Correct way to linearize node (abs in the example)

[meditans]

I'm struggling with writing linearization for nodes; consider this simple model

using RxInfer

@model function example2(y)
    x1 ~ NormalMeanPrecision(0.4, 1)
    x2 ~ NormalMeanPrecision(0.7, 10)
    diff := x1 - x2
    y := abs(diff)
end

@meta function abs_meta()
    abs(diff) -> Linearization()
end

# Inference
result2 = infer(
    model = example2(),
    data=(y=0.5,),
    iterations = 20,
    meta = abs_meta()
)

This causes the julia interpreter to briefly emit a warning, then loop forever. What am I missing?

[wouterwln]

Hey @meditans , thanks for trying out RxInfer! For me, when I run your code, it does not emit a warning and then loop forever, but an error in the inference procedure is being thrown. This is because the Linearization only works with Normal in and outputs see docs Since you are passing data, this assumption is invalidated. A way to fix it is by wrapping y in a Normal with very small variance, like so:

using RxInfer

@model function example2(y)
    x1 ~ NormalMeanPrecision(0.4, 1)
    x2 ~ NormalMeanPrecision(0.7, 10)
    diff := x1 - x2
    y ~ NormalMeanVariance(abs(diff), 1e-6)
end

@meta function abs_meta()
    abs() -> Linearization()                 # NOTE I also made a change here!
end

# Inference
result2 = infer(
    model = example2(),
    data=(y=0.5,),
    iterations = 1,                             # Your model does not contain loops and you do regular sum-product BP, so it will converge in 1 iteration
    meta = abs_meta()
)

This gives me an inference result. Hoping this solves your problem!

[meditans]

Thank you for your help @wouterwln!

[bvdmitri]

As a note, Linearization works best for differentiable functions (where gradient is a continuous function), it should work on abs but no guarantees