Gauging Variational Inference
This work addresses a fundamental inference task in graphical models for applications in machine learning and statistics, but it is incremental as it builds upon existing variational methods.
The paper tackles the problem of computing partition functions in graphical models, which is computationally intractable, by proposing two new variational schemes, Gauged-MF and Gauged-BP, that improve upon mean-field and belief propagation methods. The result includes proofs of exactness for single-loop structures and experimental confirmation of outperformance on models with up to 300 variables.
Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice, where mean-field (MF) and belief propagation (BP) are arguably the most popular and successful approaches of a variational type. In this paper, we propose two new variational schemes, coined Gauged-MF (G-MF) and Gauged-BP (G-BP), improving MF and BP, respectively. Both provide lower bounds for the partition function by utilizing the so-called gauge transformation which modifies factors of GM while keeping the partition function invariant. Moreover, we prove that both G-MF and G-BP are exact for GMs with a single loop of a special structure, even though the bare MF and BP perform badly in this case. Our extensive experiments, on complete GMs of relatively small size and on large GM (up-to 300 variables) confirm that the newly proposed algorithms outperform and generalize MF and BP.