The generalized distributive law

The generalized distributive law

In this semitutorial paper we discuss a general message passing algorithm, which we call the generalized distributive law (GDL). The GDL is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities. It includes as special cases the Baum–Welch algorithm, the fast Fourier transform (FFT) on any...

The Generalized Distributive Law and Free Energy Minimization∗

In an important recent paper, Yedidia, Freeman, and Weiss [7] showed that there is a close connection between the belief propagation algorithm for probabilistic inference and the Bethe-Kikuchi approximation to the variational free energy in statistical physics. In this paper, we will recast the YFW results in the context of the “generalized distributive law” [1] formulation of belief propagatio...

Distributive Injustice and Private Law

Logic as a distributive law

We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad Calc : Cat → Cat for the free calculus on a category of terms and rewrites and a 2-monad BoolAlg for the free Boolean algebra on a category, we get a 2-monad Form = BoolAlg + Calc for the free category of formulae and proofs. We also get the 2-monad BoolA...

Generalized Almost Distributive Lattices-I

The concept of a GADL as a generalization of an ADL is introduced. Necessary and sufficient conditions for a GADL to become a distributive lattice and a GADL to become an ADL are obtained. We also study the maximal sets in a GADL and give equivalent conditions for a GADL to become a distributive lattice in terms of maximal