Author: Bianco
Year: 2013
- sparse approximation of marginalization using chow liu tree
- computationnal complexity depends only on the number of nodes removed, not on the size of the whole graph
- pairwise measurement composition != marginalization: some of the composed measurements share common information, ie. are not independant
- interesting notations for marginalization
- GLC factor = unique factor to represent marginalization over the elimination clique
- marginalization induces n nary factors -> explicitly shows the correlation between measurements
- the target information matrix
$\Lambda_t$ may not be full rank - idea: builds a n nary factor with the pseudo inverse of
$\Lambda_t$ - adapt it to relative frame by setting the first pose as an arbitrary origin -> ensure that the jacobians are invertibles
- CLT = maximum spanning tree over all possible pairwise information
Build CLT over
- take joint marginal
$p(x_i, x_j)$ (how? with$\Lambda_t$ inversion apparently SCHUR COMPLEMENT) - as CLT only need to sort mutual information, the absolute value doesn't matter -> Tikhonov regularization is ok
- A CLT approximation has a complexity of
$\mathcal{O}(m^2 log \ m)$ - how to compute every spanning tree?
Conclusion:
- GLC can represent either dense marginalization, either sparse CLT
- superior in term of KLD than pairwise measurement composition