Federated Bayesian Learning: 

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Motivated by decentralized approaches to machine learning, we                                                                         propose a collaborative Bayesian learning algorithm taking the form                                                                     of decentralized Langevin dynamics in a non-convex setting. Our                                                                            analysis show that the initial KL-divergence between the Markov Chain                                                                  and the target posterior distribution is exponentially decreasing while                                                                      the error contributions to the overall KL-divergence from the

additive noise is decreasing in polynomial time. We further show that

the polynomial-term experiences speed-up with number of agents

and provide sufficient conditions on the time-varying step-sizes to guarantee convergence to the desired distribution. The performance of the proposed algorithm is evaluated on a wide variety of machine learning tasks. The empirical results show that the performance of individual agents with locally available data is on par with the centralized setting with considerable improvement in the convergence rate.

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Observability Enhancement in Systems with Partial Observability: 

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This work addresses the problem of collecting information about system states 

when the system itself is partially observable. Major research questions addre-

ssed in this work include:

1. What are the best  set of measurements that give maximum information

about the states.

2. How to collect the measurements that maximize information content? 

The system considered in this work is a set of aerial vehicles with measurements 

being the angular separation between the vehicles. In this setting, the separation 

between the vehicles (R) is normally unobservable.  Major tools used in  this

research are information-theoretic notions such as observability gramian, 

                                                                                                          An Illustration of a set of aerial vehicles

Fisher Information Matrix, etc. A key finding from this work is that all the measurements differ in the information content about the estimation process, and the information-theoretic notion represents a better way to select measurements to bring additional information. As seen in the Figure, separation R between the two aerial vehicles is crucial in this  setting when the only information available is the angle between the vehicles. 

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