Category Archives: Probability theory

Crash course on learning theory, part 2

It might be useful to refresh your memory on the concepts we saw in part 1 (particularly the notions of VC dimension and Rademacher complexity). In this second and last part we will discuss two of the most successful algorithm paradigms in … Continue reading

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Crash course on learning theory, part 1

This week and next week I’m giving 90 minutes lectures at MSR on the fundamentals of learning theory. Below you will find my notes for the first course, where we covered the basic setting of statistical learning theory, Glivenko-Cantelli classes, Rademacher complexity, VC … Continue reading

Posted in Optimization, Probability theory, Theoretical Computer Science | 7 Comments

Some stuff I learned this week

This week I had the pleasure to spend 3 days at a wonderful workshop (disclaimer: I was part of the organization, with Ofer Dekel, Yuval Peres and James Lee, so I might be a bit biased). Below you will find … Continue reading

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Some pictures in geometric probability

As I discussed in a previous blog post, I have been recently interested in models of randomly growing networks. As a starting point I focused my attention on the preferential attachment rule and its variants, in part because its ubiquity … Continue reading

Posted in Probability theory, Random graphs | 2 Comments

Komlos conjecture, Gaussian correlation conjecture, and a bit of machine learning

Today I would like to talk (somewhat indirectly) about a beautiful COLT 2014 paper by Nick Harvey and Samira Samadi. The problem studied in this paper goes as follows: imagine that you have a bunch of data points in with a certain … Continue reading

Posted in Optimization, Probability theory, Theoretical Computer Science | 5 Comments

Probability in high dimension

The Barcelona events have just ended, and I’m happy to report that everything went very smoothly. In my opinion the quality of the works presented at COLT and at the Foundations of Learning Theory workshop were truly outstanding. I hope … Continue reading

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The hunter and the rabbit

In this post I will tell you the story of the hunter and the rabbit. To keep you interested let me say that in the story we will see a powerful (yet trivial) inequality that I learned today from Yuval … Continue reading

Posted in Probability theory | 2 Comments