From 626309b8e2dacf82cc0ec98518b3849f3abc6556 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Wed, 1 Dec 2021 18:13:00 +0100
Subject: [PATCH 1/8] First go at the augmentation tutorial

---
 examples/d-augmented-gp/Manifest.toml | 1272 +++++++++++++++++++++++++
 examples/d-augmented-gp/Project.toml  |   11 +
 examples/d-augmented-gp/script.jl     |  218 +++++
 3 files changed, 1501 insertions(+)
 create mode 100644 examples/d-augmented-gp/Manifest.toml
 create mode 100644 examples/d-augmented-gp/Project.toml
 create mode 100644 examples/d-augmented-gp/script.jl

diff --git a/examples/d-augmented-gp/Manifest.toml b/examples/d-augmented-gp/Manifest.toml
new file mode 100644
index 00000000..32c10710
--- /dev/null
+++ b/examples/d-augmented-gp/Manifest.toml
@@ -0,0 +1,1272 @@
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+
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+version = "3.5.0+0"
+
+[[deps.xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "0.9.1+5"
diff --git a/examples/d-augmented-gp/Project.toml b/examples/d-augmented-gp/Project.toml
new file mode 100644
index 00000000..a78be1e3
--- /dev/null
+++ b/examples/d-augmented-gp/Project.toml
@@ -0,0 +1,11 @@
+[deps]
+ApproximateGPs = "298c2ebc-0411-48ad-af38-99e88101b606"
+AugmentedGaussianProcesses = "38eea1fd-7d7d-5162-9d08-f89d0f2e271e"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
+Optim = "429524aa-4258-5aef-a3af-852621145aeb"
+ParameterHandling = "2412ca09-6db7-441c-8e3a-88d5709968c5"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
diff --git a/examples/d-augmented-gp/script.jl b/examples/d-augmented-gp/script.jl
new file mode 100644
index 00000000..bbe5afba
--- /dev/null
+++ b/examples/d-augmented-gp/script.jl
@@ -0,0 +1,218 @@
+# # Augmented Sparse Variational Approximation for Non-Conjugate Likelihoods,
+# # a Classification Example
+# 
+#
+# This example demonstrates how to use augmentation to improve convergence speed
+# for variational Gaussian process with non-conjugate likelihoods.
+# inference using the stochastic variational Gaussian process (SVGP) model. For
+# a basic introduction to the functionality of this library, please refer to the
+# [User Guide](@ref).
+#
+# ## Setup
+
+using ApproximateGPs
+using ParameterHandling
+using Zygote
+using Distributions
+using LinearAlgebra
+using Optim
+
+using Plots
+default(; legend=:outertopright, size=(700, 400))
+
+# We import AGP.jl for the Polya-Gamma distribution
+using AugmentedGaussianProcesses.ComplementaryDistributions: PolyaGamma
+
+using Random
+Random.seed!(1234);
+
+# ## Generate some training data
+#
+# We work in the same setting as the other [classification example](../b-classification).
+# For our binary classification model, we will use the standard approach of a
+# latent GP with a Bernoulli likelihood. This results in a generative model that
+# we can use to produce some training data.
+#
+# First, we define the underlying latent GP
+# ```math
+# f \sim \mathcal{GP}(0, k(\cdot, \cdot'))
+# ```
+# and sample a function `f`.
+
+k_true = [30.0, 1.5]
+kernel_true = k_true[1] * (Matern32Kernel() ∘ ScaleTransform(k_true[2]))
+
+jitter = 1e-6  # for numeric stability
+lik = BernoulliLikelihood()
+lgp = LatentGP(GP(kernel_true), lik, jitter)
+x_true = 0:0.02:6
+f_true, y_true = rand(lgp(x_true))
+
+plot(x_true, f_true; seriescolor="red", label="")  # Plot the sampled function
+
+# Then, the output of this sampled function is pushed through a logistic sigmoid
+# `μ = σ(f)` to constrain the output to `[0, 1]`.
+
+μ = mean.(lgp.lik.(f_true))
+plot(x_true, μ; seriescolor="red", label="")
+
+# Finally, the outputs `y` of the process are sampled from a Bernoulli
+# distribution with mean `μ`. We're only interested in the outputs at a subset
+# of inputs `x`, so we first pick some random input locations and then find the
+# corresponding values for `y`.
+
+N = 200  # The number of training points
+mask = sample(1:length(x_true), N; replace=false, ordered=true)  # Subsample some input locations
+x, y = x_true[mask], y_true[mask]
+
+scatter(x, y; label="Sampled outputs")
+plot!(x_true, mean.(lgp.lik.(f_true)); seriescolor="red", label="True mean")
+
+# Let's first see how we can obtain the optimal variational parameters
+# for our variational distribution q(u) = N(m, S).
+# We will for now use the true kernel parameters,
+# We define the inducing points locations and the associated `FiniteGP`
+M = 15;
+z = range(0.1, 5.9; length=M);
+fz = GP(kernel_true)(z, jitter);
+
+# We initialize the variational parameters q(u) = N(m, S) and q(ωᵢ) = p(ωᵢ) = PolyaGamma(1,0)
+m = zeros(M);
+S = Matrix{Float64}(I(M));
+qω = [PolyaGamma(1, 0.0) for _ in 1:length(x)];
+
+# Following the derivations from the paper [Efficient Gaussian Process Classification Using Polya-Gamma Data Augmentation](https://arxiv.org/abs/1802.06383),
+# we build the following `cavi!` function which will update the parameters `m` and `S` as well as the variables `ω`
+
+function cavi!(fz::AbstractGPs.FiniteGP, x, y, m, S, qω; niter=10)
+    K = ApproximateGPs._chol_cov(fz)
+    κ = K \ cov(fz.f, fz.x, x)
+    y_sign = sign.(y .- 0.5)
+    for _ in 1:niter
+        postu = posterior(SparseVariationalApproximation(Centered(), fz, MvNormal(m, S)))
+        postfs = marginals(postu(x))
+        marginals_to_aug_posterior!(qω, postfs)
+        S .= inv(Symmetric(inv(K) + project(Diagonal(mean.(qω)), κ)))
+        m .= S * (project(y_sign / 2, κ) - K \ mean(fz))
+    end
+    return m, S, qω
+end
+
+function marginals_to_aug_posterior!(qω::AbstractVector, ps::AbstractVector{<:Normal})
+    map!(qω, ps) do p
+        PolyaGamma(1, sqrt(abs2(mean(p)) + var(p)))
+    end
+end
+
+# where `project` which project the noise to the right dimension
+project(x::AbstractVector, κ) = κ * x
+project(X::AbstractMatrix, κ) = κ * X * κ'
+
+# Let's now compare both results
+post_svgp_init = posterior(SparseVariationalApproximation(Centered(), fz, MvNormal(m, S)))
+cavi!(fz, x, y, m, S, qω) # m, S and qω are going to be modified
+post_svgp_opt = posterior(SparseVariationalApproximation(Centered(), fz, MvNormal(m, S)))
+
+pf = scatter(x, y; legend=false, xlabel="x", ylabel="f")
+plot!(x_true, f_true; seriescolor="red", label="True latent")
+plot!(x_true, post_svgp_init(x_true); label="Initial Posterior")
+plot!(x_true, post_svgp_opt(x_true); label="Final Posterior")
+py = scatter(x, y; label="Training data", xlabel="x", ylabel="y")
+plot!(x_true, mean.(lik.(f_true)); label="True mean")
+plot!(x_true, mean.(lik.(mean(post_svgp_init(x_true)))); label="Initial Posterior")
+plot!(x_true, mean.(lik.(mean(post_svgp_opt(x_true)))); label="Final Posterior")
+plot(pf, py)
+# ## Optimizing the hyperparameters
+
+# What if like in the [classical optimization case](../b-classification)
+# we want to optimize hyperparameters as well?
+# Let's use the same approach!
+raw_initial_params = (
+    k=(var=positive(rand()), precision=positive(rand())),
+    z=bounded.(range(0.1, 5.9; length=M), 0.0, 6.0),  # constrain z to simplify optimisation
+);
+flat_init_params, unflatten = ParameterHandling.flatten(raw_initial_params)
+unpack = ParameterHandling.value ∘ unflatten;
+
+# We now need to pass our variational parameters and modify the elbo
+# to be able to infer correctly the results.
+# This means we will have to implicitly pass the variational parameters
+# `var_params` and update them after each update of the hyperparameters
+
+# ### The augmented ELBO
+function augmented_elbo(
+    sva::SparseVariationalApproximation,
+    lfx::AbstractGPs.LatentFiniteGP,
+    y::AbstractVector,
+    qω::AbstractVector;
+    num_data=length(y),
+)
+    post = posterior(sva)
+    q_f = marginals(post(lfx.fx.x))
+    variational_exp = expected_aug_loglik(y, q_f, lfx.lik, qω)
+
+    n_batch = length(y)
+    scale = num_data / n_batch
+    # We ignore the KL divergence regarding the augmented variables as it does
+    # not depend on the kernel parameters
+    return sum(variational_exp) * scale - Zygote.@ignore(kl_term(lik, qω)) - ApproximateGPs.kl_term(sva, post)
+end
+
+function kl_term(::BernoulliLikelihood{<:LogisticLink}, qω::AbstractVector{<:PolyaGamma})
+    sum(qω) do q
+        c = q.c
+        - abs2(c) * mean(q) + 2log(cosh(c / 2))
+    end
+end
+
+function expected_aug_loglik(y, q_f, ::BernoulliLikelihood, qω)
+    return map(y, q_f, qω) do y, q, qω
+        m = mean(q)
+        sign(y - 0.5) * m / 2 - (abs2(m) + var(q)) * mean(qω) / 2 - log(2)
+    end
+end
+
+# ### The complete inference process
+function loss(params::NamedTuple)
+    fz, lf = build_fz_lf(params)
+    fx = lf(x)
+    # We ignore this part as it involves inplace operations
+    # and does not contribute to the final elbo
+    Zygote.@ignore cavi!(fz, x, y, m, S, qω; niter=1)
+    augsvgp = SparseVariationalApproximation(Centered(), fz, MvNormal(m, Symmetric(S)))
+    return -augmented_elbo(augsvgp, fx, y, qω)
+end
+
+function build_fz_lf(params::NamedTuple)
+    kernel = params.k.var * (Matern32Kernel() ∘ ScaleTransform(params.k.precision))
+    lf = LatentGP(GP(kernel), lik, jitter)
+    fz = GP(kernel)(params.z)
+    return fz, lf
+end
+
+opt = optimize(
+    loss ∘ unpack,
+    θ -> only(Zygote.gradient(loss ∘ unpack, θ)),
+    flat_init_params,
+    LBFGS(;
+        alphaguess=Optim.LineSearches.InitialStatic(; scaled=true),
+        linesearch=Optim.LineSearches.BackTracking(),
+    ),
+    Optim.Options(; iterations=100);
+    inplace=false,
+)
+
+# And we can now compare with the optimal result we obtained earlier
+θ_opt = unpack(opt.minimizer)
+fz_opt, lf_opt = build_fz_lf(θ_opt)
+post_svgp_hpopt = posterior(SparseVariationalApproximation(Centered(), fz_opt, MvNormal(m, S)))
+
+pf = scatter(x, y; legend=false, xlabel="x", ylabel="f")
+plot!(x_true, f_true; seriescolor="red", label="True latent")
+plot!(x_true, post_svgp_opt(x_true); label="Posterior")
+plot!(x_true, post_svgp_hpopt(x_true); label="Posterior (hp opt)")
+py = scatter(x, y; label="Training data", xlabel="x", ylabel="y")
+plot!(x_true, mean.(lik.(f_true)); label="True mean")
+plot!(x_true, mean.(lik.(mean(post_svgp_opt(x_true)))); label="Posterior")
+plot!(x_true, mean.(lik.(mean(post_svgp_hpopt(x_true)))); label="Posterior (hp opt)")
+plot(pf, py)
\ No newline at end of file

