Archive for the University life Category

ABC with path signatures [One World ABC seminar, 2/2/23]

Posted in Books, pictures, Running, Statistics, Travel, University life with tags , , , , , , , on January 29, 2023 by xi'an

The next One World ABC seminar is by Joel Dyer (Oxford) at 1:30pm (UK time) on 02 February.

Title: Approximate Bayesian Computation with Path Signatures

Abstract: Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation (ABC) generates likelihood-free posterior samples by comparing simulated and observed data through some distance measure, but existing approaches are often poorly suited to time series simulators, for example due to an independent and identically distributed data assumption. In this talk, we will discuss our work on the use of path signatures in ABC as a means to handling the sequential nature of time series data of different kinds. We will begin by discussing popular approaches to ABC and how they may be extended to time series simulators. We will then introduce path signatures, and discuss how signatures naturally lead to two instances of ABC for time series simulators. Finally, we will demonstrate that the resulting signature-based ABC procedures can produce competitive Bayesian parameter inference for simulators generating univariate, multivariate, irregularly spaced, and even non-Euclidean sequences.

Reference: J. Dyer, P. Cannon, S. M Schmon (2022). Approximate Bayesian Computation with Path Signatures. arXiv preprint 2106.12555

latest math stats exam

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , , , , on January 28, 2023 by xi'an

As I finished grading our undergrad math stats exam (in Paris Dauphine) over the weekend, which was very straightforward this year, the more because most questions had already been asked on weekly quizzes or during practicals, some answers stroke me as atypical (but ChatGPT is not to blame!). For instance, in question 1, (c) received a fair share of wrong eliminations as g not being necessarily bounded. Rather than being contradicted by (b) being false. (ChatGPT managed to solve that question, except for the L² convergence!)

Question 2 was much less successful than we expected, most failures due to a catastrophic change of parameterisation for computing the mgf that could have been ignored given this is a Bernoulli model, right?! Although the students wasted quite a while computing the Fisher information for the Binomial distribution in Question 3… (ChatGPT managed to solve that question!)

Question 4 was intentionally confusing and while most (of those who dealt with the R questions) spotted the opposition between sample and distribution, hence picking (f), a few fell into the trap (d).

Question 7 was also surprisingly incompletely covered by a significant fraction of the students, as they missed the sufficiency in (c). (ChatGPT did not manage to solve that question, starting with the inverted statement that “a minimal sufficient statistic is a sufficient statistic that is not a function of any other sufficient statistic”…)

And Question 8 was rarely complete, even though many recalled Basu’s theorem for (a) [more rarely (d)] and flunked (c). A large chunk of them argued that the ancilarity of statistics in (a) and (d) made them [distributionally] independent of μ, therefore [probabilistically] of the empirical mean! (Again flunked by ChatGPT, confusing completeness and sufficiency.)

séminaire parisien de statistique [09/01/23]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , on January 22, 2023 by xi'an

I had missed the séminaire parisien de statistique for most of the Fall semester, hence was determined to attend the first session of the year 2023, the more because the talks were close to my interest. To wit, Chiara Amorino spoke about particle systems for McKean-Vlasov SDEs, when those are parameterised by several parameters, when observing repeatedly discretised versions, hereby establishing the consistence of a contrast estimator of these estimators. I was initially confused by the mention of interacting particles, since the work is not at all about related with simulation. Just wondering whether this contrast could prove useful for a likelihood-free approach in building a Gibbs distribution?

Valentin de Bortoli then spoke on diffusion Schrödinger bridges for generative models, which allowed me to better my understanding of this idea presented by Arnaud at the Flatiron workshop last November. The presentation here was quite different, using a forward versus backward explanation via a sequence of transforms that end up approximately Gaussian, once more reminiscent of sequential Monte Carlo. The transforms are themselves approximate Gaussian versions relying on adiscretised Ornstein-Ulhenbeck process, with a missing score term since said score involves a marginal density at each step of the sequence. It can be represented [as below] as an expectation conditional on the (observed) variate at time zero (with a connection with Hyvärinen’s NCE / score matching!) Practical implementation is done via neural networks.

Last but not least!, my friend Randal talked about his Kick-Kac formula, which connects with the one we considered in our 2004 paper with Jim Hobert. While I had heard earlier version, this talk was mostly on probability aspects and highly enjoyable as he included some short proofs. The formula is expressing the stationary probability measure π of the original Markov chain in terms of explorations between two visits to an accessible set C, more general than a small set. With at first an annoying remaining term due to the set not being Harris recurrent but which eventually cancels out. Memoryless transportation can be implemented because C is free for the picking, for instance the set where the target is bounded by a manageable density, allowing for an accept-reject step. The resulting chain is non-reversible. However, due to the difficulty to simulate from the target restricted to C, a second and parallel Markov chain is instead created. Performances, unsurprisingly, depend on the choice of C, but it can be adapted to the target on the go.

MCMC postdoc positions at Bocconi

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , , on January 17, 2023 by xi'an

[A call for postdoc candidates to work in Milano with Giacomo Zanella in the coming years under ERC funding. In case you are interested with a postdoctoral position with me at Paris Dauphine on multi-agent decision-making, data sharing, and fusion algorithms, do not hesitate to contact me, the official call for applications should come up soon!]

Three postdoc positions available at Bocconi University (Milan, Italy), under the supervision of Giacomo Zanella and funded by the ERC Starting Grant “Provable Scalability for high-dimensional Bayesian Learning”. Details and links to apply available online.

The deadline for application is 28/02/2023 and the planned starting date is 01/05/2023 (with some flexibility). Initial contracts are for 1 year and are extendable for further years under mutual agreement.

Candidates will conduct research on computational aspects of statistical and machine learning methods, with a particular focus on Bayesian methodologies. The research activity, both in terms of specific topic and research approach, can adapt to the profile and interests of the successful candidates. Beyond working with the supervisor and coauthors on topics related to the grant project (see here and there for more details on the research topics of the supervisor and grant project), candidates will get the chance to interact with various faculty members, postdocs and PhD students of the Stats&ML group at Bocconi (see e.g. researchers at Bocconi).

Interested candidates can write to giacomo zanella at unibocconi for more information about the positions.

recommendation letters

Posted in Kids, University life, pictures with tags , , , , , on January 14, 2023 by xi'an

Another spam from China [hence an opportunity to repost this 2012 shot of the Huangpu River from the Bund!] worth mentioning:

It’s Jesse from XXX. XXX mainly provides services for students need apply universities. We wish to get your recommendation letter for our students. We will give you about 10,000 USD as reward per month for your recommendation. The content of the recommendation letters can be further discussed with you.

While it is tempting (!!) to considerably increase my salary (!), the spirit of this proposal is most appalling, either because it is genuine or because it is a scam capitalising on the greed of its victims.

%d bloggers like this: