inferlo.pairwise.optimization.convex_hierarchies.lasserre

inferlo.pairwise.optimization.convex_hierarchies.lasserre(model: PairWiseFiniteModel, level=1) → lasserre_result[source]

This is an implementation of Lasserre hierarchy. This method p roduces hierarchy of semidefinite programming (SDP) relaxations for the most probable state estimation (MAP problem).

Let k be the level of hierarchy. Then we consider all clusters of variables of size k, and construct their moment matrix. Denote alphabet size by q. Then for every cluster of size t we introduce q^t indicator binary variables and get moment matrix.

After solving the corresponding SDP, we get upper bound to the energy function at a most probable state and extract the resulting moment matrix.

More on Lasserre hierarchies may be found in M.Wainwright and M. Jordan’s book “Graphical Models, Exponential Families, and Variational Inference”, section 9. https://people.eecs.berkeley.edu/~wainwrig/Papers/WaiJor08_FTML.pdf