The statistician, econometrician, macro- and micro-economist, Edmond Malinvaud died on Saturday, March 7. He had been director of my alma mater ENSAE (1962–1966), directeur de la Prévision at the Finance Department (1972–1974), director of INSEE (1974–1987), and Professeur at Collège de France (1988–1993). While primarily an economist, with his theories of disequilibrium and unemployment, reflected in his famous book Théorie macro-économique (1981) that he taught us at ENSAE, he was also instrumental in shaping the French econometrics school, see his equally famous Statistical Methods of Econometrics (1970), and in the reorganisation of INSEE as the post-war State census and economic planning tool. He was also an honorary Fellow of the Royal Statistical Society and the 1981 president of the International Institute of Statistics. Edmond Malinvaud studied under Maurice Allais, Nobel Prize in economics in 1988, and was himself considered as a potential Nobel for several years. My personal memories of him at ENSAE and CREST are of a very clear teacher and of a kind and considerate man, with the reserve and style of a now-bygone era…
Archive for CREST
There is an opening at the Statistics School ENSAE for a Statistics associate or full professor position, starting on September 2015. Currently located on the South-West boundary of Paris, the school is soon to move to the mega-campus of Paris Saclay, near École Polytechnique, along with a dozen other schools. See this description of the position. The deadline is very close, March 23!
When Andrew was in Paris, we discussed at length about using EP for handling big datasets in a different way than running parallel MCMC. A related preprint came out on arXiv a few days ago, with an introduction on Andrews’ blog. (Not written two months in advance as most of his entries!)
The major argument in using EP in a large data setting is that the approximation to the true posterior can be build using one part of the data at a time and thus avoids handling the entire likelihood function. Nonetheless, I still remain mostly agnostic about using EP and a seminar this morning at CREST by Guillaume Dehaene and Simon Barthelmé (re)generated self-interrogations about the method that hopefully can be exploited towards the future version of the paper.
One of the major difficulties I have with EP is about the nature of the resulting approximation. Since it is chosen out of a “nice” family of distributions, presumably restricted to an exponential family, the optimal approximation will remain within this family, which further makes EP sound like a specific variational Bayes method since the goal is to find the family member the closest to the posterior in terms of Kullback-Leibler divergence. (Except that the divergence is the opposite one.) I remain uncertain about what to do with the resulting solution, as the algorithm does not tell me how close this solution will be from the true posterior. Unless one can use it as a pseudo-distribution for indirect inference (a.k.a., ABC)..?
Another thing that became clear during this seminar is that the decomposition of the target as a product is completely arbitrary, i.e., does not correspond to an feature of the target other than the later being the product of those components. Hence, the EP partition could be adapted or even optimised within the algorithm. Similarly, the parametrisation could be optimised towards a “more Gaussian” posterior. This is something that makes EP both exciting as opening many avenues for experimentation and fuzzy as its perceived lack of goal makes comparing approaches delicate. For instance, using MCMC or HMC steps to estimate the parameters of the tilted distribution is quite natural in complex settings but the impact of the additional approximation must be gauged against the overall purpose of the approach.
As posted a few days ago, Mathieu Gerber and Nicolas Chopin will read this afternoon a Paper to the Royal Statistical Society on their sequential quasi-Monte Carlo sampling paper. Here are some comments on the paper that are preliminaries to my written discussion (to be sent before the slightly awkward deadline of Jan 2, 2015).
Quasi-Monte Carlo methods are definitely not popular within the (mainstream) statistical community, despite regular attempts by respected researchers like Art Owen and Pierre L’Écuyer to induce more use of those methods. It is thus to be hoped that the current attempt will be more successful, it being Read to the Royal Statistical Society being a major step towards a wide diffusion. I am looking forward to the collection of discussions that will result from the incoming afternoon (and bemoan once again having to miss it!).
