M. Ashok Kumar and Rajesh Sundaresan from the ECE department win the best paper award in NCC 2015!

[5th Mar, 15]: M. Ashok Kumar and Prof. Rajesh Sundaresan's paper titled "Relative α-Entropy Minimizers Subject to Linear Statistical Constraints" has won the Best Paper Award in NCC 2015 held at IIT Bombay. Below is a briefing by M. Ashok on the findings of their paper.

  • Congratulations Ashok and Prof. Rajesh! Can you state the highlights of the paper?

Relative α-entropy is a parametric generalization of the usual relative entropy (or the Kullback-Leibler divergence). Relative α-entropy shares several interesting and useful properties with relative entropy. Motivated by the well-known maximum entropy principle of statistical physics, we studied the problem of minimizing relative α-entropy subject to certain moment constraints on the underlying probability distribution. We had two major contributions in the paper: (a) We explicitly found the minimizing probability distribution. The minimizer suggests a parametric family of probability distributions, which we call an α-powerlaw family. This α-power law family generalizes the well-known exponential family in statistics. (b) We also explored the geometry associated with the minimizer.

  • How did you choose the problem addressed in the paper? Was it novel to you from the start itself or during the course of the work you realized its importance?

Rajesh Sundaresan (also the co-author of the paper) identified the emergence of relative α-entropy in the context of guessing and source coding. He also noticed that relative α-entropy is closely associated with Renyi/Tsallis entropy and that it shares several interesting properties with the usual relative entropy. When I joined him, he suggested me to explore these further. Later, during the course of time, we also came to know the relevance of relative α-entropy in a statistical estimation problem.

  • Having come this far, now how do you see the impact of these findings?

I can see two possible impacts. One, the α-power law distributions that we identified can be useful for statistical modelling purposes. Second, the geometry associated with the α-power law family may be helpful in reducing the complexity involved in a statistical estimation problem (this particular problem is not addressed in the current paper though).

  • What’s next from here? I assume you are waiting for your PhD defense.

Yes, of course I do! The next thing would be to explore more on the usefulness of the tools developed in my thesis, especially the geometry we explored, in simplifying certain statistical estimation problems.

Thank you very much!

Dept. ECE, IISc Banaglore.