# Author Archives: Sebastien Bubeck

## 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

## The entropic barrier: a simple and optimal universal self-concordant barrier

Ronen Eldan and I have just uploaded our new paper on the arxiv (it should appear tomorrow, for the moment you can see it here). The abstract reads as follows: We prove that the Fenchel dual of the log-Laplace transform … Continue reading

## What’s the (hi)story of my network?

First an announcement: we have researcher and postdoc positions available in Theory Group at MSR, and I may have a position for an intern in the summer. If you are a talented young mathematician with interests in the kind of … Continue reading

## 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

## 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

## 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

## Theory of Convex Optimization for Machine Learning

I am extremely happy to release the first draft of my monograph based on the lecture notes published last year on this blog. (Comments on the draft are welcome!) The abstract reads as follows: This monograph presents the main mathematical … Continue reading

## COLT 2014 accepted papers

The accepted papers for COLT 2014 have just been posted! This year we had a record number of 140 submissions, out of which 52 were accepted (38 for a 20mn presentation and 14 for a 5mn presentation). In my opinion … Continue reading

## On the influence of the seed graph in the preferential attachment model

The preferential attachment model, introduced in 1992 by Mahmoud and popularized in 1999 by Barabási and Albert, has attracted a lot of attention in the last decade. In its simplest form it describes the evolution of a random tree. Formally we denote by … Continue reading

## Nesterov’s Accelerated Gradient Descent for Smooth and Strongly Convex Optimization

About a year ago I described Nesterov’s Accelerated Gradient Descent in the context of smooth optimization. As I mentioned previously this has been by far the most popular post on this blog. Today I have decided to revisit this post to give a … Continue reading