVariationalInference +using ComponentArrays: ComponentArrays as CA +using Bijectors +using SimpleChains +using MLUtils +using JLD2 +using Random +using CairoMakie +using PairPlots # scatterplot matrices +``` + +This tutorial reuses and modifies the fitted object saved at the end of the +[Basic workflow without GPU](@ref) tutorial, that used a log-Likelihood +function assuming observation error to be distributed independently normal. + +``` julia +fname = "intermediate/basic_cpu_results.jld2" +print(abspath(fname)) +prob = probo_normal = load(fname, "probo"); +``` + +## Write the LogLikelihood Function + +The function signature corresponds to the one of [`neg_logden_indep_normal`](@ref). +of signature + +`neg_log_den_user(y_pred, y_obs, y_unc; kwargs...)` + +It takes inputs of predictions, `y_pred`, observations, `y_obs`, +and uncertainties parameters, `y_unc` and returns the logarithm of the +likelihhood up to a constant. + +All of the arguments are vectors of the same length specifying predictions and +observations for one site. +If `y_pred`, `y_obs` are given as a matrix of several column-vectors, their summed +Likelihood is computed. + +The density of a LogNormal distribution is + +$$ +\frac{ 1 }{ x \sqrt{2 \pi \sigma^2} } \exp\left( -\frac{ (\ln x-\mu)^2 }{2 \sigma^2} \right)$$ + +where x is the observation, μ is the log of the prediction, and σ is the scale +parameter that is related to the relative error, $c_v$ by $\sigma = \sqrt{ln(c^2_v + 1)}$. + +Taking the log: + +$$ + -ln x -\frac{1}{2} ln \sigma^2 -\frac{1}{2} ln (2 \pi) -\frac{ (\ln x-\mu)^2 }{2 \sigma^2}$$ + +Negating and dropping the constants $-\frac{1}{2} ln (2 \pi)$ and $-\frac{1}{2} ln \sigma^2$ + +$$ + ln x + \frac{1}{2} \left(\frac{ (\ln x-\mu)^2 }{\sigma^2} \right)$$ + +``` julia +function neg_logden_lognormalep_lognormal(y_pred, y_obs::AbstractArray{ET}, y_unc; + σ2 = log(abs2(ET(0.02)) + ET(1))) where ET + lnx = log.(CA.getdata(y_obs)) + μ = log.(CA.getdata(y_pred)) + nlogL = sum(lnx .+ abs2.(lnx .- μ) ./ (ET(2) .* σ2)) + #nlogL = sum(lnx + (log(σ2) .+ abs2.(lnx .- μ) ./ σ2) ./ ET(2)) # nonconstant σ2 + return (nlogL) +end +``` + +If information on the different relative error by observation was available, +we could pass that information using the DataLoader with `y_unc`, rather than +assuming a constant relative error across observations. + +## Update the problem and redo the inversion + +HybridProblem has keyword argument `py` to specify the function of negative Log-Likelihood. + +``` julia +prob_lognormal = HybridProblem(prob; py = neg_logden_lognormalep_lognormal) + +using OptimizationOptimisers +import Zygote + +solver = HybridPosteriorSolver(; alg=Adam(0.02), n_MC=3) + +(; probo) = solve(prob_lognormal, solver; + callback = callback_loss(100), # output during fitting + epochs = 20, +); probo_lognormal = probo; +``` + +## Compare results between assumptions of observation error + +First, draw a sample form the inversion assumping normal and a sample from +the inversion assuming loglornally distributed observation errors. + +``` julia +n_sample_pred = 400 +(y_normal, θsP_normal, θsMs_normal) = (; y, θsP, θsMs) = predict_hvi( + Random.default_rng(), probo_normal; n_sample_pred) +(y_lognormal, θsP_lognormal, θsMs_lognormal) = (; y, θsP, θsMs) = predict_hvi( + Random.default_rng(), probo_lognormal; n_sample_pred) +``` + +Get the original observations from the DataLoader of the problem, and +compute the residuals. + +``` julia +train_loader = get_hybridproblem_train_dataloader(probo_normal; scenario=()) +y_o = train_loader.data[3] +resid_normal = y_o .- y_normal +resid_lognormal = y_o .