Probability interface tutorial (#404)

First addition to the DynamicPPL tutorials; breaking this up as Hong suggested. Goes over how to use the basic interfaces (e.g. logjoint, loglikelihood, logdensityof).

Co-authored-by: Hong Ge <[email protected]>
Co-authored-by: David Widmann <[email protected]>

Author: 3 people

docs/Project.toml

@@ -1,11 +1,13 @@
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 
 [compat]
 Distributions = "0.25"
 Documenter = "0.27"
+FillArrays = "0.13"
 Setfield = "0.7.1, 0.8, 1"
 StableRNGs = "1"

docs/make.jl

@@ -11,7 +11,11 @@ makedocs(;
     sitename="DynamicPPL",
     format=Documenter.HTML(),
     modules=[DynamicPPL],
-    pages=["Home" => "index.md", "API" => "api.md"],
+    pages=[
+        "Home" => "index.md",
+        "API" => "api.md",
+        "Tutorials" => ["tutorials/prob-interface.md"],
+    ],
     strict=true,
     checkdocs=:exports,
 )

docs/src/assets/dynamicppl.svg renamed to docs/src/assets/logo.svg

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+# The Probability Interface
+
+The easiest way to manipulate and query DynamicPPL models is via the DynamicPPL probability
+interface.
+
+Let's use a simple model of normally-distributed data as an example.
+```@example probinterface
+using DynamicPPL
+using Distributions
+using FillArrays
+using LinearAlgebra
+using Random
+
+Random.seed!(1776) # Set seed for reproducibility
+
+@model function gdemo(n)
+   μ ~ Normal(0, 1)
+   x ~ MvNormal(Fill(μ, n), I)
+   return nothing
+end
+nothing # hide
+```
+
+We generate some data using `μ = 0` and `σ = 1`:
+
+```@example probinterface
+dataset = randn(100)
+nothing # hide
+```
+
+## Conditioning and Deconditioning
+
+Bayesian models can be transformed with two main operations, conditioning and deconditioning (also known as marginalization).
+Conditioning takes a variable and fixes its value as known.
+We do this by passing a model and a named tuple of conditioned variables to `|`:
+```@example probinterface
+model = gdemo(length(dataset)) | (x=dataset, μ=0, σ=1)
+nothing # hide
+```
+
+This operation can be reversed by applying `decondition`:
+```@example probinterface
+decondition(model)
+nothing # hide
+```
+
+We can also decondition only some of the variables:
+```@example probinterface
+decondition(model, :μ)
+nothing # hide
+```
+
+## Probabilities and Densities
+
+We often want to calculate the (unnormalized) probability density for an event.
+This probability might be a prior, a likelihood, or a posterior (joint) density.
+DynamicPPL provides convenient functions for this.
+For example, if we wanted to calculate the probability of a draw from the prior:
+```@example probinterface
+model = gdemo(length(dataset)) | (x=dataset,)
+x1 = rand(model)
+logjoint(model, x1)
+```
+
+For convenience, we provide the functions `loglikelihood` and `logjoint` to calculate probabilities for a named tuple, given a model:
+```@example probinterface
+@assert logjoint(model, x1) ≈ loglikelihood(model, x1) + logprior(model, x1)
+```
+
+## Example: Cross-validation
+
+To give an example of the probability interface in use, we can use it to estimate the performance of our model using cross-validation. In cross-validation, we split the dataset into several equal parts. Then, we choose one of these sets to serve as the validation set. Here, we measure fit using the cross entropy (Bayes loss).¹
+``` @example probinterface
+function cross_val(model, dataset)
+   training_loss = zero(logjoint(model, rand(model)))
+
+   # Partition our dataset into 5 folds with 20 observations:
+   test_folds = collect(Iterators.partition(dataset, 20))
+   train_folds = setdiff.((dataset,), test_folds)
+
+   for (train, test) in zip(train_folds, test_folds)
+      # First, we train the model on the training set.
+      # For normally-distributed data, the posterior can be solved in closed form:
+      posterior = Normal(mean(train), 1)
+      # Sample from the posterior
+      samples = NamedTuple{(:μ,)}.(rand(posterior, 1000))
+      # Test
+      testing_model = gdemo(length(test)) | (x = test,)
+      training_loss += sum(samples) do sample
+         logjoint(testing_model, sample)
+      end
+   end
+   return training_loss
+end
+cross_val(model, dataset)
+```
+
+¹See [ParetoSmooth.jl](https://github.com/TuringLang/ParetoSmooth.jl) for a faster and more accurate implementation of cross-validation than the one provided here.