Inexact Models and Solution Accuracy

A "worse" model can yield "better" solutions

Hi Scholars!

Sometimes less accurate problem formulations
enable more accurate solution estimates to be obtained.
How? By considering all sources of error. 🤔

Yes, the solution to an exact formulation
is precisely what you want.
But, that's only part of the story.

See, iterative algorithms typically output inexact solutions
due to things like asymptotic convergence
and use of floating point arithmetic.

So, one should keep in mind the informal equation:

(error of output) = (modeling error) + (algorithm error)

Changing the model used to formulate a problem
changes what algorithms can be used.

Sometimes, an increase in modeling error can
enable better algorithms to be used such that
total error is reduced.

In other words, a "worse" model
may enable you to get "better" solutions.

The slides below walk through an example
in the computation of earth mover's distances.

Enjoy!

Howard