mbi.approximate_oracles.convex_generalized_belief_propagation

mbi.approximate_oracles.convex_generalized_belief_propagation(potentials: CliqueVector, total: float = 1, state: dict[tuple[tuple[str, ...], tuple[str, ...]], Factor] | None = None, mesh: Mesh | None = None, iters: int = 1, damping: float = 0.5) → tuple[CliqueVector, dict[tuple[tuple[str, ...], tuple[str, ...]], Factor]]

Convex generalized belief propagation for approximmate marginal inference.

The algorithms implements the Algorithm 2 in our paper [“Relaxed Marginal Consistency for Differentially Private Query Answering”](https://arxiv.org/pdf/2109.06153), which itself is based on the paper titled [“Tightening Fractional Covering Upper Bounds on the Partition

Function for High-Order Region Graphs”](https://arxiv.org/pdf/1210.4881).

Parameters:

• potentials – A CliqueVector object containing the potentials of the graphical model.

• total – The total number of records in the dataset.

• state – The state of the message passing algorithm (i.e., the messages). Useful when calling this within an iterative procedure for warm starting purposes.

• mesh – Specifies how the computation will be sharded across machines.

• iters – The number of iterations to run the algorithm.

• damping – The damping factor for the messages.

Returns:

A CliqueVector of pseudo-marginals for the cliques in the graphical model.