## data assimilation and reduced modelling for high-D problems [CIRM]

Posted in Books, Kids, Mountains, pictures, Running, Statistics, University life with tags , , , , , , , , , , , , , , , , , on February 8, 2021 by xi'an

Next summer, from 19 July till 27 August, there will be a six week program at CIRM on the above theme, bringing together scientists from both the academic and industrial communities. The program includes a one-week summer school followed by 5 weeks of research sessions on projects proposed by academic and industrial partners.

Confirmed speakers of the summer school (Jul 19-23) are:

• Albert Cohen (Sorbonne University)
• Masoumeh Dashti (University of Sussex)
• Eric Moulines (Ecole Polytechnique)
• Anthony Nouy (Ecole Centrale de Nantes)
• Claudia Schillings (Mannheim University)

Junior participants may apply for fellowships to cover part or the whole stay. Registration and application to fellowships will be open soon.

## Fermat’s Riddle

Posted in Books, Kids, R with tags , , , , , , , , , , on October 16, 2020 by xi'an

·A Fermat-like riddle from the Riddler (with enough room to code on the margin)

An  arbitrary positive integer N is to be written as a difference of two distinct positive integers. What are the impossible cases and else can you provide a list of all distinct representations?

Since the problem amounts to finding a>b>0 such that

$N=a^2-b^2=(a-b)(a+b)$

both (a+b) and (a-b) are products of some of the prime factors in the decomposition of N and both terms must have the same parity for the average a to be an integer. This eliminates decompositions with a single prime factor 2 (and N=1). For other cases, the following R code (which I could not deposit on tio.run because of the packages R.utils!) returns a list

library(R.utils)
library(numbers)
bitz<-function(i,m) #int2bits
c(rev(as.binary(i)),rep(0,m))[1:m]
ridl=function(n){
a=primeFactors(n)
if((n==1)|(sum(a==2)==1)){
print("impossible")}else{
m=length(a);g=NULL
for(i in 1:2^m){
b=bitz(i,m)
if(((d<-prod(a[!!b]))%%2==(e<-prod(a[!b]))%%2)&(d<e))
g=rbind(g,c(k<-(e+d)/2,l<-(e-d)/2))}
return(g[!duplicated(g[,1]-g[,2]),])}}


For instance,

> ridl(1456)
[,1] [,2]
[1,]  365  363
[2,]  184  180
[3,]   95   87
[4,]   59   45
[5,]   40   12
[6,]   41   15


Checking for the most prolific N, up to 10⁶, I found that N=6720=2⁶·3·5·7 produces 20 different decompositions. And that N=887,040=2⁸·3²·5·7·11 leads to 84 distinct differences of squares.

## another easy Riddler

Posted in Books, Kids, R with tags , , , , on January 31, 2020 by xi'an

A quick riddle from the Riddler

In a two-person game, Abigail and Zian both choose between a and z. Abigail win one point with probability .9 if they choose (a,a) and with probability 1 if they choose (a,z), and two points with probability .4 if they choose (z,z) and with probability .6 if they choose (z,a). Find the optimal probabilities δ and ς of choosing a for both Abigail and Zian when δ is known to Zian.

Since the average gain for Abigail is δ(1-.1ς)+2(1-δ)(.4+.2ς) the riddle sums up as solving the minmax problem

$\max_\delta \min_\varsigma\delta(1-.1\varsigma)+2(1-\delta)(.4+.2\varsigma)$

the solution in ς is either 0 or 1 depending on δ being smaller or larger than 12/22, which leads to this value as the expected gain. The saddlepoint is hardly visible in the above image. While ς is either 0 or 1 in the optimal setting,  a constant choice of 1 or 0 would modify the optimal for δ except that Abigail must declare her value of δ!

## AABI9 tidbits [& misbits]

Posted in Books, Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , on December 10, 2019 by xi'an

Today’s Advances in Approximate Bayesian Inference symposium, organised by Thang Bui, Adji Bousso Dieng, Dawen Liang, Francisco Ruiz, and Cheng Zhang, took place in front of Vancouver Harbour (and the tentalising ski slope at the back) and saw more than 400 participants, drifting away from the earlier versions which had a stronger dose of ABC and much fewer participants. There were students’ talks in a fair proportion, as well (and a massive number of posters). As of below, I took some notes during some of the talks with no pretense at exhaustivity, objectivity or accuracy. (This is a blog post, remember?!) Overall I found the day exciting (to the point I did not suffer at all from the usal naps consecutive to very short nights!) and engaging, with a lot of notions and methods I had never heard about. (Which shows how much I know nothing!)

The fourth talk was by Sergey Levine, Reinforcement Learning, Optimal , Control, and Probabilistic Inference, back to Kullback-Leibler as the objective function, with linkage to optimal control (with distributions as actions?), plus again variational inference, producing an approximation in sequential settings. This sounded like a type of return of the MaxEnt prior, but the talk pace was so intense that I could not follow where the innovations stood.

The fifth talk was by Iuliia Molchanova, on Structured Semi-Implicit Variational Inference, from BAyesgroup.ru (I did not know of a Bayesian group in Russia!, as I was under the impression that Bayesian statistics were under-represented there, but apparently the situation is quite different in machine learning.) The talk brought an interesting concept of semi-implicit variational inference, exploiting some form of latent variables as far as I can understand, using mixtures of Gaussians.

The sixth talk was by Rianne van den Berg, Normalizing Flows for Discrete Data, and amounted to covering three papers also discussed in NeurIPS 2019 proper, which I found somewhat of a suboptimal approach to an invited talk, as it turned into a teaser for following talks or posters. But the teasers it contained were quite interesting as they covered normalising flows as integer valued controlled changes of variables using neural networks about which I had just became aware during the poster session, in connection with papers of Papamakarios et al., which I need to soon read.

The seventh talk was by Matthew Hoffman: Langevin Dynamics as Nonparametric Variational Inference, and sounded most interesting, both from title and later reports, as it was bridging Langevin with VI, but I alas missed it for being “stuck” in a tea-house ceremony that lasted much longer than expected. (More later on that side issue!)

After the second poster session (with a highly original proposal by Radford Neal towards creating  non-reversibility at the level of the uniform generator rather than later on), I thus only attended Emily Fox’s Stochastic Gradient MCMC for Sequential Data Sources, which superbly reviewed (in connection with a sequence of papers, including a recent one by Aicher et al.) error rate and convergence properties of stochastic gradient estimator methods there. Another paper I need to soon read!

The one before last speaker, Roman Novak, exposed a Python library about infinite neural networks, for which I had no direct connection (and talks I have always difficulties about libraries, even without a four hour sleep night) and the symposium concluded with a mild round-table. Mild because Frank Wood’s best efforts (and healthy skepticism about round tables!) to initiate controversies, we could not see much to bite from each other’s viewpoint.

## stochastic magnetic bits, simulated annealing and Gibbs sampling

Posted in Statistics with tags , , , , , , , , , on October 17, 2019 by xi'an

A paper by Borders et al. in the 19 September issue of Nature offers an interesting mix of computing and electronics and optimisation. With two preparatory tribunes! One [rather overdone] on Feynman’s quest. As a possible alternative to quantum computers for creating probabilistic bits. And making machine learning (as an optimisation program) more efficient. And another one explaining more clearly what is in the paper. As well as the practical advantage of the approach over quantum computing. As for the paper itself, the part I understood about factorising an integer F via minimising the squared difference between a product of two integers and F and using simulated annealing sounded rather easy, while the part I did not about constructing a semi-conductor implementing this stochastic search sounded too technical (especially in the métro during rush hour). Even after checking the on-line supplementary material. Interestingly, the paper claims for higher efficiency thanks to asynchronicity than a regular Gibbs simulation of Boltzman machines, quoting Roberts and Sahu (1997) without further explanation and possibly out of context (as the latter is not concerned with optimisation).