- y_lognormal +``` + +And compare plots of some of the results. + +``` julia +i_out = 4 +i_site = 1 +fig = Figure(); ax = Axis(fig[1,1], xlabel="observations error (y_obs - y_pred)",ylabel="probability density") +#hist!(ax, resid_normal[i_out,i_site,:], label="normal", normalization=:pdf) +density!(ax, resid_normal[i_out,i_site,:], alpha = 0.8, label="normal") +density!(ax, resid_lognormal[i_out,i_site,:], alpha = 0.8, label="lognormal") +axislegend(ax, unique=true) +fig +``` + +![](logden_user_files/figure-commonmark/cell-8-output-1.png) + +The density plot of the observation residuals does not show the lognormal shape. +The used synthetic observations were actually noramally +distributed around predictions with true parameters. + +How does the wrong assumption of observation error influence the parameter +posterior? + +``` julia +i_site = 1 +fig = Figure(); ax = Axis(fig[1,1], xlabel="global parameter K2",ylabel="probability density") +#hist!(ax, resid_normal[i_out,i_site,:], label="normal", normalization=:pdf) +density!(ax, θsP_normal[:K2,:], alpha = 0.8, label="normal") +density!(ax, θsP_lognormal[:K2,:], alpha = 0.8, label="lognormal") +axislegend(ax, unique=true) +fig +``` + +![](logden_user_files/figure-commonmark/cell-9-output-1.png) + +The marginal posterior of the global parameters is also similar, with a small +trend of lower values. + +``` julia +i_site = 1 +θln = vcat(θsP_lognormal, θsMs_lognormal[i_site,:,:]) +θln_nt = NamedTuple(Symbol("$(k)_lognormal") => CA.getdata(θln[k,:]) for k in keys(θln[:,1])) # +#θn = vcat(θsP_normal, θsMs_normal[i_site,:,:]) +#θn_nt = NamedTuple(Symbol("$(k)_normal") => CA.getdata(θn[k,:]) for k in keys(θn[:,1])) # +# ntc = (;θn_nt..., θln_nt...) +plt = pairplot(θln_nt) +``` + +![](logden_user_files/figure-commonmark/cell-10-output-1.png) + +The corner plot of the independent-parameters estimate +looks similar and shows correlations between site parameters, $r_1$ and $K_1$. + +``` julia +i_out = 4 +fig = Figure(); ax = Axis(fig[1,1], xlabel="mean(y)",ylabel="sd(y)") +ymean_normal = [mean(y_normal[i_out,s,:]) for s in axes(y_normal, 2)] +ysd_normal = [std(y_normal[i_out,s,:]) for s in axes(y_normal, 2)] +scatter!(ax, ymean_normal, ysd_normal, label="normal") +ymean_lognormal = [mean(y_lognormal[i_out,s,:]) for s in axes(y_lognormal, 2)] +ysd_lognormal = [std(y_lognormal[i_out,s,:]) for s in axes(y_lognormal, 2)] +scatter!(ax, ymean_lognormal, ysd_lognormal, label="lognormal") +axislegend(ax, unique=true) +fig +``` + +![](logden_user_files/figure-commonmark/cell-11-output-1.png) + +The predicted magnitude of error in predictions for the fourth observation across sites +is of the same magnitude, +and still shows (although weaker) pattern of decreasing uncertainty with +increasing value. + +``` julia +plot_sd_vs_mean = (par) -> begin + fig = Figure(); ax = Axis(fig[1,1], xlabel="mean($par)",ylabel="sd($par)") + θmean_normal = [mean(θsMs_normal[s,par,:]) for s in axes(θsMs_normal, 1)] + θsd_normal = [std(θsMs_normal[s,par,:]) for s in axes(θsMs_normal, 1)] + scatter!(ax, θmean_normal, θsd_normal, label="correlated") + θmean_lognormal = [mean(θsMs_lognormal[s,par,:]) for s in axes(θsMs_lognormal, 1)] + θsd_lognormal = [std(θsMs_lognormal[s,par,:]) for s in axes(θsMs_lognormal, 1)] + scatter!