A general formula for the Magnus expansion in terms of iterated integrals of right-nested commutators

We present a general expression for any term of the Magnus series as an iterated integral of a linear combination of independent right-nested commutators with given coefficients. The relation with the Malvenuto--Reutenauer Hopf algebra of permutations is also discussed.Comment: 16 page

Approximate Decentralized Bayesian Inference

This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning agent to generate a local approximate posterior, the agents transmit their local posteriors to other agents in the network, and finally each agent combines its set of received local posteriors. The key insight in this work is that, for many Bayesian models, approximate inference schemes destroy symmetry and dependencies in the model that are crucial to the correct application of Bayes' rule when combining the local posteriors. The proposed method addresses this issue by including an additional optimization step in the combination procedure that accounts for these broken dependencies. Experiments on synthetic and real data demonstrate that the decentralized method provides advantages in computational performance and predictive test likelihood over previous batch and distributed methods.Comment: This paper was presented at UAI 2014. Please use the following BibTeX citation: @inproceedings{Campbell14_UAI, Author = {Trevor Campbell and Jonathan P. How}, Title = {Approximate Decentralized Bayesian Inference}, Booktitle = {Uncertainty in Artificial Intelligence (UAI)}, Year = {2014}