A Modern Retrospective on Probabilistic Numerics

arXiv.org Machine Learning

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).


Machine learning prowess on display

#artificialintelligence

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.


An Evolutionary Hierarchical Interval Type-2 Fuzzy Knowledge Representation System (EHIT2FKRS) for Travel Route Assignment

arXiv.org Artificial Intelligence

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.


DDoS-for-Hire website taken down in global collaboration of law enforcement agencies

#artificialintelligence

Webstresser.org, a popular DDoS-for-Hire website service on Wednesday was taken down by authorities from the US, UK, Netherlands, and various other countries in a major international investigation and arrests have been made. The website is blamed for more than four million cyber attacks globally in the past three years and had over 134,000 registered users at the time of the takedown. The operation, dubbed "Operation Power OFF," targeted Webstresser.org, It involved law enforcement agencies from the Netherlands, United Kingdom, Serbia, Croatia, Spain, Italy, Germany, Australia, Hongkong, Canada, and United States of America, coordinating with Europol. The domain name was seized by the US Department of Defence.


The workplaces of the future will be more human, not less

#artificialintelligence

In the 18th century, those operating at the highest levels of society, from London to Moscow, needed to be able to speak French, then the language of status, the nobility, politics, intellectual life and modernisation. A hundred years later, British advances in industry, science and engineering meant that English succeeded French: a tongue with West Germanic origins replaced a romance language as the means of conducting business and diplomacy on the international stage. Today, even in some parts of China, English is still used as the global lingua franca, a leveller that enables deals to get done and the wheels of commerce and technology to spin. Around a decade ago, another type of language – one that was written rather than spoken – was held up as a deterministic factor for those seeking to gain influence or advantage in the digital age: coding. Its champions proselytised that proficiency in programming would determine employability and access to a thrusting, energetic entrepreneurial future. Over two or three years, a small industry sprang up, intent on instructing those who had no formal education in computer science to create products using C .