(ax, θmean_lognormal, θsd_lognormal, label="independent") + axislegend(ax, unique=true) + fig +end +plot_sd_vs_mean(:K1) +``` + +![](logden_user_files/figure-commonmark/cell-12-output-1.png) + +For the assumed fixed relative error,the uncertainty in the model +parameters, $K_1$, across sites is similar to the uncertainty with nornal log-likelihood. diff --git a/docs/src/tutorials/logden_user.qmd b/docs/src/tutorials/logden_user.qmd new file mode 100644 index 0000000..1837470 --- /dev/null +++ b/docs/src/tutorials/logden_user.qmd @@ -0,0 +1,231 @@ +--- +title: "How to specify a custom LogLikelihood of the observations" +engine: julia +execute: + echo: true + output: false + daemon: 3600 +format: + commonmark: + variant: -raw_html+tex_math_dollars + wrap: preserve +bibliography: twutz_txt.bib +--- + +``` @meta +CurrentModule = HybridVariationalInference +``` + +This guide shows how the user can specify a customized log-density function. + +## Motivation +The loglikelihood function assigns a cost to the mismatch between predictions and +observations. This often needs to be customized to the specific inversion. + +This guide walks through he specification of such a function and inspects +differences among two log-likelihood functions. +Specifically, it will assume observation errors to be independently distributed +according to a LogNormal distribution with a specified fixed relative error, +compared to an inversion assuming observation error to be distributed independently normal. + +First load necessary packages. +```{julia} +using HybridVariationalInference +using ComponentArrays: ComponentArrays as CA +using Bijectors +using SimpleChains +using MLUtils +using JLD2 +using Random +using CairoMakie +using PairPlots # scatterplot matrices +``` + +This tutorial reuses and modifies the fitted object saved at the end of the +[Basic workflow without GPU](@ref) tutorial, that used a log-Likelihood +function assuming observation error to be distributed independently normal. + +```{julia} +fname = "intermediate/basic_cpu_results.jld2" +print(abspath(fname)) +prob = probo_normal = load(fname, "probo"); +``` + +## Write the LogLikelihood Function + +The function signature corresponds to the one of [`neg_logden_indep_normal`](@ref). +of signature + + `neg_log_den_user(y_pred, y_obs, y_unc; kwargs...)` + +It takes inputs of predictions, `y_pred`, observations, `y_obs`, +and uncertainties parameters, `y_unc` and returns the logarithm of the +likelihhood up to a constant. + +All of the arguments are vectors of the same length specifying predictions and +observations for one site. +If `y_pred`, `y_obs` are given as a matrix of several column-vectors, their summed +Likelihood is computed. + +The density of a LogNormal distribution is + +$$ +\frac{ 1 }{ x \sqrt{2 \pi \sigma^2} } \exp\left( -\frac{ (\ln x-\mu)^2 }{2 \sigma^2} \right)$$ + +where x is the observation, μ is the log of the prediction, and σ is the scale +parameter that is related to the relative error, $c_v$ by $\sigma = \sqrt{ln(c^2_v + 1)}$. + +Taking the log: + +$$ + -ln x -\frac{1}{2} ln \sigma^2 -\frac{1}{2} ln (2 \pi) -\frac{ (\ln x-\mu)^2 }{2 \sigma^2}$$ + +Negating and dropping the constants $-\frac{1}{2} ln (2 \pi)$ and $-\frac{1}{2} ln \sigma^2$ + +$$ + ln x + \frac{1}{2} \left(\frac{ (\ln x-\mu)^2 }{\sigma^2} \right)$$ + +```{julia} +function neg_logden_lognormalep_lognormal(y_pred, y_obs::AbstractArray{ET}, y_unc; + σ2 = log(abs2(ET(0.02)) + ET(1))) where ET + lnx = log.(CA.getdata(y_obs)) + μ = log.(CA.getdata(y_pred)) + nlogL = sum(lnx .+ abs2.(lnx .- μ) ./ (ET(2) .* σ2)) + #nlogL = sum(lnx + (log(σ2) .+ abs2.(lnx .