“It is also the resampling step that makes the introduction of QMC into SMC sampling non-trivial.” (p.3)
At a mathematical level, the fact that randomised low discrepancy sequences produce both unbiased estimators and error rates of order
means that randomised quasi-Monte Carlo methods should always be used, instead of regular Monte Carlo methods! So why is it not always used?! The difficulty stands [I think] in expressing the Monte Carlo estimators in terms of a deterministic function of a fixed number of uniforms (and possibly of past simulated values). At least this is why I never attempted at crossing the Rubicon into the quasi-Monte Carlo realm… And maybe also why the step had to appear in connection with particle filters, which can be seen as dynamic importance sampling methods and hence enjoy a local iid-ness that relates better to quasi-Monte Carlo integrators than single-chain MCMC algorithms. For instance, each resampling step in a particle filter consists in a repeated multinomial generation, hence should have been turned into quasi-Monte Carlo ages ago. (However, rather than the basic solution drafted in Table 2, lower variance solutions like systematic and residual sampling have been proposed in the particle literature and I wonder if any of these is a special form of quasi-Monte Carlo.) In the present setting, the authors move further and apply quasi-Monte Carlo to the particles themselves. However, they still assume the deterministic transform
which the q-block on which I stumbled each time I contemplated quasi-Monte Carlo… So the fundamental difficulty with the whole proposal is that the generation from the Markov proposal
has to be of the above form. Is the strength of this assumption discussed anywhere in the paper? All baseline distributions there are normal. And in the case it does not easily apply, what would the gain bw in only using the second step (i.e., quasi-Monte Carlo-ing the multinomial simulation from the empirical cdf)? In a sequential setting with unknown parameters θ, the transform is modified each time θ is modified and I wonder at the impact on computing cost if the inverse cdf is not available analytically. And I presume simulating the θ’s cannot benefit from quasi-Monte Carlo improvements.
The paper obviously cannot get into every detail, obviously, but I would also welcome indications on the cost of deriving the Hilbert curve, in particular in connection with the dimension d as it has to separate all of the N particles, and on the stopping rule on m that means only Hm is used.
Another question stands with the multiplicity of low discrepancy sequences and their impact on the overall convergence. If Art Owen’s (1997) nested scrambling leads to the best rate, as implied by Theorem 7, why should we ever consider another choice?
In connection with Lemma 1 and the sequential quasi-Monte Carlo approximation of the evidence, I wonder at any possible Rao-Blackwellisation using all proposed moves rather than only those accepted. I mean, from a quasi-Monte Carlo viewpoint, is Rao-Blackwellisation easier and is it of any significant interest?
What are the computing costs and gains for forward and backward sampling? They are not discussed there. I also fail to understand the trick at the end of 4.2.1, using SQMC on a single vector instead of (t+1) of them. Again assuming inverse cdfs are available? Any connection with the Polson et al.’s particle learning literature?
Last questions: what is the (learning) effort for lazy me to move to SQMC? Any hope of stepping outside particle filtering?
On December 4-5, Université Paris-Dauphine will host the 6th French Econometric Conference, which celebrates Christian Gouriéroux and his contributions to econometrics. (Christian was my statistics professor during my graduate years at ENSAE and then Head of CREST when I joined this research unit, first as a PhD student and later as Head of the statistics group. And he has always been a tremendous support for me.)
Not only is the program quite impressive, with co-authors of Christian Gouriéroux and a few Nobel laureates (if not the latest, Jean Tirole, who taught economics at ENSAE when I was a student there), but registration is free. I will most definitely attend the talks, as I am in Paris-Dauphine at this time of year (the week before NIPS). In particular, looking forward to Gallant’s views on Bayesian statistics.
Here is a call from ENSAE about two positions in statistics/machine learning, starting next semester:
ENSAE ParisTech and CREST is currently inviting applications for one position at the level associate or full professor from outstanding candidates having demonstrated abilities in both research and teaching. We are interested in candidates with a Ph.D. in Statistics or Machine Learning (or related field) whose research interests are in high dimensional statistical inference, learning theory or statistics of networks.
The appointment could begin as soon as September 1, 2014. The position is for an initial three-year term, with a possible renewal option in case of positive evaluation of research and teaching activities. Salary for suitably qualified applicants is competitive and commensurate with experience. The deadline for application is May 19, 2014. Full details are given here for the first position and there for the second position.