Archive for Read paper

scalable Langevin exact algorithm [armchair Read Paper]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on June 26, 2020 by xi'an

So, Murray Pollock, Paul Fearnhead, Adam M. Johansen and Gareth O. Roberts presented their Read Paper with discussions on the Wednesday aft! With a well-sized if virtual audience of nearly a hundred people. Here are a few notes scribbled during the Readings. And attempts at keeping the traditional structure of the meeting alive.

In their introduction, they gave the intuition of a quasi-stationary chain as the probability to be in A at time t while still alice as π(A) x exp(-λt) for a fixed killing rate λ. The concept is quite fascinating if less straightforward than stationarity! The presentation put the stress on the available recourse to an unbiased estimator of the κ rate whose initialisation scaled as O(n) but allowed a subsampling cost reduction afterwards. With a subsampling rat connected with Bayesian asymptotics, namely on how quickly the posterior concentrates. Unfortunately, this makes the practical construction harder, since n is finite and the concentration rate is unknown (although a default guess should be √n). I wondered if the link with self-avoiding random walks was more than historical.

The initialisation of the method remains a challenge in complex environments. And hence one may wonder if and how better it does when compared with SMC. Furthermore, while the motivation for using a Brownian motion stems from the practical side, this simulation does not account for the target π. This completely blind excursion sounds worse than simulating from the prior in other settings.

One early illustration for quasi stationarity was based on an hypothetical distribution of lions and wandering (Brownian) antelopes. I found that the associated concept of soft killing was not necessarily well received by …. the antelopes!

As it happens, my friend and coauthor Natesh Pillai was the first discussant! I did no not get the details of his first bimodal example. But he addressed my earlier question about how large the running time T should be. Since the computational cost should be exploding with T. He also drew a analogy with improper posteriors as to wonder about the availability of convergence assessment.

And my friend and coauthor Nicolas Chopin was the second discussant! Starting with a request to… leave the Pima Indians (model)  alone!! But also getting into a deeper assessment of the alternative use of SMCs.

scalable Langevin exact algorithm [Read Paper]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , on June 23, 2020 by xi'an

Murray Pollock, Paul Fearnhead, Adam M. Johansen and Gareth O. Roberts (CoI: all with whom I have strong professional and personal connections!) have a Read Paper discussion happening tomorrow [under relaxed lockdown conditions in the UK, except for the absurd quatorzine on all travelers|, but still in a virtual format] that we discussed together [from our respective homes] at Paris Dauphine. And which I already discussed on this blog when it first came out.

Here are quotes I spotted during this virtual Dauphine discussion but we did not come up with enough material to build a significant discussion, although wondering at the potential for solving the O(n) bottleneck, handling doubly intractable cases like the Ising model. And noticing the nice features of the log target being estimable by unbiased estimators. And of using control variates, for once well-justified in a non-trivial environment.

“However, in practice this simple idea is unlikely to work. We can see this most clearly with the rejection sampler, as the probability of survival will decrease exponentially with t—and thus the rejection probability will often be prohibitively large.”

“This can be viewed as a rejection sampler to simulate from μ(x,t), the distribution of the Brownian motion at time  t conditional on its surviving to time t. Any realization that has been killed is ‘rejected’ and a realization that is not killed is a draw from μ(x,t). It is easy to construct an importance sampling version of this rejection sampler.”

unbiased MCMC discussed at the RSS tomorrow night

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

The paper ‘Unbiased Markov chain Monte Carlo methods with couplings’ by Pierre Jacob et al. will be discussed (or Read) tomorrow at the Royal Statistical Society, 12 Errol Street, London, tomorrow night, Wed 11 December, at 5pm London time. With a pre-discussion session at 3pm, involving Chris Sherlock and Pierre Jacob, and chaired by Ioanna Manolopoulou. While I will alas miss this opportunity, due to my trip to Vancouver over the weekend, it is great that that the young tradition of pre-discussion sessions has been rekindled as it helps put the paper into perspective for a wider audience and thus makes the more formal Read Paper session more profitable. As we discussed the paper in Paris Dauphine with our graduate students a few weeks ago, we will for certain send one or several written discussions to Series B!