- μ) ./ σ2) ./ ET(2)) # nonconstant σ2 + return (nlogL) +end +``` + +If information on the different relative error by observation was available, +we could pass that information using the DataLoader with `y_unc`, rather than +assuming a constant relative error across observations. + +## Update the problem and redo the inversion + +HybridProblem has keyword argument `py` to specify the function of negative Log-Likelihood. + +```{julia} +prob_lognormal = HybridProblem(prob; py = neg_logden_lognormalep_lognormal) + +using OptimizationOptimisers +import Zygote + +solver = HybridPosteriorSolver(; alg=Adam(0.02), n_MC=3) + +(; probo) = solve(prob_lognormal, solver; + callback = callback_loss(100), # output during fitting + epochs = 20, +); probo_lognormal = probo; +``` + +## Compare results between assumptions of observation error + +First, draw a sample form the inversion assumping normal and a sample from +the inversion assuming loglornally distributed observation errors. + +```{julia} +n_sample_pred = 400 +(y_normal, θsP_normal, θsMs_normal) = (; y, θsP, θsMs) = predict_hvi( + Random.default_rng(), probo_normal; n_sample_pred) +(y_lognormal, θsP_lognormal, θsMs_lognormal) = (; y, θsP, θsMs) = predict_hvi( + Random.default_rng(), probo_lognormal; n_sample_pred) +``` + +Get the original observations from the DataLoader of the problem, and +compute the residuals. + +```{julia} +train_loader = get_hybridproblem_train_dataloader(probo_normal; scenario=()) +y_o = train_loader.data[3] +resid_normal = y_o .- y_normal +resid_lognormal = y_o .- y_lognormal +``` + +And compare plots of some of the results. + +```{julia} +#| output: true +i_out = 4 +i_site = 1 +fig = Figure(); ax = Axis(fig[1,1], xlabel="observations error (y_obs - y_pred)",ylabel="probability density") +#hist!(ax, resid_normal[i_out,i_site,:], label="normal", normalization=:pdf) +density!(ax, resid_normal[i_out,i_site,:], alpha = 0.8, label="normal") +density!(ax, resid_lognormal[i_out,i_site,:], alpha = 0.8, label="lognormal") +axislegend(ax, unique=true) +fig +``` + +The density plot of the observation residuals does not show the lognormal shape. +The used synthetic observations were actually noramally +distributed around predictions with true parameters. + +How does the wrong assumption of observation error influence the parameter +posterior? + +```{julia} +#| output: true +i_site = 1 +fig = Figure(); ax = Axis(fig[1,1], xlabel="global parameter K2",ylabel="probability density") +#hist!(ax, resid_normal[i_out,i_site,:], label="normal", normalization=:pdf) +density!(ax, θsP_normal[:K2,:], alpha = 0.8, label="normal") +density!(ax, θsP_lognormal[:K2,:], alpha = 0.8, label="lognormal") +axislegend(ax, unique=true) +fig +``` + +The marginal posterior of the global parameters is also similar, with a small +trend of lower values. + +```{julia} +#| output: true +i_site = 1 +θln = vcat(θsP_lognormal, θsMs_lognormal[i_site,:,:]) +θln_nt = NamedTuple(Symbol("$(k)_lognormal") => CA.getdata(θln[k,:]) for k in keys(θln[:,1])) # +#θn = vcat(θsP_normal, θsMs_normal[i_site,:,:]) +#θn_nt = NamedTuple(Symbol("$(k)_normal") => CA.getdata(θn[k,:]) for k in keys(θn[:,1])) # +# ntc = (;θn_nt..., θln_nt...) +plt = pairplot(θln_nt) +``` +The corner plot of the independent-parameters estimate +looks similar and shows correlations between site parameters, $r_1$ and $K_1$. + +```{julia} +#| output: true +i_out = 4 +fig = Figure(); ax = Axis(fig[1,1], xlabel="mean(y)",ylabel="sd(y)") +ymean_normal = [mean(y_normal[i_out,s,:]) for s in axes(y_normal, 2)] +ysd_normal = [std(y_normal[i_out,s,:]) for s in axes(y_normal, 2)] +scatter!(ax, ymean_normal, ysd_normal, label="normal") +ymean_lognormal = [mean(y_lognormal[i_out,s,:]) for s in axes(y_lognormal, 2)] +ysd_lognormal = [std(y_lognormal[i_out,s,:]) for s in axes(y_lognormal, 2)] +scatter!