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Implicit Probabilistic Integrators for ODEs

Neural Information Processing Systems

We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams–Moulton method. The implicit construction allows for dynamic feedback from the forthcoming time-step, in contrast to previous probabilistic integrators, all of which are based on explicit methods. We begin with a concise survey of the rapidly-expanding field of probabilistic ODE solvers. We then introduce our method, which builds on and adapts the work of Conrad et al. (2016) and Teymur et al. (2016), and provide a rigorous proof of its well-definedness and convergence. We discuss the problem of the calibration of such integrators and suggest one approach.


Meet your new cloud integrators. Same as your old systems ones

ZDNet

Cloud integrators and consultants have been gobbled up and Wipro's purchase of Appirio serves as icing on the consolidation cake. The bottom line: Meet your new cloud integrators--Accenture, IBM, Deloitte et al--and realize that they may be the same as your old systems integrators. As former renegades like Salesforce and Workday increasingly become go-to cloud-first platforms, these companies' growth engines will need a boost from the same integrators that gave SAP and Oracle a big lift in the early days of enterprise resource planning applications. The surge in ERP also led to an increase of costs, multiple implementation failures and a triangle of players (customers, consultants and enterprise vendors) all pointing the finger at each other. If you listen hard enough you can hear enterprise observers mumble that Salesforce is just the new Oracle.


Dell seeks Brazilian ISVs and integrators for IoT projects

ZDNet

Dell is looking for independent software developers (ISVs) and integrators in Brazil for the development of Internet of Things (IoT) projects. The Dell IoT Solution Partner initiative is aiming at getting local partners for its ecossystem to ramp up the development and implementation of IoT projects, which already has the support of several international companies. Some 25 organizations are involved in the partner network, including Microsoft, SAP, GE, Software AG, as well as companies that develop specific technologies for IoT, including Datawatch, Eigen Innovations, Flow Control and others. Now more than ever, toymakers and smart home device manufacturers have to put security first. According to Dell, the idea is to act as a contact bridge between the partners and offer access to resources at its labs around the world, as well as discounts in equipment such as intelligent gateways for IoT, security and management tools, datacenter infrastructure kit and software for data analysis and integration.



On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators

Neural Information Processing Systems

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of the SGLD with a 1st-order Euler integrator have recently been studied, corresponding theory for general SG-MCMCs has not been explored. In this paper we consider general SG-MCMCs with high-order integrators, and develop theory to analyze finite-time convergence properties and their asymptotic invariant measures. Our theoretical results show faster convergence rates and more accurate invariant measures for SG-MCMCs with higher-order integrators. For example, with the proposed efficient 2nd-order symmetric splitting integrator, the mean square error (MSE) of the posterior average for the SGHMC achieves an optimal convergence rate of $L {-4/5}$ at $L$ iterations, compared to $L {-2/3}$ for the SGHMC and SGLD with 1st-order Euler integrators.