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On the unreasonable effectiveness of Richardson extrapolation

Posted on March 1, 2020 by Francis Bach

This month, I will follow up on last month’s blog post, and describe classical techniques from numerical analysis that aim at accelerating the convergence of a vector sequence to its limit, by only combining elements of the sequence, and without the detailed knowledge of the iterative process that has led to this sequence. Last month,…

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Are all kernels cursed?

Posted on October 8, 2019October 28, 2019 by Francis Bach

The word “kernel” appears in many areas of science (it is even worse in French with “noyau”); it can have different meanings depending on context (see here for a nice short historical review for mathematics). Within machine learning and statistics, kernels are used in two related but different contexts, with different definitions and some kernels…

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The “η-trick” reloaded: multiple kernel learning

Posted on August 5, 2019August 5, 2019 by Francis Bach

In my previous post, I described various (potentially non-smooth) functions that have quadratic (and thus smooth) variational formulations, a possibility that I referred to as the η-trick. For example, in its simplest formulation, we have \( \displaystyle |w| = \min_{ \eta \geq 0} \frac{1}{2} \frac{w^2}{\eta} + \frac{1}{2} \eta\). While it seems most often used for…

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Recent Posts

  • Unraveling spectral properties of kernel matrices – II
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  • Unraveling spectral properties of kernel matrices – I
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About

I am Francis Bach, a researcher at INRIA in the Computer Science department of Ecole Normale Supérieure, in Paris, France. I have been working on machine learning since 2000, with a focus on algorithmic and theoretical contributions, in particular in optimization. All of my papers can be downloaded from my web page or my Google Scholar page. I also have a Twitter account.

Recent Posts

  • Unraveling spectral properties of kernel matrices – II
  • My book is (at last) out!
  • Scaling laws of optimization
  • Unraveling spectral properties of kernel matrices – I
  • Revisiting the classics: Jensen’s inequality

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  • Francis Bach on Unraveling spectral properties of kernel matrices – I

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