### The Loss Rank Principle by Marcus Hutter

I found the paper posted by Marcus Hutter on arxiv quite interesting. The paper is about model (or rather predictor) selection. The idea is a familiar one, but the details appear to be novel: You want to find a model which yields small loss on the dataset available, while yielding a larger loss on most other datasets.

Classification: The simplest case is when we consider supervised learning and the target set is finite. Then you can count the number of target label variations such that the predictor's loss is smaller than its loss when the true targets are used. This idea sounds very similar to the way Rademacher complexity works, see e.g. the paper of Lugosi and Wegkamp, where a localized version of Rademacher complexity is investigated.

Regression: For continuous targets you can use a grid with an increasing resolution (assume that the range of targets is bounded) and count the number of gridpoints such that the predictor's loss is less than its loss on the true dataset.
With an appropriate normalization this converges to the volume of such target values (hopefully this set is measurable:)).

The paper does not go very far: Some examples are given that demonstrate that the criterion gives a computable procedure and that this procedure is reasonable. A quick comparison to alternatives is given. It will be interesting to see the further developments!

### Keynote vs. Powerpoint vs. Beamer

A few days ago I decided to give Keynote, Apple's presentation software, a try (part of iWork '09). Beforehand I used MS Powerpoint 2003, Impress from NeoOffice 3.0 (OpenOffice's native Mac version) and LaTeX with beamer. Here is a comparison of the ups and downs of these software, mainly to remind myself when I will reconsider my choice in half a year and also to help people decide what to use for their presentation. Comments, suggestions, critics are absolutely welcome, as usual. Btw, while preparing this note I have learned that go-oo.org has a native Mac Aqua version of OpenOffice. Maybe I will try it some day and update the post. It would also be good to include a recent version of Powerpoint in the comparison.
StabilityKeynote: Excellent
After a few days of usage, so take this statement with a grain of salt..MS Powerpoint 2003: ExcellentImpress: Poor
Save your work very oftenBeamer: ExcellentCreating visually appealing slides, graphics on slides
Keynote: Excellent
Posit…

### Approximating inverse covariance matrices

Phew, the last time I have posted an entry to my blog was a loong time ago.. Not that there was nothing interesting to blog about, just I always delayed things. (Btw, google changed the template which eliminated the rendering of the latex formulae, not happy.. Luckily, I could change back the template..) Now, as the actual contents:

I have just read the PAMI paper "Accuracy of Pseudo-Inverse Covariance Learning-A Random Matrix Theory Analysis" by D Hoyle (IEEE T. PAMI, 2011 vol. 33 (7) pp. 1470--1481).

The paper is about pseudo-inverse covariance matrices and their analysis based on random matrix theory analysis and I can say I enjoyed this paper quite a lot.

In short, the author's point is this:
Let \$d,n>0\$ be integers. Let $\hat{C}$ be the sample covariance matrix of some iid data $X_1,\ldots,X_n\in \mathbb{R}^d$ based on $n$ datapoints and let $C$ be the population covariance matrix (i.e., $\hat{C}=\mathbb{E}[X_1 X_1^\top]$). Assume that $d,n\rightarrow \infty$ …

### Useful latex/svn tools (merge, clean, svn, diff)

This blog is about some tools that I have developed (and yet another one that I have downloaded) which help me to streamline my latex work cycle. I make the tools available, hoping that other people will find them useful. However, they are admittedly limited (more about this) and as usual for free stuff they come with zero guarantee. Use them at your own risk.

The first little tool is for creating a cleaned up file before submitting it to a publisher who asks for source files. I call it ltxclean.pl, it is developed in Perl. It can be downloaded from here.
The functionality is