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v1

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v1.1

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v1.1.0/.documenter-siteinfo.json

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+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-03T11:21:04","documenter_version":"1.6.0"}}

v1.1.0/_intro.qmd

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+
+# LaplaceRedux
+
+```{julia}
+#| echo: false
+using Pkg; Pkg.activate("docs")
+# Import libraries
+using Flux, Plots, TaijaPlotting, Random, Statistics, LaplaceRedux, LinearAlgebra
+```
+
+`LaplaceRedux.jl` is a library written in pure Julia that can be used for effortless Bayesian Deep Learning through Laplace Approximation (LA). In the development of this package I have drawn inspiration from this Python [library](https://aleximmer.github.io/Laplace/index.html#setup) and its companion [paper](https://arxiv.org/abs/2106.14806) [@daxberger2021laplace].
+
+## 🚩 Installation
+
+The stable version of this package can be installed as follows:
+
+```{.julia}
+using Pkg
+Pkg.add("LaplaceRedux.jl")
+```
+
+The development version can be installed like so:
+
+```{.julia}
+using Pkg
+Pkg.add("https://github.com/JuliaTrustworthyAI/LaplaceRedux.jl")
+```
+
+## 🏃 Getting Started
+
+If you are new to Deep Learning in Julia or simply prefer learning through videos, check out this awesome YouTube [tutorial](https://www.youtube.com/channel/UCQwQVlIkbalDzmMnr-0tRhw) by [doggo.jl](https://www.youtube.com/@doggodotjl/about) 🐶. Additionally, you can also find a [video](https://www.youtube.com/watch?v=oWko8FRj_64) of my presentation at JuliaCon 2022 on YouTube. 
+
+## 🖥️ Basic Usage
+
+`LaplaceRedux.jl` can be used for any neural network trained in [`Flux.jl`](https://fluxml.ai/Flux.jl/dev/). Below we show basic usage examples involving two simple models for a regression and a classification task, respectively.
+
+### Regression
+
+```{julia}
+#| echo: false
+
+using LaplaceRedux
+using LaplaceRedux.Data: toy_data_regression
+using Flux.Optimise: update!, Adam
+
+# Data:
+n = 150           # number of observations
+σtrue = 0.3       # true observational noise
+x, y = toy_data_regression(n; noise=σtrue)
+xs = [[x] for x in x]
+X = permutedims(x)
+data = zip(xs,y)
+
+# Model:
+n_hidden = 50
+D = size(X,1)
+nn = Chain(
+    Dense(D, n_hidden, tanh),
+    Dense(n_hidden, 1)
+)  
+loss(x, y) = Flux.Losses.mse(nn(x), y)
+
+# Training:
+opt = Adam(1e-3)
+epochs = 1000
+avg_loss(data) = mean(map(d -> loss(d[1],d[2]), data))
+show_every = epochs/10
+
+for epoch = 1:epochs
+  for d in data
+    gs = gradient(Flux.params(nn)) do
+      l = loss(d...)
+    end
+    update!(opt, Flux.params(nn), gs)
+  end
+  if epoch % show_every == 0
+    println("Epoch " * string(epoch))
+    @show avg_loss(data)
+  end
+end
+```
+
+A complete worked example for a regression model can be found in the [docs](https://www.paltmeyer.com/LaplaceRedux.jl/dev/tutorials/regression/). Here we jump straight to Laplace Approximation and take the pre-trained model `nn` as given. Then LA can be implemented as follows, where we specify the model `likelihood`. The plot shows the fitted values overlaid with a 95% confidence interval. As expected, predictive uncertainty quickly increases in areas that are not populated by any training data.
+
+```{julia}
+#| output: true
+
+
+la = Laplace(nn; likelihood=:regression)
+fit!(la, data)
+optimize_prior!(la)
+plot(la, X, y; zoom=-5, size=(500,500))
+```
+
+```{julia}
+#| echo: false
+
+using Plots.PlotMeasures
+theme(:wong)
+anim = Animation()
+N = 100
+_every = Int(round(N/10))
+zoom = -3
+for n in _every:_every:length(first(data,N))
+    la = Laplace(nn; likelihood=:regression)
+    fit!(la, Iterators.take(data,n))
+    optimize_prior!(la)
+    plt = plot(
+      la, X[:,1:n], y[1:n]; 
+      ylim=(minimum(y)+zoom,maximum(y)-zoom),
+      zoom=-2, size=(600,200), clegend=false, axis=nothing, legend=false, margin = -5mm, ms=4
+    )
+    frame(anim, plt)
+end
+gif(anim, "dev/www/intro.gif", fps=1)
+```
+
+### Binary Classification
+
+```{julia}
+#| echo: false
+
+using LaplaceRedux.Data: toy_data_non_linear
+
+# Data:
+xs, ys = toy_data_non_linear(200)
+X = hcat(xs...)     # bring into tabular format
+data = zip(xs,ys)
+
+# Model:
+n_hidden = 10
+D = size(X,1)
+nn = Chain(
+    Dense(D, n_hidden, σ),
+    Dense(n_hidden, 1)
+)  
+loss(x, y) = Flux.Losses.logitbinarycrossentropy(nn(x), y) 
+
+# Training:
+opt = Adam()
+epochs = 500
+avg_loss(data) = mean(map(d -> loss(d[1],d[2]), data))
+show_every = epochs/10
+
+for epoch = 1:epochs
+  for d in data
+    gs = gradient(Flux.params(nn)) do
+      l = loss(d...)
+    end
+    update!(opt, Flux.params(nn), gs)
+  end
+  if epoch % show_every == 0
+    println("Epoch " * string(epoch))
+    @show avg_loss(data)
+  end
+end
+```
+
+Once again we jump straight to LA and refer to the [docs](https://www.paltmeyer.com/LaplaceRedux.jl/dev/tutorials/mlp/) for a complete worked example involving binary classification. In this case we need to specify `likelihood=:classification`. The plot below shows the resulting posterior predictive distributions as contours in the two-dimensional feature space: note how the **Plugin** Approximation on the left compares to the Laplace Approximation on the right.
+
+```{julia}
+#| output: true
+
+la = Laplace(nn; likelihood=:classification)
+fit!(la, data)
+la_untuned = deepcopy(la)   # saving for plotting
+optimize_prior!(la; n_steps=100)
+
+# Plot the posterior predictive distribution:
+zoom=0
+p_plugin = plot(la, X, ys; title="Plugin", link_approx=:plugin, clim=(0,1))
+p_untuned = plot(la_untuned, X, ys; title="LA - raw (λ=$(unique(diag(la_untuned.prior.P₀))[1]))", clim=(0,1), zoom=zoom)
+p_laplace = plot(la, X, ys; title="LA - tuned (λ=$(round(unique(diag(la.prior.P₀))[1],digits=2)))", clim=(0,1), zoom=zoom)
+plot(p_plugin, p_untuned, p_laplace, layout=(1,3), size=(1700,400))
+```
+
+
+## 📢 JuliaCon 2022
+
+This project was presented at JuliaCon 2022 in July 2022. See [here](https://pretalx.com/juliacon-2022/talk/Z7MXFS/) for details.
+
+## 🛠️ Contribute
+
+Contributions are very much welcome! Please follow the [SciML ColPrac guide](https://github.com/SciML/ColPrac). You may want to start by having a look at any open [issues](https://github.com/JuliaTrustworthyAI/LaplaceRedux.jl/issues). 
+
+## 🎓 References
+
+