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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.


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.


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.


On Dissipative Symplectic Integration with Applications to Gradient-Based Optimization

arXiv.org Machine Learning

Recently, continuous dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in this line of work is how to discretize the system in such a way that its stability and rates of convergence are preserved. In this paper we propose a geometric framework in which such discretizations can be realized systematically, enabling the derivation of "rate-matching" optimization algorithms without the need for a discrete convergence analysis. More specifically, we show that a generalization of symplectic integrators to dissipative Hamiltonian systems is able to preserve continuous rates of convergence up to a controlled error. Moreover, such methods preserve a perturbed Hamiltonian despite the absence of a conservation law, extending key results of symplectic integrators to dissipative cases. Our arguments rely on a combination of backward error analysis with fundamental results from symplectic geometry.