Author: Mazuran
Year: 2015
- method to recover best set of non linear factor (NFR) to represent marginal distribution
- 5 steps:
- Markov Blanket extraction
- Markov Blanket optimization (optional) : local linearization point or global
- Node marginalization with Schurr
- Factor retrieval
- X is the inverse of the covariance of all measurement != I
$$
I = A^T X A
$$
with
$A = \frac{\partial f}{\partial x}|_{x=\mu}$ - If we find X we have all our factors
- Closed form solution if A is invertible
- Efficiency of PQN strongly depends on initialization
- Why for SE(n) measurements,
$\Omega$ is rank defficient? Because we are in the context of node removal with only relative transform - Project information matrix on lower space where it is full rank
Topology:
- Chow liu tree is the sparsest
- Mutual information is undefined with under constrained pb => Tikhonov regularization
$\Omega + \epsilon I$ - subgraph topology starts from chow liu tree and adds most informative edges
- Cliquey subgraph is the more dense that leads to closed from computation
Theory:
- Non optimality of error propagation wrt KLD (some dudes just fuse some succesive poses to reduce the amount of information)
- Show the equivalence between local linearization and global linearization
Experiments:
- use g2o (g2o uses sym gradient isam uses numeric gradient)