(ax, ymean_lognormal, ysd_lognormal, label="lognormal") +axislegend(ax, unique=true) +fig +``` + +The predicted magnitude of error in predictions for the fourth observation across sites +is of the same magnitude, +and still shows (although weaker) pattern of decreasing uncertainty with +increasing value. + +```{julia} +#| output: true +plot_sd_vs_mean = (par) -> begin + fig = Figure(); ax = Axis(fig[1,1], xlabel="mean($par)",ylabel="sd($par)") + θmean_normal = [mean(θsMs_normal[s,par,:]) for s in axes(θsMs_normal, 1)] + θsd_normal = [std(θsMs_normal[s,par,:]) for s in axes(θsMs_normal, 1)] + scatter!(ax, θmean_normal, θsd_normal, label="correlated") + θmean_lognormal = [mean(θsMs_lognormal[s,par,:]) for s in axes(θsMs_lognormal, 1)] + θsd_lognormal = [std(θsMs_lognormal[s,par,:]) for s in axes(θsMs_lognormal, 1)] + scatter!(ax, θmean_lognormal, θsd_lognormal, label="independent") + axislegend(ax, unique=true) + fig +end +plot_sd_vs_mean(:K1) +``` + +For the assumed fixed relative error,the uncertainty in the model +parameters, $K_1$, across sites is similar to the uncertainty with nornal log-likelihood. + + + diff --git a/docs/src/tutorials/logden_user_files/figure-commonmark/cell-10-output-1.png b/docs/src/tutorials/logden_user_files/figure-commonmark/cell-10-output-1.png new file mode 100644 index 0000000000000000000000000000000000000000..dd132d4c0a89df00a056fb8f33788a3022a75056 GIT binary patch literal 96146 zcmbrn30Tf+_x^3uCS)wioFti&3T22Wib9cTXDBHdl2WECPsqEUm^4Qkb@ 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zAD__<%?|nb{apLtHk73V1Ozl6gFr#8($kaq;)N|WulhczLi4llQymVAuUjXA$r7hL zmHQ9!Ab|H{IF{ujK|^J2Ro&|y9X0p&SH^hlN13P}@qjW{ zINSd@WmcGnk9Ki!IdSF;#hzKL9JRZzJIV9Y@k|J6}bD6%NmU zeuXy@-$_DJk}>G7LB@-tvslYR|7wLyjrU@;O$BQ_fi|XtHZ9C>GYsUx&dP#^QUJzY z$jcj1iH0l1dMH6yJxp%hx~$WfawQ@H{vdJH6WW4_*wvMGr0@*#Hkz4X`&8?~uV24D zfBjlh|MF!PR(CBt$&C@s1Fd-;kDHt0j~{0r*4NYH;^scO8*WogME?229a)MI>N-Bq z+O-3Xrh={XE)mB_y{sgE9eZ9RKc6|BsbF_bCBmq%zSsq<%TSI~f zZEbjWA6v8>Y5LgP|JOVo*}mR#i~sNC!1QIN#CldU4vY04yov*d|1s7#)4QtU81{bv D*cKfq literal 0 HcmV?d00001 From 5fc8fcd8d1f203d23031f77d2a1d031399937fe6 Mon Sep 17 00:00:00 2001 From: Thomas Wutzler Date: Tue, 2 Sep 2025 14:39:11 +0200 Subject: [PATCH 5/5] typo --- docs/src/tutorials/logden_user.md | 2 +- docs/src/tutorials/logden_user.qmd | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/src/tutorials/logden_user.md b/docs/src/tutorials/logden_user.md index 9e60941..240f4a1 100644 --- a/docs/src/tutorials/logden_user.md +++ b/docs/src/tutorials/logden_user.md @@ -222,4 +222,4 @@ plot_sd_vs_mean(:K1) ![](logden_user_files/figure-commonmark/cell-12-output-1.png) For the assumed fixed relative error,the uncertainty in the model -parameters, $K_1$, across sites is similar to the uncertainty with nornal log-likelihood. +parameters, $K_1$, across sites is similar to the uncertainty with normal log-likelihood. diff --git a/docs/src/tutorials/logden_user.qmd b/docs/src/tutorials/logden_user.qmd index 1837470..06f3043 100644 --- a/docs/src/tutorials/logden_user.qmd +++ b/docs/src/tutorials/logden_user.qmd @@ -16,7 +16,7 @@ bibliography: twutz_txt.bib CurrentModule = HybridVariationalInference ``` -This guide shows how the user can specify a customized log-density function. +This guide shows how the user can specify a customized log-Likelihood function. ## Motivation The loglikelihood function assigns a cost to the mismatch between predictions and @@ -225,7 +225,7 @@ plot_sd_vs_mean(:K1) ``` For the assumed fixed relative error,the uncertainty in the model -parameters, $K_1$, across sites is similar to the uncertainty with nornal log-likelihood. +parameters, $K_1$, across sites is similar to the uncertainty with normal log-likelihood.