From dcef734c6df06ba01cf8e126aae1929e0fe26bb2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Wed, 1 Dec 2021 18:17:53 +0100
Subject: [PATCH 2/8] Apply suggestions from code review

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
---
 examples/d-augmented-gp/script.jl | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/examples/d-augmented-gp/script.jl b/examples/d-augmented-gp/script.jl
index bbe5afba..0c3ed7ba 100644
--- a/examples/d-augmented-gp/script.jl
+++ b/examples/d-augmented-gp/script.jl
@@ -155,13 +155,14 @@ function augmented_elbo(
     scale = num_data / n_batch
     # We ignore the KL divergence regarding the augmented variables as it does
     # not depend on the kernel parameters
-    return sum(variational_exp) * scale - Zygote.@ignore(kl_term(lik, qω)) - ApproximateGPs.kl_term(sva, post)
+    return sum(variational_exp) * scale - Zygote.@ignore(kl_term(lik, qω)) -
+           ApproximateGPs.kl_term(sva, post)
 end
 
 function kl_term(::BernoulliLikelihood{<:LogisticLink}, qω::AbstractVector{<:PolyaGamma})
     sum(qω) do q
         c = q.c
-        - abs2(c) * mean(q) + 2log(cosh(c / 2))
+        -abs2(c) * mean(q) + 2log(cosh(c / 2))
     end
 end
 
@@ -205,7 +206,9 @@ opt = optimize(
 # And we can now compare with the optimal result we obtained earlier
 θ_opt = unpack(opt.minimizer)
 fz_opt, lf_opt = build_fz_lf(θ_opt)
-post_svgp_hpopt = posterior(SparseVariationalApproximation(Centered(), fz_opt, MvNormal(m, S)))
+post_svgp_hpopt = posterior(
+    SparseVariationalApproximation(Centered(), fz_opt, MvNormal(m, S))
+)
 
 pf = scatter(x, y; legend=false, xlabel="x", ylabel="f")
 plot!(x_true, f_true; seriescolor="red", label="True latent")

