Standardize IIF.Mixture

[dehann]

We want to be able to make mixture distributions by combining different componets, for example MvNormal with a ManifoldKernelDensity with a FluxDistribution. The current code is first implementation which reversed the API, the current older code does:

IIF.Mixture(Pose2Pose2, (MvNormal, ManifoldKernelDensity, FluxDistr), (0.5,0.2,0.3))

However, all throughout stats literature as well as Julia/StatsBase, Mixture is used as follows (and what i'm suggesting we do as well):

Pose2Pose2( IIF.Mixture((MvN, MKD, FluxDistr), (0.5,0.2,0.3)) )

Then also the name conflict with StatsBase. We cannot use StatsBase.Mixture because they only allow <:Distribution, yet we need to allow more diverse components <:IIF.SamplableBelief. So my suggestion is we just dont export, and write all the documentation as IIF.Mixture(...).

[dehann]

Mixture should just be a density/distribution in its own right. We can sample from it like any other, it's integral still adds up to 1, etc.

[dehann]

And also just to link between related information:
https://juliarobotics.org/Caesar.jl/latest/concepts/dataassociation/#Mixture-Models

[GearsAD]

Got it. Should I wait for the new Mixturesv2 factors, or can we go ahead for now with the existing pattern and then make a Mixturesv2 factor?

[dehann]

Think for time sensitivity on ICRA we've gone with existing pattern for now. I would like to fix this to the better standard as soon we can though -- before the current 'bad' pattern propagates too far.

Question becomes, what is cleanest way to update the SDKs once we change IIF?

[Affie]

Can we have <:IIF.SamplableBelief be Distributions.Sampleable

[dehann]

Yes, but not directly. We probably should adopt a blend:

IIF.SamplableBelief = Union{<:Distributions.Sampleable, AMP.MKD, IIF.AliasingSS, IIF.HSD, IIF.LSD, ...}

https://github.com/JuliaRobotics/IncrementalInference.jl/blob/0f63b500191e35b3ec34f86bbe1185fce756ee80/src/entities/BeliefTypes.jl#L22

[Affie]

What I was wondering here is if we can have AMP and IIF inherit from Distributions.Sampleable but that is probably too restricting.

This is maybe one of those cases where a SamplableBelief trait would have worked nicely. I'll play with that a bit at some stage.

[Affie]

Is there any use in having a mixture of factor mechanics? For example a Pose2Pose2 and FluxPose2Pose2 factor. I guess one can just create a custom factor that handles the mixing.

[dehann]

There is a big need for having a mixture of Distribution with Flux (or MKD, or AliasingSampler, ...). This mixture would plug into any factor.

I regret using the word mechanics here :-P

[Affie]

Once we standardize, we can remove:

getFactorMechanics(f::AbstractFactor) = f
getFactorMechanics(f::Mixture) = f.mechanics