Posted on Categories Computer Science, Expository Writing, Programming, TutorialsTags , , , , , , 1 Comment on On indexing operators and composition

On indexing operators and composition

In this article I will discuss array indexing, operators, and composition in depth. If you work through this article you should end up with a very deep understanding of array indexing and the deep interpretation available when we realize indexing is an instance of function composition (or an example of permutation groups or semigroups: some very deep yet accessible pure mathematics).


NewImage

A permutation of indices

In this article I will be working hard to convince you a very fundamental true statement is in fact true: array indexing is associative; and to simultaneously convince you that you should still consider this amazing (as it is a very strong claim with very many consequences). Array indexing respecting associative transformations should not be a-priori intuitive to the general programmer, as array indexing code is rarely re-factored or transformed, so programmers tend to have little experience with the effect. Consider this article an exercise to build the experience to make this statement a posteriori obvious, and hence something you are more comfortable using and relying on.

R‘s array indexing notation is really powerful, so we will use it for our examples. This is going to be long (because I am trying to slow the exposition down enough to see all the steps and relations) and hard to follow without working examples (say with R), and working through the logic with pencil and a printout (math is not a spectator sport). I can’t keep all the steps in my head without paper, so I don’t really expect readers to keep all the steps in their heads without paper (though I have tried to organize the flow of this article and signal intent often enough to make this readable). Continue reading On indexing operators and composition

Posted on Categories Mathematics, StatisticsTags , , , , , , 2 Comments on A budget of classifier evaluation measures

A budget of classifier evaluation measures

Beginning analysts and data scientists often ask: “how does one remember and master the seemingly endless number of classifier metrics?”

My concrete advice is:

  • Read Nina Zumel’s excellent series on scoring classifiers.
  • Keep notes.
  • Settle on one or two metrics as you move project to project. We prefer “AUC” early in a project (when you want a flexible score) and “deviance” late in a project (when you want a strict score).
  • When working on practical problems work with your business partners to find out which of precision/recall, or sensitivity/specificity most match their business needs. If you have time show them and explain the ROC plot and invite them to price and pick points along the ROC curve that most fit their business goals. Finance partners will rapidly recognize the ROC curve as “the efficient frontier” of classifier performance and be very comfortable working with this summary.

That being said it always seems like there is a bit of gamesmanship in that somebody always brings up yet another score, often apparently in the hope you may not have heard of it. Some choice of measure is signaling your pedigree (precision/recall implies a data mining background, sensitivity/specificity a medical science background) and hoping to befuddle others.


Mathmanship

Stanley Wyatt illustration from “Mathmanship” Nicholas Vanserg, 1958, collected in A Stress Analysis of a Strapless Evening Gown, Robert A. Baker, Prentice-Hall, 1963

The rest of this note is some help in dealing with this menagerie of common competing classifier evaluation scores.

Continue reading A budget of classifier evaluation measures