Patterns of Scalable Bayesian Inference

Datasets are growing not just in size but in complexity, creating a demand for rich models and quantification of uncertainty. Bayesian methods are an excellent fit for this demand, but scaling Bayesian inference is a challenge. In response to this challenge, there has been considerable recent work based on varying assumptions about model structure, underlying computational resources, and the importance of asymptotic correctness. As a result, there is a zoo of ideas with few clear overarching principles. In this paper, we seek to identify unifying principles, patterns, and intuitions for scaling Bayesian inference. We review existing work on utilizing modern computing resources with both MCMC and variational approximation techniques. From this taxonomy of ideas, we characterize the general principles that have proven successful for designing scalable inference procedures and comment on the path forward

Asynchronous Stochastic Variational Inference

Stochastic variational inference (SVI) employs stochastic optimization to scale up Bayesian computation to massive data. Since SVI is at its core a stochastic gradient-based algorithm, horizontal parallelism can be harnessed to allow larger scale inference. We propose a lock-free parallel implementation for SVI which allows distributed computations over multiple slaves in an asynchronous style. We show that our implementation leads to linear speed-up while guaranteeing an asymptotic ergodic convergence rate O(1/√T) given that the number of slaves is bounded by √T (T is the total number of iterations). The implementation is done in a high-performance computing (HPC) environment using message passing interface (MPI) for python (MPI4py). The extensive empirical evaluation shows that our parallel SVI is lossless, performing comparably well to its counterpart serial SVI with linear speed-up

Asynchronous Stochastic Variational Inference

Stochastic variational inference (SVI) employs stochastic optimization to scale up Bayesian computation to massive data. Since SVI is at its core a stochastic gradient-based algorithm, horizontal parallelism can be harnessed to allow larger scale inference. We propose a lock-free parallel implementation for SVI which allows distributed computations over multiple slaves in an asynchronous style. We show that our implementation leads to linear speed-up while guaranteeing an asymptotic ergodic convergence rate $O(1/\sqrt(T)$ ) given that the number of slaves is bounded by $\sqrt(T)$ ($T$ is the total number of iterations). The implementation is done in a high-performance computing (HPC) environment using message passing interface (MPI) for python (MPI4py). The extensive empirical evaluation shows that our parallel SVI is lossless, performing comparably well to its counterpart serial SVI with linear speed-up.Comment: 7 pages, 8 figures, 1 table, 2 algorithms, The paper has been submitted for publicatio

Federated Generalized Bayesian Learning via Distributed Stein Variational Gradient Descent

This paper introduces Distributed Stein Variational Gradient Descent (DSVGD), a non-parametric generalized Bayesian inference framework for federated learning. DSVGD maintains a number of non-random and interacting particles at a central server to represent the current iterate of the model global posterior. The particles are iteratively downloaded and updated by one of the agents with the end goal of minimizing the global free energy. By varying the number of particles, DSVGD enables a flexible trade-off between per-iteration communication load and number of communication rounds. DSVGD is shown to compare favorably to benchmark frequentist and Bayesian federated learning strategies, also scheduling a single device per iteration, in terms of accuracy and scalability with respect to the number of agents, while also providing well-calibrated, and hence trustworthy, predictions

A method of evaluation of high-performance computing batch schedulers

According to Sterling et al., a batch scheduler, also called workload management, is an application or set of services that provide a method to monitor and manage the flow of work through the system [Sterling01]. The purpose of this research was to develop a method to assess the execution speed of workloads that are submitted to a batch scheduler. While previous research exists, this research is different in that more complex jobs were devised that fully exercised the scheduler with established benchmarks. This research is important because the reduction of latency even if it is miniscule can lead to massive savings of electricity, time, and money over the long term. This is especially important in the era of green computing [Reuther18]. The methodology used to assess these schedulers involved the execution of custom automation scripts. These custom scripts were developed as part of this research to automatically submit custom jobs to the schedulers, take measurements, and record the results. There were multiple experiments conducted throughout the course of the research. These experiments were designed to apply the methodology and assess the execution speed of a small selection of batch schedulers. Due to time constraints, the research was limited to four schedulers. x The measurements that were taken during the experiments were wall time, RAM usage, and CPU usage. These measurements captured the utilization of system resources of each of the schedulers. The custom scripts were executed using, 1, 2, and 4 servers to determine how well a scheduler scales with network growth. The experiments were conducted on local school resources. All hardware was similar and was co-located within the same data-center. While the schedulers that were investigated as part of the experiments are agnostic to whether the system is grid, cluster, or super-computer; the investigation was limited to a cluster architecture