Sat 02 January 2016
by Steven E. Pav
I recently released a package to CRAN called
madness. The eponymous object
supports 'multivariate' automatic
differentiation by forward accumulation. By 'multivariate', I mean it allows
you to track (and automatically computes) the derivative of a scalar, or
vector, or matrix, or multidimensional array with respect to a scalar, vector,
matrix or multidimensional array.
The primary use case in mind is the
multivariate delta method,
where one has an estimate of a population quantity and the variance-covariance
of the same, and wants to perform inference on some transform of that
population quantity. With the values stored in a
madness object, one merely
performs the transforms directly on the estimate, and the derivatives are
computed automatically. A secondary use case would be for the automatic
computation of gradients when optimizing some complex function, e.g. in the
computation of the MLE of some quantity.
madness object contains a value,
val, as well as the derivative of
val with respect to some \(X\), called
dvdx. The derivative is stored
as a matrix in 'numerator layout' convention: if
\(m\) values, and \(X\) holds \(n\) values, then
dvdx is a \(m \times n\) matrix.
This unfortunately means that a gradient is stored as a row vector.
Numerator layout feels more natural (to me, at least) when propagating
derivatives via the chain rule.
For convenience, one can also store the 'tags' of the value and \(X\), in
xtag, respectively. The
vtag will be modified when computations
are performed, which can be useful for debugging. One can also store
the variance-covariance matrix of \(X\) in
Here is an example session showing the use of a
madness object. Note that by
default if one does not feed in
dvdx, the object constructor assumes that
the value is equal to \(X\), and so …
Inference on Sorts
Wed 30 December 2015
by Steven E. Pav
Previously, I described a
model for taste preference appropriate
for some experiments in cocktail design I conducted years ago.
I noted that this model was so elegant and simple, it must have been discovered
previously, and have a rich theory around it. In the two weeks since then,
I discovered a new paper on arxiv about
inference on ranks from comparisons. They review a model much like the one I
outlined, calling it the
model. (Hey, look, there is indeed a
package on CRAN
for this with a vignette!)
The paper by Shah and Wainright outlines a very simple method for estimating
the top \(k\) of \(n\) participants when the contests include exactly two
participants each. If I am reading it correctly, you take the average number
of observed wins for each contestant, then grab the top \(k\). They prove that
this algorithm is optimal under certain conditions. This seems to me
like an ideal outcome for a research result: the algorithm is dead simple,
and people have likely been using it for years, while the proof is somewhat
intricate. Unfortunately, it does not seem straightforward to generalize
the algorithm to the case where there are covariates, or 'features' about
the various contestants, nor necessarily to the case of multiple contestants
in a given contest. The Bradley-Terry model, on the other hand, is readily
adaptable to these modifications.
Using vim as an IDE
Tue 29 December 2015
by Steven E. Pav
For a number of years now, I have been using vim as a lightweight IDE. The
ecosystem of vim addons is rich. There are numerous plugins for creating tags
to navigate a project, browse files in directories, highlight syntax and so on.
What really makes it an IDE is the ability to execute code within the context
I realize this probably sounds 'charming' to disciples of that other
text editor, but it might seem like an unnatural urge to my vim
correligionists. The piece that glues it all together is
easiest way to get conque in ubuntu is via
apt as follows:
sudo apt-get install vim-addon-manager vim-conque
sudo vim-addons -w install conqueterm
The skinny on using conque is that you can visual-select code that you are
<F9>, and it will be transfered to the execution window,
newlines and all. So you can test out code while you are writing it. You
can also work the other way, testing out code in a REPL, then, when it is
working as expected, escape insert mode in the REPL, yank the working code to a
register, and copy it into the file you are working on.
Dockerfile or it didn't happen!
This kind of advice is a bit abstract, so I put a working example on
dockerhub. You can run it
yourself via docker:
# this might take a little while to download
docker pull shabbychef/vim-conque
docker run --rm -it shabbychef/vim-conque
This will feel a bit odd: when you run the last command, you are in vim, but
you are in vim in a docker container. When you terminate, your changes will
not be saved (this is the
--rm flag). Directions are given in the file
on how to start conque with a screen …
No Accounting for Taste
Sat 19 December 2015
by Steven E. Pav
Many years ago, before I had kids, I was afflicted with a mania for
Italian bitters. A particularly ugly chapter of this time included
participating (at least in my own mind) in a contest to design a
cocktail containing [obnoxious brand] Amaro. I was determined to win
this contest, and win it with science.
After weeks of scattershot development (with permanent damage to our livers),
the field of potential candidates was winnowed down to around 12 or so.
I then planned a 'party' with a few dozen friend-tasters to determine
the final entrant into the contest.
As I had no experience with market research or experimental design, I was
nervous about making rookie mistakes.
I was careful, or so I thought, about the
experimental design--assigning raters to cocktails in a balanced design,
assigning random one-time codes to the cocktails, adding control cocktails,
double blinding the tastings, and so on. The part that I was completely
fanatical about was that tasters should not assign numerical
ratings to the cocktails. I reasoned that the intra-rater and inter-rater
reliability was far too poor. Instead, each rater would be presented with
two cocktails, and state their preference. While in some situations,
with experienced raters using the same rating scale, this might result in a
loss of power, in my situation, with a gaggle of half-drunk friends,
it solved the problem of inconsistent application of numerical ratings.
The remaining issue was how to interpret the data to select a winner.
Tell me what you really think.
You can consider my cocktail party as a series of 'elections', each with two
or more 'candidates' (in my case exactly two every time), and a single winner
for each election. For each candidate in each election, you have some
'covariates', or 'features' as the ML people would call …