I recently had the
pleasure to give a talk about the information dimension of stochastic
processes at the Workshop on Causality and Dynamics in Brain Networks which was held in conjunction with the
Int. Joint Conf. On Neural Networks in Budapest. Our paper on this
work is published in the IEEE Transactions on Information Theory and
available on arXiv. The slides of my talk can (as always) be accessed
by clicking on the image below.
This work on
information dimension means a lot to me, and I’d like to let you
know how it all started. I had come into contact with Renyi’s
information dimension in 2012, when I worked on the information lossin principal components analysis. Back then I was considering only
random variables, but in the summer of 2013, when I was investigating
the information loss in anti-aliasing filters, I had the feeling that
there should be a similar definition also for stochastic processes. I
somehow managed to get the results published at the Int. Zurich
Seminar in 2014, even though I have to admit that some of the more
interesting results were obtained only with the help of two
Assumptions, which would have been theorems had the results on
information dimension already existed. I was certain at this point
that a proper definition of the information dimension of a stochastic
process must be connected with the bandwidth of the process.
After my PhD, I
spent some time at TU Munich as a postdoc. My Schroedinger grant from
the Austria Science Fund allowed me to work on information-theoretic
reduction of Markov models. The first year though, which was funded
directly by my boss Prof. Gerhard Kramer, I set out to work on “Two
Little (?) Problems” - at least that was the title under which I
presented these two problems to my colleagues during our winter
retreat in the beautiful village of Stilfs in early 2015. The two
problems were the fractal properties of polar codes (which are an
entirely different story) and the information dimension of stochastic
processes. While my work on polar codes progressed quickly, I was
stuck on the other problem. In the meantime I have found out that researchers published a possible definition of information dimension for stochastic processes. But I was not able to pursue this further until I met Stefan Moser and Tobi Koch
at the Int. Zurich Seminar in 2016 (where I presented my work on
polar codes). I’ve met both of them before and I read some of their
works – I just knew that they were able to help me.
Long story short,
Tobi was strongly interested and invited me to stay with him at
Universidad Carlos III de Madrid later this year. The stay was
amazing: Late breakfasts, dinners at 9 pm, a dry 40 degress weather,
and ice cold beer at night to cool down. Most importantly, we got a
good way towards proving the connection between information dimension
– defined differently than previously suggested –
and bandwidth, at least for Gaussian processes.
Over the coming
months our results were refined and extended, and now it feels as if
there is not much important left to do. It seems as if both of my “Two Little (?) Problems” are solved now.
A collection of mathematical curiosities, chosen purely based on my own interest. Be prepared for a little information theory, combinatorics, and probability! (This blog is trackable: 5ZVNC2)
Monday, July 22, 2019
Tuesday, June 4, 2019
Talk at LSIT 2019
On May 30th,
I had the great pleasure to give a talk at the 5th London Symposium on Information Theory. The symposium is a revival of a
conference series that was started in the 50s and 60s, with notable
speakers such as Shannon and Turing. As back then, this year’s LSIT
was jointly organized by Imperial College London (Deniz Gündüz) and King’s College London (Osvaldo Simeone). It was a great honor to be
one of the invited speakers, and I was happy to talk about the
potentials and pitfalls of training neural networks to minimize the
information bottleneck functional (joint work with Ali Amjad from TUM). The paper accompanying this work is accepted for publication in the IEEE Transactions on Pattern Analysis and Machine Intelligence (but you can also find it on arXiv). If you are interested in the talk, as always you can download it by clicking on the image below.
Unfortunately, my stay at this symposium was the shorted I ever had (and, hopefully, will ever have): I got notice on the morning of my talk that my wife and my son fell sick, so I decided to fly back right after my talk to support them as best as I can. Apparently, the universe decided at the same time to make my trip back home as complicated as possible: The mobile website of Austrian Airlines claimed that my last name is invalid (whatever that means), a two-mile run to get my luggage from the hotel that made me all sweaty, and a fire alarm right in the middle of my talk overthrew the conference schedule. I still managed to hold my talk – it would not have been possible without the generous help of the organizers and the kind understanding of the entire audience.
Leaving a conference right after the talk is rude; it does not give your colleagues the opportunity to discuss your own ideas offline over coffee (or beer). Even worse, it can be seen as an expression of the disinterest in the talks of your colleagues. In my case, leaving the conference so early made me sad in one more way: I had to leave a group of people – information theorists – that I consider my academic family (and many of which I consider even friends). Only my own family could make me do that – and I know that the attendees of the London Symposium understand. Thanks!
Unfortunately, my stay at this symposium was the shorted I ever had (and, hopefully, will ever have): I got notice on the morning of my talk that my wife and my son fell sick, so I decided to fly back right after my talk to support them as best as I can. Apparently, the universe decided at the same time to make my trip back home as complicated as possible: The mobile website of Austrian Airlines claimed that my last name is invalid (whatever that means), a two-mile run to get my luggage from the hotel that made me all sweaty, and a fire alarm right in the middle of my talk overthrew the conference schedule. I still managed to hold my talk – it would not have been possible without the generous help of the organizers and the kind understanding of the entire audience.
#LSIT is back in session after a short break due to fire alarm 🚨 pic.twitter.com/SXSVvaOytr— Deniz Gunduz (@DenizGunduz1) May 30, 2019
Leaving a conference right after the talk is rude; it does not give your colleagues the opportunity to discuss your own ideas offline over coffee (or beer). Even worse, it can be seen as an expression of the disinterest in the talks of your colleagues. In my case, leaving the conference so early made me sad in one more way: I had to leave a group of people – information theorists – that I consider my academic family (and many of which I consider even friends). Only my own family could make me do that – and I know that the attendees of the London Symposium understand. Thanks!
Monday, April 15, 2019
Talk at apc|m 2019
I recently attended the 19th European Advanced Process Control and Manufacturing Conference, held this year in the nice city of Villach, Austria. The conference hosts experts in semiconductor manufacturing from both academia and industry.
I had the pleasure to talk about our work on an information-theoretic similarity measure for patterns on analog wafermaps. Analog wafermaps depict electrical measurement values of devices on a wafer, and patterns on these wafermaps may indicate process deviations. Detection and classifying these patterns, and reacting appropriately, can prevent further such deviations and, consequently, yield loss. Our work, a collaboration between Know-Center and K-AI within the SemI40 project, makes use of a feature extraction pipeline that was recently accepted for publication in the IEEE Transactions on Semiconductor Manufacturing. If you are interested in the slides, just click on the image below.
I had the pleasure to talk about our work on an information-theoretic similarity measure for patterns on analog wafermaps. Analog wafermaps depict electrical measurement values of devices on a wafer, and patterns on these wafermaps may indicate process deviations. Detection and classifying these patterns, and reacting appropriately, can prevent further such deviations and, consequently, yield loss. Our work, a collaboration between Know-Center and K-AI within the SemI40 project, makes use of a feature extraction pipeline that was recently accepted for publication in the IEEE Transactions on Semiconductor Manufacturing. If you are interested in the slides, just click on the image below.
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