## Bolztmann optimisation as simulating device

Posted in Books, Statistics, University life with tags , , , , , , on June 18, 2020 by xi'an

“The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem” Maddison et al., 2014

I recently learned about the Gumbel-Max “trick” proposed by Chris Maddison, Daniel Tarlow, and Tom Minka in a 2014 NIPS talk. Namely that, to generate from a Boltzmann distribution

$p_j=\frac{\exp\{g_j\}}{\sum_i \exp\{g_i\}}$

is equivalent to adding standard Gumbel noise to the energies and taking the maximum. A rare (?) instance, compared with the reverse of using simulation to reach maxima. Of course, this requires as many simulations as there as terms in the sum. Or a clever way to avoid this exhaustive listing.

“According to Gumbel’s statistics, 326 out of 354 political murders by right-wing factions in the early Weimar Republic went unpunished, and four out of the 22 left-wing capital crimes.” Science News

As an historical aside I discovered Gumbel’s anti-Nazi activism while in Germany in the 1920’s and early 1930’s (until expelled from the University of Heidelberg). Including the 1932 call against Nazis (which Albert Einstein and Heinrich Mann also signed), hence the above poster.

## both sides [no comment]

Posted in Statistics with tags , , , , , , , , , , , , , , , , , on August 28, 2017 by xi'an

“I think there is blame on both sides and I have no doubt about it.” Donald Trump, Aug 15, 2017

“What I condemn is the violence that’s been done by any side, by all sides, in all this.” Jeremy Corbyn, Aug 7, 2017