Traditionally, machine learning uses numerical algorithms as tools. However, many tasks in numerics can be viewed as learning problems. As examples:

* How can optimizers learn about the objective function, and how should they update their search direction?

* How should a quadrature method estimate an integral given observations of the integrand, and where should these methods put their evaluation nodes?

* Can approximate inference techniques be applied to numerical problems?

Many such issues can be seen as special cases of decision theory, active learning, or reinforcement learning.

We invite contribution of recent results in the development and analysis of numerical analysis methods based on probability theory. This includes, but is not limited to the areas of optimization, sampling, linear algebra, quadrature and the solution of differential equations.

Submission instructions are available at http://www.probabilistic-numerics.org/Call.html.