The field of probabilistic numerics (PN), loosely speaking, attempts to provide a statistical treatment of the errors and/or approximations that are made en route to the output of a deterministic numerical method, e.g. the approximation of an integral by quadrature, or the discretised solution of an ordinary or partial differential equation. This decade has seen a surge of activity in this field. In comparison with historical developments that can be traced back over more than a hundred years, the most recent developments are particularly interesting because they have been characterised by simultaneous input from multiple scientific disciplines: mathematics, statistics, machine learning, and computer science. The field has, therefore, advanced on a broad front, with contributions ranging from the building of overarching generaltheory to practical implementations in specific problems of interest. Over the same period of time, and because of increased interaction among researchers coming from different communities, the extent to which these developments were -- or were not -- presaged by twentieth-century researchers has also come to be better appreciated. Thus, the time appears to be ripe for an update of the 2014 Tübingen Manifesto on probabilistic numerics[Hennig, 2014, Osborne, 2014d,c,b,a] and the position paper[Hennig et al., 2015] to take account of the developments between 2014 and 2019, an improved awareness of the history of this field, and a clearer sense of its future directions. In this article, we aim to summarise some of the history of probabilistic perspectives on numerics (Section 2), to place more recent developments into context (Section 3), and to articulate a vision for future research in, and use of, probabilistic numerics (Section 4).
More than 80 Amazon scientists and engineers will attend this year's International Conference on Machine Learning (ICML) in Stockholm, Sweden, with 11 papers co-authored by Amazonians being presented. "ICML is one of the leading outlets for machine learning research," says Neil Lawrence, director of machine learning for Amazon's Supply Chain Optimization Technologies program. "It's a great opportunity to find out what other researchers have been up to and share some of our own learnings." At ICML, members of Lawrence's team will present a paper titled "Structured Variationally Auto-encoded Optimization," which describes a machine-learning approach to optimization, or choosing the values for variables in some process that maximize a particular outcome. The first author on the paper is Xiaoyu Lu, a graduate student at the University of Oxford who worked on the project as an intern at Amazon last summer, then returned in January to do some follow-up work.
British healthcare workers are hostile to their robotic co-workers, committing "minor acts of sabotage" such as standing in their way, according to a recent study by De Montfort University, which chided the humans for "not playing along with" their automated peers. The researchers contrasted the "problematic" British attitude with that of Norwegian workers, who embraced their silicon colleagues, even giving them friendly nicknames. Some 30 percent of UK jobs will be lost to automation within 15 years if current trends continue apace, according to PricewaterhouseCoopers. The percentage is even greater in the US (38 percent) as well as Germany and France (37 percent), but falls to 25 percent in Scandinavian countries like Norway and Finland. Perhaps this explains the difference in workplace interactions between the British and the Norwegians - the latter aren't as worried about losing their jobs to an electronic interloper.
Urban Traffic Networks are characterized by high dynamics of traffic flow and increased travel time, including waiting times. This leads to more complex road traffic management. The present research paper suggests an innovative advanced traffic management system based on Hierarchical Interval Type-2 Fuzzy Logic model optimized by the Particle Swarm Optimization (PSO) method. The aim of designing this system is to perform dynamic route assignment to relieve traffic congestion and limit the unexpected fluctuation effects on traffic flow. The suggested system is executed and simulated using SUMO, a well-known microscopic traffic simulator. For the present study, we have tested four large and heterogeneous metropolitan areas located in the cities of Sfax, Luxembourg, Bologna and Cologne. The experimental results proved the effectiveness of learning the Hierarchical Interval type-2 Fuzzy logic using real time particle swarm optimization technique PSO to accomplish multiobjective optimality regarding two criteria: number of vehicles that reach their destination and average travel time. The obtained results are encouraging, confirming the efficiency of the proposed system.
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [Poyiadjis, Doucet and Singh, Biometrika 2018], a recursive maximum likelihood algorithm based on a particle approximation to the optimal filter derivative has been proposed and studied through numerical simulations. Here, this algorithm and its asymptotic behavior are analyzed theoretically. We show that the algorithm accurately estimates maxima to the underlying (average) log-likelihood when the number of particles is sufficiently large. We also derive (relatively) tight bounds on the estimation error. The obtained results hold under (relatively) mild conditions and cover several classes of non-linear state-space models met in practice.