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).


Upcoming Practical Data Science courses in London, Chicago, Zurich, Oslo and Stockholm

#artificialintelligence

If you'd like to learn how to run R within Azure Machine Learning and SQL Server, you may be interested in these upcoming 4-day Practical Data Science courses, presented by Rafal Lukawiecki from Project Botticelli. In this classroom-based course, you will learn machine learning, data mining, some statistics, data preparation, and how to interpret the results. You will also learn how to formulate business questions in terms of data science hypotheses and experiments, and how to prepare inputs to answer those questions. Rafal will share his decade of hands-on experience while teaching you about Azure Machine Learning (Azure ML) which is the foundation of Cortana Analytics Suite, and its highly-visual, on-premise companion, the SQL Server Analysis Services Data Mining engine, supplemented with the free Microsoft R Open and Microsoft R Server software. By the end of this course you will be able to plan and run data science projects.


Amazon CloudFront reaches 100 PoPs following latest Tokyo addition

ZDNet

Amazon Web Services said Wednesday that it's adding its 100th Amazon CloudFront Point of Presence, the fifth one in Tokyo and the sixth in Japan. Amazon CloudFront now has 89 Edge Locations and 11 Regional Edge Caches, with sites in 50 cities and 23 countries. In the past year, AWS said it increased the size of its network by nearly 60 percent, adding 37 locations, including Berlin, Germany; Minneapolis, Minnesota; Prague, Czech Republic; Boston, Massachusetts; Munich, Germany; Vienna, Austria; Kuala Lumpur, Malaysia; Philadelphia, Pennsylvania; and Zurich, Switzerland. AWS also recently announced support for Windows-based Virtual Private Servers (VPS) to its Lightsail service. Launched last year, Lightsail is Amazon's rival product to virtual private server companies such as Bluehost, Digital Ocean, and Linode, which provide remote servers for developers, websites, and businesses needing certain internet services.


Moscow is a terrifying city for drivers. So what if a car doesn't have one?

The Guardian

In certain sunny climes, self-driving cars are multiplying. Dressed in signature spinning sensors, the vehicles putter along roads in California, Arizona and Nevada, hoovering up data that will one day make them smart enough to run without humans.


UK was given details of alleged contacts between Trump campaign and Moscow

The Guardian

The UK government was given details last December of allegedly extensive contacts between the Trump campaign and Moscow, according to court papers. Reports by Christopher Steele, a former MI6 officer, on possible collusion between the the Trump camp and the Kremlin are at the centre of a political storm in the US over Moscow's role in getting Donald Trump elected. It was not previously known that the UK intelligence services had also received the dossier but Steele confirmed in a court filing earlier this month that he handed a memorandum compiled in December to a "senior UK government national security official acting in his official capacity, on a confidential basis in hard copy form". The court papers say Steele decided to pass on the information he had collected because it was "of considerable importance in relation to alleged Russian interference in the US presidential election", that it "had implications for the national security of the US and the UK" and "needed to [be] analysed and further investigated/verified". The December memo alleged that four Trump representatives travelled to Prague in August or September in 2016 for "secret discussions with Kremlin representatives and associated operators/hackers", about how to pay hackers secretly for penetrating Democratic party computer systems and "contingency plans for covering up operations".