Piecewise Deterministic Monte Carlo algorithms enable simulation from a posterior distribution, whilst only needing to access a sub-sample of data at each iteration. We show how they can be implemented in settings where the parameters live on a restricted domain. * joris.bierkens@tudelft.nl; Corresponding Author arXiv:1701.04244v3 [stat.ME]

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This paper makes two contributions to Bayesian machine learning algorithms. Firstly, we propose stochastic natural gradient expectation propagation (SNEP), a novel alternative to expectation propagation (EP), a popular variational inference algorithm. SNEP is a black box variational algorithm, in that it does not require any simplifying assumptions on the distribution of interest, beyond the existence of some Monte Carlo sampler for estimating the moments of the EP tilted distributions. Further, as opposed to EP which has no guarantee of convergence, SNEP can be shown to be convergent, even when using Monte Carlo moment estimates. Secondly, we propose a novel architecture for distributed Bayesian learning which we call the posterior server. The posterior server allows scalable and robust Bayesian learning in cases where a data set is stored in a distributed manner across a cluster, with each compute node containing a disjoint subset of data. An independent Monte Carlo sampler is run on each compute node, with direct access only to the local data subset, but which targets an approximation to the global posterior distribution given all data across the whole cluster. This is achieved by using a distributed asynchronous implementation of SNEP to pass messages across the cluster. We demonstrate SNEP and the posterior server on distributed Bayesian learning of logistic regression and neural networks.

This chapter investigates the potential of algorithms and machine learning (ML) to improve decision-making. It considers the best roles for algorithms while maintaining important elements of human judgment. There are essential human skills in judging, but algorithms could help systematize the judicial function and thus reduce the risk of human error, inconsistency, and individual bias. Algorithmic decision-making and ML could in principle mitigate these problems since algorithms are more consistent and rely on and can synthesize more data than a human. Yet, recent proposals to use algorithms in the civil justice system are still underdeveloped and face scepticism. This chapter evaluates the risks and benefits of using algorithms in adjudication by pointing out specific elements of legal skill and expertise and identifying tasks better suited for an algorithm. While there are significant reliability and fairness limitations in using AI to make legal decisions, it is important to recognize that many of these weaknesses already exist to varying degrees in human judicial decision-making.

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