Large-cardinality HMMs

[dellaert]

I have been thinking some HMM-specific classes might be a good addition. If we provide a shared pointer to sparse Eigen matrices we can

• save tons of memory
• support very large state/observation cardinalities
• create a sum-product example that calculates the stationary distribution, which we can check with the transition matrix Eigenvector...
• implement EM for parameter estimation, e.g., here https://gtbook.github.io/gtsam-examples/intro.html

[dellaert]

Possible class names:

• DiscreteTransition inherits from DiscreteConditional
• DiscreteMeasurement inherits from DiscreteConditional
• DiscreteMeasurementFactor inherits from DiscreteFactor, produced by DiscreteMeasurement::likelihood

[dellaert]

Here are some proposed API calls:

S = Sparse(m,n)
T = Sparse(n,n)
hmm = HMM(S, T);
bn = hmm.bayesNet(5);
measured = DiscreteValues {...};
fg = hmm.factorGraph(measured);
hmm = hmm.stepEM(measured);