Category Archives: Theoretical Computer Science

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

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Guest post by Sasho Nikolov: Beating Monte Carlo

If you work long enough in any mathematical science, at some point you will need to estimate an integral that does not have a simple closed form. Maybe your function is really complicated. Maybe it’s really high dimensional. Often you … Continue reading

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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

A zest of number theory

I just encountered an amazing number theoretic result. It is probably very well known, but for those who never saw it it’s quite something, so I thought I would share it. Let be a positive integer. A partition of is … Continue reading

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First week of activity at the Simons Institute

This first week at the Simons Institute was a lot of fun! I attended the first workshop in the Real Analysis program which was about Testing, Learning and Inapproximability. There was plenty of good talks and I learned a lot of … Continue reading

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Random-Approx 2013

Last week I attended the Random-Approx conference at Berkeley. I missed quite a few talks as I was also settling in my new office for the semester at the Simons Institute so I will just report on the three invited talks: Luca Trevisan gave a … Continue reading

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Embeddings of finite metric spaces in Hilbert space

In this post we discuss the following notion: Let and be two metric spaces, one says that embeds into with distortion if there exists and such that for any ,     We write this as . Note that if … Continue reading

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ORF523: Getting around NP-hardness

In this post I would like to argue that showing -completeness of a problem is in fact only a weak certificate of difficulty. Dynamic Programming Consider the problem of the previous lecture (which is -complete): given positive integers , does … Continue reading

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ORF523: P vs. NP, NP-completeness

We are now going to restrict our attention to Boolean functions . Computing a Boolean function is called a decision problem, since we need to decide for whether or not it is in the set . We call such a set … Continue reading

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