Domains and Tasks in machine learning | one minute introduction

What is your basic knowledge of this domain?

You might see the terms domain and task used in machine learning papers, especially in the context of transfer learning or domain adaptation, but what do they actually mean?

1. What (simple)? A domain (in math/machine learning) is all the values that can (i.e. that make sense given the context) go into a function. A task (in general) is a piece of work to be done or undertaken (e.g. figuring out the function).
2. What (technical)? Given a set of inputs X (from feature space X) and corresponding labels Y (from label space Y), a domain D is defined by X and the (marginal) probability distribution P(X), while the task T is defined by Y and the conditional probability distribution P(Y|X). In supervised learning, P(Y|X) is the function that is learned.

Final thoughts: These are often brought up in the context of comparing different domains and/or tasks (e.g. when relating a source domain (or task) to a target domain (or task)).