SPCOM 2014: tutorials

I just attended SPCOM 2014 at the Indian Institute of Science in Bangalore — many thanks to the organizers for the invitation! SPCOM 2014 happens every two years and is a mix of invited and submitted papers (much like Allerton). This year they mixed the invited talks with the regular talks which I thought was a great idea — since invited papers were not for specific sessions, it makes a lot more sense to do it that way, plus it avoids a sort of “two-tier” system.

I arrived early enough to catch the tutorials on the first day. There was a 3 hour session in the morning and another on the in afternoon. For the morning I decided to expand my horizons by attending Manoj Gopalkrishnan‘s tutorial on the physics of computation. Manoj focused on the question of how much energy it takes to erase or copy a bit of information. He started with some historical context via von Neumann, Szilard, and Landauer to build a correspondence between familiar information theoretic concepts and their physical counterparts. So in this correspondence, relative entropy is the same as free energy. He then turned to look at what one might call “finite time” thermodynamics. Suppose that you have to apply a control that operates in finite time in order to change a bit. One way to look at this is through controlling the transition probabilities in a two-state Markov chain representing the value of the bit you want to fix. You want to drive the resting state (with stationary distribution (1/2,1/2) to something like (\epsilon, 1 - \epsilon) within time T. At this level I more or less understood what was going on, but since my physics background is pretty poor, I think I missed out on how the physical intuition/constraints impact what control strategies you can choose.

Prasad Santhanam gave the other tutorial, which was a bit more solid ground for me. This was not quite a tutorial on large-alphabet probability estimation, but more directly on universal compression and redundancy calculations. The basic setup is that you have a family of distributions \mathcal{P} and you don’t know which distribution p \in \mathcal{P} will generate your data. Based on the data sample you want to do something: estimate some property of the distribution, compress the sample to a size close to its entropy, etc. A class can be weakly or strongly compressible, or insurable (which means being able to estimate quantiles), and so on. These problems turn out to be a bit different from each other depending on some topological features of the class. One interesting thing to consider for the machine learners out there this stopping time that you need in some analyses. As you are going along, observing the data and doing your task (estimation, compression, etc) can you tell from the data that you are doing well? This has major implications for whether or not an online algorithm can even work the way we want it to, and is something Prasad calls “data-driven compressible.”

I’ll try to write another post or two about the talks I saw as well!

Lossless compression via the memoizer

Via Andrew Gelman comes a link to deplump, a new compression tool. It runs the data through a predictive model (like most lossless compressors), but:

Deplump compression technology is built on a probabilistic discrete sequence predictor called the sequence memoizer. The sequence memoizer has been demonstrated to be a very good predictor for discrete sequences. The advantage deplump demonstrates in comparison to other general purpose lossless compressors is largely attributable to the better guesses made by the sequence memoizer.

The paper on the sequence memoizer (by Wood et al.) appeared at ICML 2009, with follow-ups at DCC and ICML 2010 It uses as its probabilistic model a version of the Pitman-Yor process, which is a generalization of the “Chinese restaurant”/”stick-breaking” process. Philosophically, the idea seems to be this : since we don’t know the order of the Markov process which best models the data, we will let the model order be “infinite” using the Pitman-Yor process and just infer the right parameters, hopefully avoiding overfitting while being efficient. The key challenge is that since the process can have infinite memory, the encoding seems to get hairy, which is why “memoization” becomes important. It seems that the particular parameterization of the PY process is important to reduce the number of parameters, but I didn’t have time to look at the paper in that much detail. Besides, I’m not as much of a source coding guy!

I tried it out on Leo Breiman’s paper Statistical Modeling: The Two Cultures. Measured in bytes:

307458 Breiman01StatModel.pdf         original
271279 Breiman01StatModel.pdf.bz2     bZip (Burrows-Wheeler transform)
269646 Breiman01StatModel.pdf.gz      gzip
269943 Breiman01StatModel.pdf.zip     zip
266310 Breiman01StatModel.pdf.dpl     deplump

As promised, it is better than the alternatives, (but not by much for this example).

What is interesting is that they don’t seem to cite much from the information theory literature. I’m not sure if this is a case of two communities working on related problems and unaware of the connections or that the problems are secretly not related, or that information theorists mostly “gave up” on this problem (I doubt this, but like I said, I’m not a source coding guy…)