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}

Second-order Quantile Methods for Experts and Combinatorial Games

We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision tasks. We are not satisfied with just guaranteeing minimax regret rates, but we want our algorithms to perform significantly better on easy data. Two popular ways to formalize such adaptivity are second-order regret bounds and quantile bounds. The underlying notions of 'easy data', which may be paraphrased as "the learning problem has small variance" and "multiple decisions are useful", are synergetic. But even though there are sophisticated algorithms that exploit one of the two, no existing algorithm is able to adapt to both. In this paper we outline a new method for obtaining such adaptive algorithms, based on a potential function that aggregates a range of learning rates (which are essential tuning parameters). By choosing the right prior we construct efficient algorithms and show that they reap both benefits by proving the first bounds that are both second-order and incorporate quantiles