softdot message for theta on structured VMP seems wrong

[Raphael-Tresor]

I tried to compute the outgoing message $\nu(\theta)$ with structured VMP:
$$q(y,\theta,x,\gamma) = q(y,x) q(\theta) q(\gamma)$$

I do not get the same value for $\xi$, the mean of the normal distribution :

ReactiveMP.jl/src/rules/softdot/theta.jl

Line 28 in b88de4d

ξ = (Vyx + mx * my') * mγ

Maybe I made a mistake, I got :

$$\xi = (Vyx + mx * my') * ((Vx + mx * mx')^{-1}) $$

Could someone take a look at this?

[Raphael-Tresor]

I searched https://www.overleaf.com/project/5c374a6301e80746b4f21243 to see if you keep track of your derivation here, but I could not find a derivation for this message.

[albertpod]

The derivations for the structured version of softdot weren't documented. The reason is that this node and this particular factorisation is a buffer-free case of autoregressive node. So it should look very much like here:

Note that ξ is not a mean it's a weighted mean (precision x mean) which effectively means that you got exactly same answer, though it probably should be:
$$\text{mean}_x=(Vx + mx * mx')^{-1}*(Vyx + mx * my)$$
Note that my is a value, there shouldn't be any transpose. Plus, this whole expression is a vector (Vyx + mx * my) so it must be from right side, not left side.

[Raphael-Tresor]

Oh, thank you for the answer @albertpod !
I am lost in the different parameterization names for the normal distribution. The ReactiveMP formula was correct, thank you very much for the explanation :)
I will close the issue.