Bayesian LASSO in a distributed architecture

We present a distributed framework for finding the full posterior distribution associated with LASSO problems. We leverage our recent results of formulating Bayesian inference as a KL divergence minimization problem that can be solved with linear algebra updates and a series of convex point estimation problems. We show that drawing samples from the Bayesian LASSO posterior can be done by iteratively solving LASSO problems in parallel. Motivated by wearable applications where (a) the energy cost of continuous wireless transmission is prohibitive and (b) cloud storage of data induces privacy vulnerabilities, we propose a class of `analog-to-information' architectures that only transmit the minimal relevant information (e.g. the posterior) for optimal decision-making. We instantiate this result with an analog-implementable solver and show that the posterior can be calculated with systems of low-energy analog circuits in a distributed manner.