From 4cffc9f751358893710f068ebf2e939867578378 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Wed, 1 Dec 2021 18:18:12 +0100
Subject: [PATCH 3/8] Update script.jl

---
 examples/d-augmented-gp/script.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/examples/d-augmented-gp/script.jl b/examples/d-augmented-gp/script.jl
index 0c3ed7ba..94bee3f5 100644
--- a/examples/d-augmented-gp/script.jl
+++ b/examples/d-augmented-gp/script.jl
@@ -218,4 +218,4 @@ py = scatter(x, y; label="Training data", xlabel="x", ylabel="y")
 plot!(x_true, mean.(lik.(f_true)); label="True mean")
 plot!(x_true, mean.(lik.(mean(post_svgp_opt(x_true)))); label="Posterior")
 plot!(x_true, mean.(lik.(mean(post_svgp_hpopt(x_true)))); label="Posterior (hp opt)")
-plot(pf, py)
\ No newline at end of file
+plot(pf, py)

From 30b933ec54dd52d2d995f45fbd4b52e41b893c6d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Wed, 1 Dec 2021 18:35:52 +0100
Subject: [PATCH 4/8] Use latest julia version for docs

---
 .github/workflows/Docs.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/Docs.yml b/.github/workflows/Docs.yml
index 009fcdef..a032455f 100644
--- a/.github/workflows/Docs.yml
+++ b/.github/workflows/Docs.yml
@@ -14,7 +14,7 @@ jobs:
       - uses: actions/checkout@v2
       - uses: julia-actions/setup-julia@latest
         with:
-          version: '1.6'
+          version: '1.7'
       - name: Install dependencies
         run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
       - name: Build and deploy

From f23aa66152a580431858947168c1b2498fc1b1c5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Wed, 1 Dec 2021 18:49:09 +0100
Subject: [PATCH 5/8] Moved comments out

---
 examples/d-augmented-gp/script.jl | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/examples/d-augmented-gp/script.jl b/examples/d-augmented-gp/script.jl
index 94bee3f5..8aae3c37 100644
--- a/examples/d-augmented-gp/script.jl
+++ b/examples/d-augmented-gp/script.jl
@@ -153,11 +153,12 @@ function augmented_elbo(
 
     n_batch = length(y)
     scale = num_data / n_batch
-    # We ignore the KL divergence regarding the augmented variables as it does
-    # not depend on the kernel parameters
+
     return sum(variational_exp) * scale - Zygote.@ignore(kl_term(lik, qω)) -
            ApproximateGPs.kl_term(sva, post)
 end
+# We ignored the gradient of the KL divergence with respect to the augmented
+# variables as it does not depend on the kernel parameters
 
 function kl_term(::BernoulliLikelihood{<:LogisticLink}, qω::AbstractVector{<:PolyaGamma})
     sum(qω) do q
@@ -177,13 +178,14 @@ end
 function loss(params::NamedTuple)
     fz, lf = build_fz_lf(params)
     fx = lf(x)
-    # We ignore this part as it involves inplace operations
-    # and does not contribute to the final elbo
     Zygote.@ignore cavi!(fz, x, y, m, S, qω; niter=1)
     augsvgp = SparseVariationalApproximation(Centered(), fz, MvNormal(m, Symmetric(S)))
     return -augmented_elbo(augsvgp, fx, y, qω)
 end
 
+# We ignore the `cavi!` part as it involves inplace operations
+# and does not contribute to the final elbo
+
 function build_fz_lf(params::NamedTuple)
     kernel = params.k.var * (Matern32Kernel() ∘ ScaleTransform(params.k.precision))
     lf = LatentGP(GP(kernel), lik, jitter)

From d10de1366d60eb1f5a016e55dc675afbba72aa3b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Wed, 1 Dec 2021 19:18:34 +0100
Subject: [PATCH 6/8] Ugly hack to avoid a call to blas?

---
 examples/b-classification/Manifest.toml | 537 ++++++++++++------------
 src/expected_loglik.jl                  |   2 +-
 2 files changed, 281 insertions(+), 258 deletions(-)

diff --git a/examples/b-classification/Manifest.toml b/examples/b-classification/Manifest.toml
index a8b06699..7cb8e9b6 100644
--- a/examples/b-classification/Manifest.toml
+++ b/examples/b-classification/Manifest.toml
@@ -1,1094 +1,1117 @@
 # This file is machine-generated - editing it directly is not advised
 
-[[AbstractFFTs]]
+julia_version = "1.7.0"
+manifest_format = "2.0"
+
+[[deps.AbstractFFTs]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
 uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
 version = "1.0.1"
 
-[[AbstractGPs]]
+[[deps.AbstractGPs]]
 deps = ["ChainRulesCore", "Distributions", "FillArrays", "IrrationalConstants", "KernelFunctions", "LinearAlgebra", "Random", "RecipesBase", "Reexport", "Statistics", "StatsBase", "Test"]
-git-tree-sha1 = "e2af18922f65ea8cee7b8cd97a1668691f76f4b2"
+git-tree-sha1 = "821d37c2f571ed5f2dfa028f03e324abd12f9910"
 uuid = "99985d1d-32ba-4be9-9821-2ec096f28918"
-version = "0.5.3"
+version = "0.5.4"
 
-[[Adapt]]
+[[deps.Adapt]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 version = "3.3.1"
 
-[[ApproximateGPs]]
+[[deps.ApproximateGPs]]
 deps = ["AbstractGPs", "ChainRulesCore", "Distributions", "FastGaussQuadrature", "FillArrays", "ForwardDiff", "GPLikelihoods", "KLDivergences", "LinearAlgebra", "Reexport", "SpecialFunctions", "Statistics", "StatsBase"]
-path = "../.."
+git-tree-sha1 = "d3ee4cb601c3a519706c7e32abded2c77312ce76"
 uuid = "298c2ebc-0411-48ad-af38-99e88101b606"
-version = "0.2.0"
+version = "0.2.3"
 
-[[ArgTools]]
+[[deps.ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 
-[[ArrayInterface]]
+[[deps.ArrayInterface]]
 deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
-git-tree-sha1 = "e527b258413e0c6d4f66ade574744c94edef81f8"
+git-tree-sha1 = "265b06e2b1f6a216e0e8f183d28e4d354eab3220"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "3.1.40"
+version = "3.2.1"
 
-[[Artifacts]]
+[[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 
-[[Base64]]
+[[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
-[[Bzip2_jll]]
+[[deps.Bzip2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
 uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
 version = "1.0.8+0"
 
-[[Cairo_jll]]
+[[deps.Cairo_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
 git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
 uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
 version = "1.16.1+0"
 
-[[ChainRules]]
+[[deps.ChainRules]]
 deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "RealDot", "Statistics"]
-git-tree-sha1 = "035ef8a5382a614b2d8e3091b6fdbb1c2b050e11"
+git-tree-sha1 = "65a0826ac25869556070076459925d1700316aab"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.12.1"
+version = "1.14.0"
 
-[[ChainRulesCore]]
+[[deps.ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
 git-tree-sha1 = "f885e7e7c124f8c92650d61b9477b9ac2ee607dd"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 version = "1.11.1"
 
-[[ColorSchemes]]
+[[deps.ChangesOfVariables]]
+deps = ["LinearAlgebra", "Test"]
+git-tree-sha1 = "9a1d594397670492219635b35a3d830b04730d62"
+uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+version = "0.1.1"
+
+[[deps.ColorSchemes]]
 deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
 git-tree-sha1 = "a851fec56cb73cfdf43762999ec72eff5b86882a"
 uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
 version = "3.15.0"
 
-[[ColorTypes]]
+[[deps.ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
 git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
 uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
 version = "0.11.0"
 
-[[Colors]]
+[[deps.Colors]]
 deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
 git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
 uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
 version = "0.12.8"
 
-[[CommonSubexpressions]]
+[[deps.CommonSubexpressions]]
 deps = ["MacroTools", "Test"]
 git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
 uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
 version = "0.3.0"
 
-[[Compat]]
+[[deps.Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
 git-tree-sha1 = "dce3e3fea680869eaa0b774b2e8343e9ff442313"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
 version = "3.40.0"
 
-[[CompilerSupportLibraries_jll]]
+[[deps.CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 
-[[CompositionsBase]]
+[[deps.CompositionsBase]]
 git-tree-sha1 = "455419f7e328a1a2493cabc6428d79e951349769"
 uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
 version = "0.1.1"
 
-[[Contour]]
+[[deps.Contour]]
 deps = ["StaticArrays"]
 git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
 uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
 version = "0.5.7"
 
-[[DataAPI]]
+[[deps.DataAPI]]
 git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
 uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
 version = "1.9.0"
 
-[[DataStructures]]
+[[deps.DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
 git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 version = "0.18.10"
 
-[[DataValueInterfaces]]
+[[deps.DataValueInterfaces]]
 git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
 uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
 version = "1.0.0"
 
-[[Dates]]
+[[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
-[[DelimitedFiles]]
+[[deps.DelimitedFiles]]
 deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
-[[DiffResults]]
+[[deps.DensityInterface]]
+deps = ["InverseFunctions", "Test"]
+git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
+uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+version = "0.4.0"
+
+[[deps.DiffResults]]
 deps = ["StaticArrays"]
 git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805"
 uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
 version = "1.0.3"
 
-[[DiffRules]]
+[[deps.DiffRules]]
 deps = ["LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
-git-tree-sha1 = "3287dacf67c3652d3fed09f4c12c187ae4dbb89a"
+git-tree-sha1 = "d8f468c5cd4d94e86816603f7d18ece910b4aaf1"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "1.4.0"
+version = "1.5.0"
 
-[[Distances]]
+[[deps.Distances]]
 deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
 git-tree-sha1 = "837c83e5574582e07662bbbba733964ff7c26b9d"
 uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
 version = "0.10.6"
 
-[[Distributed]]
+[[deps.Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
-[[Distributions]]
-deps = ["ChainRulesCore", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
-git-tree-sha1 = "72dcda9e19f88d09bf21b5f9507a0bb430bce2aa"
+[[deps.Distributions]]
+deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
+git-tree-sha1 = "7f3bec11f4bcd01bc1f507ebce5eadf1b0a78f47"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.25.24"
+version = "0.25.34"
 
-[[DocStringExtensions]]
+[[deps.DocStringExtensions]]
 deps = ["LibGit2"]
 git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b"
 uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 version = "0.8.6"
 
-[[Downloads]]
+[[deps.Downloads]]
 deps = ["ArgTools", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 
-[[EarCut_jll]]
+[[deps.EarCut_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
 uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
 version = "2.2.3+0"
 
-[[Expat_jll]]
+[[deps.Expat_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
 uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
 version = "2.2.10+0"
 
-[[FFMPEG]]
+[[deps.FFMPEG]]
 deps = ["FFMPEG_jll"]
 git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
 uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
 version = "0.4.1"
 
-[[FFMPEG_jll]]
+[[deps.FFMPEG_jll]]
 deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
 git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
 uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
 version = "4.4.0+0"
 
-[[FastGaussQuadrature]]
+[[deps.FastGaussQuadrature]]
 deps = ["LinearAlgebra", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "5829b25887e53fb6730a9df2ff89ed24baa6abf6"
+git-tree-sha1 = "58d83dd5a78a36205bdfddb82b1bb67682e64487"
 uuid = "442a2c76-b920-505d-bb47-c5924d526838"
-version = "0.4.7"
+version = "0.4.9"
 
-[[FillArrays]]
+[[deps.FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
 git-tree-sha1 = "8756f9935b7ccc9064c6eef0bff0ad643df733a3"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
 version = "0.12.7"
 
-[[FiniteDiff]]
+[[deps.FiniteDiff]]
 deps = ["ArrayInterface", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
 git-tree-sha1 = "8b3c09b56acaf3c0e581c66638b85c8650ee9dca"
 uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
 version = "2.8.1"
 
-[[FixedPointNumbers]]
+[[deps.FixedPointNumbers]]
 deps = ["Statistics"]
 git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
 uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
 version = "0.8.4"
 
-[[Fontconfig_jll]]
+[[deps.Fontconfig_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
 git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
 uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
 version = "2.13.93+0"
 
-[[Formatting]]
+[[deps.Formatting]]
 deps = ["Printf"]
 git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
 uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
 version = "0.4.2"
 
-[[ForwardDiff]]
-deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "ef3fec65f9db26fa2cf8f4133c697c5b7ce63c1d"
+[[deps.ForwardDiff]]
+deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
+git-tree-sha1 = "6406b5112809c08b1baa5703ad274e1dded0652f"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.22"
+version = "0.10.23"
 
-[[FreeType2_jll]]
+[[deps.FreeType2_jll]]
 deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
 git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
 uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
 version = "2.10.4+0"
 
-[[FriBidi_jll]]
+[[deps.FriBidi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
 uuid = "559328eb-81f9-559d-9380-de523a88c83c"
 version = "1.0.10+0"
 
-[[Functors]]
+[[deps.Functors]]
 git-tree-sha1 = "e4768c3b7f597d5a352afa09874d16e3c3f6ead2"
 uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
 version = "0.2.7"
 
-[[GLFW_jll]]
+[[deps.GLFW_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
 git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
 uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
 version = "3.3.5+1"
 
-[[GPLikelihoods]]
-deps = ["Distributions", "Functors", "LinearAlgebra", "Random", "StatsFuns"]
-git-tree-sha1 = "bdfe8a65b3ca3aa92812d74138264570f33aa66e"
+[[deps.GPLikelihoods]]
+deps = ["Distributions", "Functors", "InverseFunctions", "LinearAlgebra", "Random", "StatsFuns"]
+git-tree-sha1 = "561e03fc0dc1d38560dc1403ad95b308418f0ed6"
 uuid = "6031954c-0455-49d7-b3b9-3e1c99afaf40"
-version = "0.2.4"
+version = "0.2.5"
 
-[[GR]]
+[[deps.GR]]
 deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
 git-tree-sha1 = "30f2b340c2fff8410d89bfcdc9c0a6dd661ac5f7"
 uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
 version = "0.62.1"
 
-[[GR_jll]]
+[[deps.GR_jll]]
 deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
 git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
 uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
 version = "0.62.0+0"
 
-[[GeometryBasics]]
+[[deps.GeometryBasics]]
 deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
 git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
 uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
 version = "0.4.1"
 
-[[Gettext_jll]]
+[[deps.Gettext_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
 git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
 uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
 version = "0.21.0+0"
 
-[[Glib_jll]]
+[[deps.Glib_jll]]
 deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
 git-tree-sha1 = "7bf67e9a481712b3dbe9cb3dac852dc4b1162e02"
 uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
 version = "2.68.3+0"
 
-[[Graphite2_jll]]
+[[deps.Graphite2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
 uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
 version = "1.3.14+0"
 
-[[Grisu]]
+[[deps.Grisu]]
 git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
 uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
 version = "1.0.2"
 
-[[HTTP]]
+[[deps.HTTP]]
 deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
-git-tree-sha1 = "14eece7a3308b4d8be910e265c724a6ba51a9798"
+git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
 uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
-version = "0.9.16"
+version = "0.9.17"
 
-[[HarfBuzz_jll]]
+[[deps.HarfBuzz_jll]]
 deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
-git-tree-sha1 = "8a954fed8ac097d5be04921d595f741115c1b2ad"
+git-tree-sha1 = "129acf094d168394e80ee1dc4bc06ec835e510a3"
 uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
-version = "2.8.1+0"
+version = "2.8.1+1"
 
-[[IOCapture]]
+[[deps.IOCapture]]
 deps = ["Logging", "Random"]
 git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
 uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
 version = "0.2.2"
 
-[[IRTools]]
+[[deps.IRTools]]
 deps = ["InteractiveUtils", "MacroTools", "Test"]
-git-tree-sha1 = "95215cd0076a150ef46ff7928892bc341864c73c"
+git-tree-sha1 = "006127162a51f0effbdfaab5ac0c83f8eb7ea8f3"
 uuid = "7869d1d1-7146-5819-86e3-90919afe41df"
-version = "0.4.3"
+version = "0.4.4"
 
-[[IfElse]]
+[[deps.IfElse]]
 git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
 uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
 version = "0.1.1"
 
-[[IniFile]]
+[[deps.IniFile]]
 deps = ["Test"]
 git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
 uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
 version = "0.5.0"
 
-[[InteractiveUtils]]
+[[deps.InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
-[[InverseFunctions]]
+[[deps.InverseFunctions]]
 deps = ["Test"]
-git-tree-sha1 = "f0c6489b12d28fb4c2103073ec7452f3423bd308"
+git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
 uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
-version = "0.1.1"
+version = "0.1.2"
 
-[[IrrationalConstants]]
+[[deps.IrrationalConstants]]
 git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
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-[[IterTools]]
+[[deps.IterTools]]
 git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
 uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
 version = "1.3.0"
 
-[[IteratorInterfaceExtensions]]
+[[deps.IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
 uuid = "82899510-4779-5014-852e-03e436cf321d"
 version = "1.0.0"
 
-[[JLLWrappers]]
+[[deps.JLLWrappers]]
 deps = ["Preferences"]
 git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
 version = "1.3.0"
 
-[[JSON]]
+[[deps.JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
 git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
 uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 version = "0.21.2"
 
-[[JpegTurbo_jll]]
+[[deps.JpegTurbo_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
 uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
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-[[KLDivergences]]
+[[deps.KLDivergences]]
 deps = ["ChainRulesCore", "Distances", "Distributions", "LinearAlgebra", "PDMats", "SpecialFunctions", "StatsBase"]
 git-tree-sha1 = "b4663db8fb56053b1d1a2af80533b645eba9583a"
 uuid = "3c9cd921-3d3f-41e2-830c-e020174918cc"
 version = "0.2.1"
 
-[[KernelFunctions]]
+[[deps.KernelFunctions]]
 deps = ["ChainRulesCore", "Compat", "CompositionsBase", "Distances", "FillArrays", "Functors", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "Random", "Requires", "SpecialFunctions", "StatsBase", "TensorCore", "Test", "ZygoteRules"]
 git-tree-sha1 = "9c3d38dafc02feae68a4747813b8b0205fd03da5"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
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-[[LAME_jll]]
+[[deps.LAME_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
 uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
 version = "3.100.1+0"
 
-[[LZO_jll]]
+[[deps.LZO_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
 uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
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-[[LaTeXStrings]]
+[[deps.LaTeXStrings]]
 git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
 uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 version = "1.3.0"
 
-[[Latexify]]
+[[deps.Latexify]]
 deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
 git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
 uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
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-[[LibCURL]]
+[[deps.LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
 uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
 
-[[LibCURL_jll]]
+[[deps.LibCURL_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
 uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
 
-[[LibGit2]]
+[[deps.LibGit2]]
 deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
 
-[[LibSSH2_jll]]
+[[deps.LibSSH2_jll]]
 deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
 uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
 
-[[Libdl]]
+[[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
-[[Libffi_jll]]
+[[deps.Libffi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
-git-tree-sha1 = "761a393aeccd6aa92ec3515e428c26bf99575b3b"
+git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
 uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
-version = "3.2.2+0"
+version = "3.2.2+1"
 
-[[Libgcrypt_jll]]
+[[deps.Libgcrypt_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
 git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
 uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
 version = "1.8.7+0"
 
-[[Libglvnd_jll]]
+[[deps.Libglvnd_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
 git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
 uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
 version = "1.3.0+3"
 
-[[Libgpg_error_jll]]
+[[deps.Libgpg_error_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
 uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
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-[[Libiconv_jll]]
+[[deps.Libiconv_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
 uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
 version = "1.16.1+1"
 
-[[Libmount_jll]]
+[[deps.Libmount_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
 uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
 version = "2.35.0+0"
 
-[[Libtiff_jll]]
+[[deps.Libtiff_jll]]
 deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
 git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
 uuid = "89763e89-9b03-5906-acba-b20f662cd828"
 version = "4.3.0+0"
 
-[[Libuuid_jll]]
+[[deps.Libuuid_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
 uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
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-[[LineSearches]]
+[[deps.LineSearches]]
 deps = ["LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "Printf"]
 git-tree-sha1 = "f27132e551e959b3667d8c93eae90973225032dd"
 uuid = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 version = "7.1.1"
 
-[[LinearAlgebra]]
-deps = ["Libdl"]
+[[deps.LinearAlgebra]]
+deps = ["Libdl", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
-[[Literate]]
+[[deps.Literate]]
 deps = ["Base64", "IOCapture", "JSON", "REPL"]
 git-tree-sha1 = "d3493acfb9e6aa0cff46b09773fc2342327b0feb"
 uuid = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
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-[[LogExpFunctions]]
-deps = ["ChainRulesCore", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
-git-tree-sha1 = "6193c3815f13ba1b78a51ce391db8be016ae9214"
+[[deps.LogExpFunctions]]
+deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "be9eef9f9d78cecb6f262f3c10da151a6c5ab827"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.3.4"
+version = "0.3.5"
 
-[[Logging]]
+[[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
-[[MacroTools]]
+[[deps.MacroTools]]
 deps = ["Markdown", "Random"]
 git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 version = "0.5.9"
 
-[[Markdown]]
+[[deps.Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
-[[MbedTLS]]
+[[deps.MbedTLS]]
 deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
 git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
 uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
 version = "1.0.3"
 
-[[MbedTLS_jll]]
+[[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 
-[[Measures]]
+[[deps.Measures]]
 git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
 uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
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-[[Missings]]
+[[deps.Missings]]
 deps = ["DataAPI"]
 git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
 uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
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-[[Mmap]]
+[[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
-[[MozillaCACerts_jll]]
+[[deps.MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 
-[[NLSolversBase]]
+[[deps.NLSolversBase]]
 deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
 git-tree-sha1 = "50310f934e55e5ca3912fb941dec199b49ca9b68"
 uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
 version = "7.8.2"
 
-[[NaNMath]]
+[[deps.NaNMath]]
 git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
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-[[NetworkOptions]]
+[[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 
-[[Ogg_jll]]
+[[deps.Ogg_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
 uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
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-[[OpenLibm_jll]]
+[[deps.OpenBLAS_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
+uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
+
+[[deps.OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 
-[[OpenSSL_jll]]
+[[deps.OpenSSL_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
 uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
 version = "1.1.10+0"
 
-[[OpenSpecFun_jll]]
+[[deps.OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
 uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
 version = "0.5.5+0"
 
-[[Optim]]
+[[deps.Optim]]
 deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
 git-tree-sha1 = "35d435b512fbab1d1a29138b5229279925eba369"
 uuid = "429524aa-4258-5aef-a3af-852621145aeb"
 version = "1.5.0"
 
-[[Opus_jll]]
+[[deps.Opus_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
 uuid = "91d4177d-7536-5919-b921-800302f37372"
 version = "1.3.2+0"
 
-[[OrderedCollections]]
+[[deps.OrderedCollections]]
 git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.4.1"
 
-[[PCRE_jll]]
+[[deps.PCRE_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
 uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
 version = "8.44.0+0"
 
-[[PDMats]]
+[[deps.PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
-git-tree-sha1 = "c8b8775b2f242c80ea85c83714c64ecfa3c53355"
+git-tree-sha1 = "ee26b350276c51697c9c2d88a072b339f9f03d73"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.3"
+version = "0.11.5"
 
-[[ParameterHandling]]
+[[deps.ParameterHandling]]
 deps = ["ChainRulesCore", "Compat", "InverseFunctions", "IterTools", "LinearAlgebra", "LogExpFunctions", "SparseArrays", "Test"]
-git-tree-sha1 = "603fde842910e6d33bfce2ce7d0e0a0851d8e21e"
+git-tree-sha1 = "1e38f118bf4c0428b64f39a0722446f17e95f82a"
 uuid = "2412ca09-6db7-441c-8e3a-88d5709968c5"
-version = "0.4.0"
+version = "0.4.2"
 
-[[Parameters]]
+[[deps.Parameters]]
 deps = ["OrderedCollections", "UnPack"]
 git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
 uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
 version = "0.12.3"
 
-[[Parsers]]
+[[deps.Parsers]]
 deps = ["Dates"]
 git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
 uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
 version = "2.1.2"
 
-[[Pixman_jll]]
+[[deps.Pixman_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
 uuid = "30392449-352a-5448-841d-b1acce4e97dc"
 version = "0.40.1+0"
 
-[[Pkg]]
+[[deps.Pkg]]
 deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
-[[PlotThemes]]
+[[deps.PlotThemes]]
 deps = ["PlotUtils", "Requires", "Statistics"]
 git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
 uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
 version = "2.0.1"
 
-[[PlotUtils]]
+[[deps.PlotUtils]]
 deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
 git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
 uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
 version = "1.0.15"
 
-[[Plots]]
+[[deps.Plots]]
 deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
-git-tree-sha1 = "7dc03c2b145168f5854085a16d054429d612b637"
+git-tree-sha1 = "9c52b09e45f9926a8e50fb7d63f25066431c2e02"
 uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-version = "1.23.5"
+version = "1.24.4"
 
-[[PositiveFactorizations]]
+[[deps.PositiveFactorizations]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "17275485f373e6673f7e7f97051f703ed5b15b20"
 uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
 version = "0.2.4"
 
-[[Preferences]]
+[[deps.Preferences]]
 deps = ["TOML"]
 git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
 version = "1.2.2"
 
-[[Printf]]
+[[deps.Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
-[[Qt5Base_jll]]
+[[deps.Qt5Base_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
 git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
 uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
 version = "5.15.3+0"
 
-[[QuadGK]]
+[[deps.QuadGK]]
 deps = ["DataStructures", "LinearAlgebra"]
 git-tree-sha1 = "78aadffb3efd2155af139781b8a8df1ef279ea39"
 uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 version = "2.4.2"
 
-[[REPL]]
+[[deps.REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 
-[[Random]]
-deps = ["Serialization"]
+[[deps.Random]]
+deps = ["SHA", "Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
-[[RealDot]]
+[[deps.RealDot]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9"
 uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
 version = "0.1.0"
 
-[[RecipesBase]]
-git-tree-sha1 = "44a75aa7a527910ee3d1751d1f0e4148698add9e"
+[[deps.RecipesBase]]
+git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "1.1.2"
+version = "1.2.1"
 
-[[RecipesPipeline]]
+[[deps.RecipesPipeline]]
 deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
 git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
 uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
 version = "0.4.1"
 
-[[Reexport]]
+[[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
 version = "1.2.2"
 
-[[Requires]]
+[[deps.Requires]]
 deps = ["UUIDs"]
 git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
 version = "1.1.3"
 
-[[Rmath]]
+[[deps.Rmath]]
 deps = ["Random", "Rmath_jll"]
 git-tree-sha1 = "bf3188feca147ce108c76ad82c2792c57abe7b1f"
 uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
 version = "0.7.0"
 
-[[Rmath_jll]]
+[[deps.Rmath_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "68db32dff12bb6127bac73c209881191bf0efbb7"
 uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
 version = "0.3.0+0"
 
-[[SHA]]
+[[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 
-[[Scratch]]
+[[deps.Scratch]]
 deps = ["Dates"]
 git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
 uuid = "6c6a2e73-6563-6170-7368-637461726353"
 version = "1.1.0"
 
-[[Serialization]]
+[[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
-[[SharedArrays]]
+[[deps.SharedArrays]]
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
-[[Showoff]]
+[[deps.Showoff]]
 deps = ["Dates", "Grisu"]
 git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
 uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
 version = "1.0.3"
 
-[[Sockets]]
+[[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
-[[SortingAlgorithms]]
+[[deps.SortingAlgorithms]]
 deps = ["DataStructures"]
 git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
 uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
 version = "1.0.1"
 
-[[SparseArrays]]
+[[deps.SparseArrays]]
 deps = ["LinearAlgebra", "Random"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
-[[SpecialFunctions]]
+[[deps.SpecialFunctions]]
 deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
 git-tree-sha1 = "f0bccf98e16759818ffc5d97ac3ebf87eb950150"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
 version = "1.8.1"
 
-[[Static]]
+[[deps.Static]]
 deps = ["IfElse"]
 git-tree-sha1 = "e7bc80dc93f50857a5d1e3c8121495852f407e6a"
 uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
 version = "0.4.0"
 
-[[StaticArrays]]
+[[deps.StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
 git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
 version = "1.2.13"
 
-[[Statistics]]
+[[deps.Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
-[[StatsAPI]]
-git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+[[deps.StatsAPI]]
+git-tree-sha1 = "0f2aa8e32d511f758a2ce49208181f7733a0936a"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
-version = "1.0.0"
+version = "1.1.0"
 
-[[StatsBase]]
+[[deps.StatsBase]]
 deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
-git-tree-sha1 = "eb35dcc66558b2dda84079b9a1be17557d32091a"
+git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.33.12"
+version = "0.33.13"
 
-[[StatsFuns]]
-deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
-git-tree-sha1 = "95072ef1a22b057b1e80f73c2a89ad238ae4cfff"
+[[deps.StatsFuns]]
+deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "bedb3e17cc1d94ce0e6e66d3afa47157978ba404"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.12"
+version = "0.9.14"
 
-[[StructArrays]]
+[[deps.StructArrays]]
 deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
 git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
 uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
 version = "0.6.3"
 
-[[SuiteSparse]]
+[[deps.SuiteSparse]]
 deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
 uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
 
-[[TOML]]
+[[deps.TOML]]
 deps = ["Dates"]
 uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 
-[[TableTraits]]
+[[deps.TableTraits]]
 deps = ["IteratorInterfaceExtensions"]
 git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
 uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
 version = "1.0.1"
 
-[[Tables]]
+[[deps.Tables]]
 deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
 git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
 uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
 version = "1.6.0"
 
-[[Tar]]
+[[deps.Tar]]
 deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 
-[[TensorCore]]
+[[deps.TensorCore]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
 uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
 version = "0.1.1"
 
-[[Test]]
+[[deps.Test]]
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
-[[URIs]]
+[[deps.URIs]]
 git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
 uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
 version = "1.3.0"
 
-[[UUIDs]]
+[[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
-[[UnPack]]
+[[deps.UnPack]]
 git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
 uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 version = "1.0.2"
 
-[[Unicode]]
+[[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
-[[UnicodeFun]]
+[[deps.UnicodeFun]]
 deps = ["REPL"]
 git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
 uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
 version = "0.4.1"
 
-[[Wayland_jll]]
+[[deps.Wayland_jll]]
 deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
 git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
 uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
 version = "1.19.0+0"
 
-[[Wayland_protocols_jll]]
-deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll"]
-git-tree-sha1 = "2839f1c1296940218e35df0bbb220f2a79686670"
+[[deps.Wayland_protocols_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
 uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
-version = "1.18.0+4"
+version = "1.23.0+0"
 
-[[XML2_jll]]
+[[deps.XML2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
 git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
 uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
 version = "2.9.12+0"
 
-[[XSLT_jll]]
+[[deps.XSLT_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
 git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
 uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
 version = "1.1.34+0"
 
-[[Xorg_libX11_jll]]
+[[deps.Xorg_libX11_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
 git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
 uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
 version = "1.6.9+4"
 
-[[Xorg_libXau_jll]]
+[[deps.Xorg_libXau_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
 uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
 version = "1.0.9+4"
 
-[[Xorg_libXcursor_jll]]
+[[deps.Xorg_libXcursor_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
 git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
 uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
 version = "1.2.0+4"
 
-[[Xorg_libXdmcp_jll]]
+[[deps.Xorg_libXdmcp_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
 uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
 version = "1.1.3+4"
 
-[[Xorg_libXext_jll]]
+[[deps.Xorg_libXext_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
 git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
 uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
 version = "1.3.4+4"
 
-[[Xorg_libXfixes_jll]]
+[[deps.Xorg_libXfixes_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
 git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
 uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
 version = "5.0.3+4"
 
-[[Xorg_libXi_jll]]
+[[deps.Xorg_libXi_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
 git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
 uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
 version = "1.7.10+4"
 
-[[Xorg_libXinerama_jll]]
+[[deps.Xorg_libXinerama_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
 git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
 uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
 version = "1.1.4+4"
 
-[[Xorg_libXrandr_jll]]
+[[deps.Xorg_libXrandr_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
 git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
 uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
 version = "1.5.2+4"
 
-[[Xorg_libXrender_jll]]
+[[deps.Xorg_libXrender_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
 git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
 uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
 version = "0.9.10+4"
 
-[[Xorg_libpthread_stubs_jll]]
+[[deps.Xorg_libpthread_stubs_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
 uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
 version = "0.1.0+3"
 
-[[Xorg_libxcb_jll]]
+[[deps.Xorg_libxcb_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
 git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
 uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
 version = "1.13.0+3"
 
-[[Xorg_libxkbfile_jll]]
+[[deps.Xorg_libxkbfile_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
 git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
 uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
 version = "1.1.0+4"
 
-[[Xorg_xcb_util_image_jll]]
+[[deps.Xorg_xcb_util_image_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
 git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
 uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
 version = "0.4.0+1"
 
-[[Xorg_xcb_util_jll]]
+[[deps.Xorg_xcb_util_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
 git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
 uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
 version = "0.4.0+1"
 
-[[Xorg_xcb_util_keysyms_jll]]
+[[deps.Xorg_xcb_util_keysyms_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
 git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
 uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
 version = "0.4.0+1"
 
-[[Xorg_xcb_util_renderutil_jll]]
+[[deps.Xorg_xcb_util_renderutil_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
 git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
 uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
 version = "0.3.9+1"
 
-[[Xorg_xcb_util_wm_jll]]
+[[deps.Xorg_xcb_util_wm_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
 git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
 uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
 version = "0.4.1+1"
 
-[[Xorg_xkbcomp_jll]]
+[[deps.Xorg_xkbcomp_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
 git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
 uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
 version = "1.4.2+4"
 
-[[Xorg_xkeyboard_config_jll]]
+[[deps.Xorg_xkeyboard_config_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
 git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
 uuid = "33bec58e-1273-512f-9401-5d533626f822"
 version = "2.27.0+4"
 
-[[Xorg_xtrans_jll]]
+[[deps.Xorg_xtrans_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
 uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
 version = "1.4.0+3"
 
-[[Zlib_jll]]
+[[deps.Zlib_jll]]
 deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 
-[[Zstd_jll]]
+[[deps.Zstd_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
 uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
 version = "1.5.0+0"
 
-[[Zygote]]
+[[deps.Zygote]]
 deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "0fc9959bcabc4668c403810b4e851f6b8962eac9"
+git-tree-sha1 = "76475a5aa0be302c689fd319cd257cd1a512fb3c"
 uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
-version = "0.6.29"
+version = "0.6.32"
 
-[[ZygoteRules]]
+[[deps.ZygoteRules]]
 deps = ["MacroTools"]
 git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
 uuid = "700de1a5-db45-46bc-99cf-38207098b444"
 version = "0.2.2"
 
-[[libass_jll]]
+[[deps.libass_jll]]
 deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
 git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
 uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
 version = "0.15.1+0"
 
-[[libfdk_aac_jll]]
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+
+[[deps.libfdk_aac_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
 uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
 version = "2.0.2+0"
 
-[[libpng_jll]]
+[[deps.libpng_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
 git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
 uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
 version = "1.6.38+0"
 
-[[libvorbis_jll]]
+[[deps.libvorbis_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
 git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
 uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
 version = "1.3.7+0"
 
-[[nghttp2_jll]]
+[[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
 
-[[p7zip_jll]]
+[[deps.p7zip_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
 
-[[x264_jll]]
+[[deps.x264_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
 uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
 version = "2021.5.5+0"
 
-[[x265_jll]]
+[[deps.x265_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
 uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
 version = "3.5.0+0"
 
-[[xkbcommon_jll]]
+[[deps.xkbcommon_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
 git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
 uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
diff --git a/src/expected_loglik.jl b/src/expected_loglik.jl
index c29ff3bb..f78eaa91 100644
--- a/src/expected_loglik.jl
+++ b/src/expected_loglik.jl
@@ -75,7 +75,7 @@ function expected_loglik(
     # size(fs): (length(y), n_points)
     fs = √2 * std.(q_f) .* xs' .+ mean.(q_f)
     lls = loglikelihood.(lik.(fs), y)
-    return sum((1 / √π) * lls * ws)
+    return (1 / √π) * mapreduce(dot, +, eachrow(lls), ws)
 end
 
 ChainRulesCore.@non_differentiable gausshermite(n)

From 05349eb50ac06af20e90ca4a73c7b3d2f65ac24e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Wed, 8 Dec 2021 14:20:30 +0100
Subject: [PATCH 7/8] Switch back to original definition

---
 src/expected_loglik.jl | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/src/expected_loglik.jl b/src/expected_loglik.jl
index f78eaa91..dd96108d 100644
--- a/src/expected_loglik.jl
+++ b/src/expected_loglik.jl
@@ -72,10 +72,9 @@ function expected_loglik(
     # using a reparameterisation by change of variable
     # (see e.g. en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature)
     xs, ws = gausshermite(gh.n_points)
-    # size(fs): (length(y), n_points)
-    fs = √2 * std.(q_f) .* xs' .+ mean.(q_f)
+    fs = sqrt(2) * std.(q_f) .* xs' .+ mean.(q_f)
     lls = loglikelihood.(lik.(fs), y)
-    return (1 / √π) * mapreduce(dot, +, eachrow(lls), ws)
+    return sum(lls * ws) / sqrt(π)
 end
 
 ChainRulesCore.@non_differentiable gausshermite(n)

From b19e62d83807c6d68d3e62a46e47742abc14c04e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9o=20Galy-Fajou?= <theo.galyfajou@gmail.com>
Date: Wed, 8 Dec 2021 14:59:19 +0100
Subject: [PATCH 8/8] Updated Manifest

---
 examples/b-classification/Manifest.toml | 26 ++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/examples/b-classification/Manifest.toml b/examples/b-classification/Manifest.toml
index 7cb8e9b6..93de88a1 100644
--- a/examples/b-classification/Manifest.toml
+++ b/examples/b-classification/Manifest.toml
@@ -56,15 +56,15 @@ version = "1.16.1+0"
 
 [[deps.ChainRules]]
 deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "RealDot", "Statistics"]
-git-tree-sha1 = "65a0826ac25869556070076459925d1700316aab"
+git-tree-sha1 = "d9d08f88759465c7895db73d052c23e5c260f4a2"
 uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
-version = "1.14.0"
+version = "1.15.0"
 
 [[deps.ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "f885e7e7c124f8c92650d61b9477b9ac2ee607dd"
+git-tree-sha1 = "4c26b4e9e91ca528ea212927326ece5918a04b47"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.11.1"
+version = "1.11.2"
 
 [[deps.ChangesOfVariables]]
 deps = ["LinearAlgebra", "Test"]
@@ -160,10 +160,10 @@ uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
 version = "1.5.0"
 
 [[deps.Distances]]
-deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
-git-tree-sha1 = "837c83e5574582e07662bbbba733964ff7c26b9d"
+deps = ["LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "3258d0659f812acde79e8a74b11f17ac06d0ca04"
 uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
-version = "0.10.6"
+version = "0.10.7"
 
 [[deps.Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
@@ -306,9 +306,9 @@ version = "0.21.0+0"
 
 [[deps.Glib_jll]]
 deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
-git-tree-sha1 = "7bf67e9a481712b3dbe9cb3dac852dc4b1162e02"
+git-tree-sha1 = "74ef6288d071f58033d54fd6708d4bc23a8b8972"
 uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
-version = "2.68.3+0"
+version = "2.68.3+1"
 
 [[deps.Graphite2_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -372,9 +372,9 @@ uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
 version = "0.1.1"
 
 [[deps.IterTools]]
-git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
+git-tree-sha1 = "fa6287a4469f5e048d763df38279ee729fbd44e5"
 uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
-version = "1.3.0"
+version = "1.4.0"
 
 [[deps.IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
@@ -674,9 +674,9 @@ version = "1.0.15"
 
 [[deps.Plots]]
 deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
-git-tree-sha1 = "9c52b09e45f9926a8e50fb7d63f25066431c2e02"
+git-tree-sha1 = "3e7e9415f917db410dcc0a6b2b55711df434522c"
 uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
-version = "1.24.4"
+version = "1.25.1"
 
 [[deps.PositiveFactorizations]]
 deps = ["LinearAlgebra"]