Posted on Categories Expository Writing, History, Mathematics, Tutorials5 Comments on Let’s try to motivate schemes

## Let’s try to motivate schemes

Recently there has been some controversy over David Mumford’s Nature magazine invited obituary of Alexander Grothendieck being initially rejected on submission (see here and here). At issue was the attempt to explain the mathematical idea of schemes (one of Alexander Grothendieck’s most important contributions) to a non-mathematician audience. Professor Mumford is a mathematician of great stature and his explanation is better than anything I could even attempt. However, in addition to the issues he raises I don’t think he was sensitive enough to what a non-mathematician considers motivation.

I’ll take a quick stab at explaining a very tiny bit of the motivation of schemes. I not sure the kind of chain of analogies argument I am attempting would work in an obituary (or in a short length), so I certainly don’t presume to advise professor Mumford on his obituary of a great mathematician (and person). Continue reading Let’s try to motivate schemes

Posted on Tags 5 Comments on Is there a Kindle edition of Practical Data Science with R?

## Is there a Kindle edition of Practical Data Science with R?

We have often been asked “why is there no Kindle edition of Practical Data Science with R on Amazon.com?” The short answer is: there is an edition you can read on your Kindle: but it is from the publisher Manning (not Amazon.com). Continue reading Is there a Kindle edition of Practical Data Science with R?

Posted on 4 Comments on The Geometry of Classifiers

## The Geometry of Classifiers

As John mentioned in his last post, we have been quite interested in the recent study by Fernandez-Delgado, et.al., “Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?” (the “DWN study” for short), which evaluated 179 popular implementations of common classification algorithms over 120 or so data sets, mostly from the UCI Machine Learning Repository. For fun, we decided to do a follow-up study, using their data and several classifier implementations from `scikit-learn`, the Python machine learning library. We were interested not just in classifier accuracy, but also in seeing if there is a “geometry” of classifiers: which classifiers produce predictions patterns that look similar to each other, and which classifiers produce predictions that are quite different? To examine these questions, we put together a Shiny app to interactively explore how the relative behavior of classifiers changes for different types of data sets.

Posted on 2 Comments on A comment on preparing data for classifiers

## A comment on preparing data for classifiers

I have been working through (with some honest appreciation) a recent article comparing many classifiers on many data sets: “Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?” Manuel Fernández-Delgado, Eva Cernadas, Senén Barro, Dinani Amorim; 15(Oct):3133−3181, 2014 (which we will call “the DWN paper” in this note). This paper applies 179 popular classifiers to around 120 data sets (mostly from the UCI Machine Learning Repository). The work looks good and interesting, but we do have one quibble with the data-prep on 8 of the 123 shared data sets. Given the paper is already out (not just in pre-print) I think it is appropriate to comment publicly. Continue reading A comment on preparing data for classifiers