The Geometry of Losses

author: Robert C. Williamson, Australian National University
published: July 15, 2014,   recorded: June 2014,   views: 2319


Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.


Loss functions are central to machine learning because they are the means by which the quality of a prediction is evaluated. Any loss that is not proper, or can not be transformed to be proper via a link function is inadmissible. All admissible losses for n-class problems can be obtained in terms of a convex body in Rn. We show this explicitly and show how some existing results simplify when viewed from this perspective. This allows the development of a rich algebra of losses induced by binary operations on convex bodies (that return a convex body). Furthermore it allows us to define an “inverse loss” which provides a universal “substitution function” for the Aggregating Algorithm. In doing so we show a formal connection between proper losses and norms.

See Also:

Download slides icon Download slides: colt2014_williamson_geometry.pdf (2.2 MB)

Help icon Streaming Video Help

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: