A call for contribution to the 3rd Conference on Geometric Science of Information that I was asked to advertise. (I would have used Sciences instead of Science.) With a nice background picture related to Adelard de Bath, who among other things in natural philosophy introduced the Hindu-Arabic numerals in Europe [and later to America, even though the use of Arabic numerals there may soon come to an end]. And which Latin translation of Euclid’s Elements includes the above picture. The conference is on November 7-9, 2017, in the centre of Paris (Écoles de Mines, next to Luxembourg). (As I cannot spot the registration rates of that conference on the website, I cannot at this stage bring full support to the conference!)
Archive for Paris
For a rather convoluted reason, I happened to visit the Brain and Spine Institute (ICM, Institut du Cerveau et de la Moelle Épinière) yesterday, in Paris, within the Pitié-Salpétrière Hospital. And saw this row of brains, printed by 3D printers, rather than standing in jars. (Like Abe Normal’s.) Which produced brain shadows, not commonly seen otherwise!
This (whining) post is of little interest to anyone but French runners: last week I ordered a new pair of running shoes as mine had suffered too many kilometres to keep going and came upon a sale offer on 21run.fr that suited my needs. Checking similar offers on other running sites made this sale the best choice and hence I ordered the shoes. As is often the case with running shoes, the size varies with the brand and the pair of Asics I received was too small. Nothing unusual with that, but I then found out that the company is actually located in Germany, despite the website being integrally in French, plus advertising in the Paris métro, which again is not an issue per se, except that it charges returns outside Germany. Meaning that I ended up paying 17% of the overall price just to return shoes that were not my size.
When I worked with Jean-Michel Marin at Institut Henri Poincaré the week before Xmas, there was this framed picture standing on the ground, possibly in preparation for exhibition in the Institute. I found this superposition of the lady cleaning the blackboard from its maths formulas and of the seemingly unaware mathematician both compelling visually in the sheer geometric aesthetics of the act and somewhat appalling in its message. Especially when considering the initiatives taken by IHP towards reducing the gender gap in maths. After inquiring into the issue, I found that this picture was part of a whole photograph exhibit on IHP by Vincent Moncorgé, now published into a book, La Maison des Mathématiques by Villani, Uzan, and Moncorgé. Most pictures are on-line and I found them quite appealing. Except again for the above.
Today, I alas missed a seminar at BiPS on the Zig-Zag (sub-)sampler of Joris Bierkens, Paul Fearnhead and Gareth Roberts, presented here in Paris by James Ridgway. Fortunately for me, I had some discussions with Murray Pollock in Warwick and then again with Changye Wu in Dauphine that shed some light on this complex but highly innovative approach to simulating in Big Data settings thanks to a correct subsampling mechanism.
The zig-zag process runs a continuous process made of segments that turn from one diagonal to the next at random times driven by a generator connected with the components of the gradient of the target log-density. Plus a symmetric term. Provided those random times can be generated, this process is truly available and associated with the right target distribution. When the components of the parameter are independent (an unlikely setting), those random times can be associated with an inhomogeneous Poisson process. In the general case, one needs to bound the gradients by more manageable functions that create a Poisson process that can later be thinned. Next, one needs to simulate the process for the upper bound, a task that seems hard to achieve apart from linear and piecewise constant upper bounds. The process has a bit of a slice sampling taste, except that it cannot be used as a slice sampler but requires continuous time integration, given that the length of each segment matters. (Or maybe random time subsampling?)
A highly innovative part of the paper concentrates on Big Data likelihoods and on the possibility to subsample properly and exactly the original dataset. The authors propose Zig-Zag with subsampling by turning the gradients into random parts of the gradients. While remaining unbiased. There may be a cost associated with this gain of one to n, namely that the upper bounds may turn larger as they handle all elements in the likelihood at once, hence become (even) less efficient. (I am more uncertain about the case of the control variates, as it relies on a Lipschitz assumption.) While I still miss an easy way to implement the approach in a specific model, I remain hopeful for this new approach to make a major dent in the current methodologies!