This is a Julia implementation in Flux of the Evidential Deep Learning framework. It strives to estimate heteroskedastic aleatoric uncertainty as well as epistemic uncertainty along with every prediction made. All of it calculated in one glorious forward pass. Boom!

If you want bleeding edge you can install it directly from my repo like this:

`using Pkg; Pkg.add(url="https://github.com/DoktorMike/EvidentialFlux.jl")`

Otherwise just do

`using Pkg; Pkg.add("EvidentialFlux.jl")`

Below is an example of how to train Deep Evidential Regression model, extract the predictions as well as the epistemic and aleatoric uncertainty. For a more elaborate example have a look in the examples folder.

```
using Flux
using EvidentialFlux
x = Float32.(-4:0.1:4)
y = x .^3 .+ randn(Float32, length(x)) .* 3
lr = 0.0005
m = Chain(Dense(1 => 100, relu), Dense(100 => 100, relu), Dense(100 => 100, relu), NIG(100 => 1))
opt = AdamW(lr, (0.89, 0.995), 0.001)
pars = Flux.params(m)
for epoch in 1:500
grads = Flux.gradient(pars) do
ŷ = m(x')
γ, ν, α, β = ŷ[1, :], ŷ[2, :], ŷ[3, :], ŷ[4, :]
trnloss = Statistics.mean(nigloss2(y, γ, ν, α, β, 0.01, 2))
trnloss
end
Flux.Optimise.update!(opt, pars, grads)
end
γ, ν, α, β = predict(m, x)
eu = epistemic(ν)
au = aleatoric(ν, α, β)
```

Deep evidential modeling works for classification as well as for regression. In the plot below you can see the epistemic uncertainty as a consequence of position in the plot. The task is to separate three Gaussians in 2D. The code for this example can be found in classification.jl.

In the case of a regression problem, we utilize the NormalInverseGamma distribution to model a type II likelihood function that then explicitly models the aleatoric and epistemic uncertainty. The code for the example producing the plot below can be found in regression.jl.

Uncertainty is crucial for the deployment and utilization of robust machine learning in production. No model is perfect and each one of them has strengths and weaknesses, but as a minimum requirement, we should all at least demand that our models report uncertainty in every prediction.