No review this summer

Posted in Books, Statistics, University life with tags , , , , , , , , on September 19, 2019 by xi'an

A recent editorial in Nature was a declaration by a biologist from UCL on her refusal to accept refereeing requests during the summer (or was it the summer break), which was motivated by a need to reconnect with her son. Which is a good enough reason (!), but reflects sadly on the increasing pressure on one’s schedule to juggle teaching, research, administration, grant hunting, society service, along with a balanced enough family life. (Although I have been rather privileged in this regard!) Given that refereeing or journal editing is neither visible nor rewarded, it comes as the first task to be postponed or abandoned, even though most of us realise it is essential to keep science working as a whole and to make our own papers published. I have actually noticed an increasing difficulty in the past decade to get (good) referees to accept new reviews, often asking for deadlines that are hurting the authors, like six months. Making them practically unavailable. As I mentioned earlier on this blog, it could be that publishing referees’ reports as discussions would help, since they would become recognised as (unreviewed!) publications, but it is unclear this is the solution. If judging from the similar difficulty in getting discussions for discussed papers. (As an aside, there are two exciting papers coming up for discussion in Series B, ‘Unbiased Markov chain Monte Carlo methods with couplings’ by  Pierre E. Jacob, John O’Leary and Yves F. Atchadé and in Bayesian Analysis, Latent nested nonparametric priors by Frederico Camerlenghi, David Dunson, Antonio Lijoi, Igor Prünster, and Abel Rodríguez). Which is surprising when considering the willingness of a part of the community to engage into forii discussions, sometimes of a considerable length as illustrated on Andrew’s blog.

Another entry in Nature mentioned the case of two University of København tenured professors in geology who were fired for either using a private email address (?!) or being away on field work during an exam and at a conference without permission from the administration. Which does not even remotely sound like a faulty behaviour to me or else I would have been fired eons ago..!

O’Bayes 19/2

Posted in Books, pictures, Running, Travel, University life with tags , , , , , , , , , , , , , , , , , on July 1, 2019 by xi'an

One talk on Day 2 of O’Bayes 2019 was by Ryan Martin on data dependent priors (or “priors”). Which I have already discussed in this blog. Including the notion of a Gibbs posterior about quantities that “are not always defined through a model” [which is debatable if one sees it like part of a semi-parametric model]. Gibbs posterior that is built through a pseudo-likelihood constructed from the empirical risk, which reminds me of Bissiri, Holmes and Walker. Although requiring a prior on this quantity that is  not part of a model. And is not necessarily a true posterior and not necessarily with the same concentration rate as a true posterior. Constructing a data-dependent distribution on the parameter does not necessarily mean an interesting inference and to keep up with the theme of the conference has no automated claim to [more] “objectivity”.

And after calling a prior both Beauty and The Beast!, Erlis Ruli argued about a “bias-reduction” prior where the prior is solution to a differential equation related with some cumulants, connected with an earlier work of David Firth (Warwick).  An interesting conundrum is how to create an MCMC algorithm when the prior is that intractable, with a possible help from PDMP techniques like the Zig-Zag sampler.

While Peter Orbanz’ talk was centred on a central limit theorem under group invariance, further penalised by being the last of the (sun) day, Peter did a magnificent job of presenting the result and motivating each term. It reminded me of the work Jim Bondar was doing in Ottawa in the 1980’s on Haar measures for Bayesian inference. Including the notion of amenability [a term due to von Neumann] I had not met since then. (Neither have I met Jim since the last summer I spent in Carleton.) The CLT and associated LLN are remarkable in that the average is not over observations but over shifts of the same observation under elements of a sub-group of transformations. I wondered as well at the potential connection with the Read Paper of Kong et al. in 2003 on the use of group averaging for Monte Carlo integration [connection apart from the fact that both discussants, Michael Evans and myself, are present at this conference].