Sampling test for Hybrid Posterior

[varunagrawal]

This test checks for correctness of the hybrid posterior using a sampling based approach.

Specifically, given a simple factor graph as below

 M0\
X0 -*- X1 

we compute the posterior P(x0, m0, x1| z0, z1) given measurements z0, z1.

The test, at a high level performs the following steps:

1. Start with the factor graph and linearize FG .
2. Eliminate into a bayes net BN.
3. Sample from the bayes net.
4. Check BN(x)/FG(x) equals the same value for all samples.

Since we don't have a sample method for the hybrid bayes net, we perform a sampling scheme similar to a mixture model where,

1. We sample from a discrete distribution weighted by the mixing weights $\pi$.
2. Given the discrete sample value, pick the corresponding bayes net and factor graph.
3. Sample as described above.

Sample Method Update

Since the linearized factor graph and the eliminated bayes net do not record the noise model, sampling from the Bayes Net throws an error. To overcome this, I've added an optional parameter to the sample method SharedDiagonal model, and if the conditional to sample from doesn't have a noise model associated with it, then it will sample from the provided model. This model should be the same one that is provided to the original factor in the Nonlinear/Gaussian Factor Graph, making it a convenient addition.

[dellaert]

Can I ask to create a separate PR (to develop) with sampling for hybrid BNs? Seeing that in isolation will be easier to review.

[dellaert]

Also, convert to draft PR? Don’t think we should run CI as long as we don’t target develop

[varunagrawal]

Can I ask to create a separate PR (to develop) with sampling for hybrid BNs? Seeing that in isolation will be easier to review.

So a HybridBayesNet::sample method? Can do!

[dellaert]

Many comments…

[dellaert]

Let’s merge