Archive for HMM

ISBA 2021.3

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on July 1, 2021 by xi'an

Now on the third day which again started early with a 100% local j-ISBA session. (After a group run to and around Mont Puget, my first real run since 2020!!!) With a second round of talks by junior researchers from master to postdoc level. Again well-attended. A talk about Bayesian non-parametric sequential taxinomy by Alessandro Zito used the BayesANT acronym, which reminded me of the new vave group Adam and the Ants I was listening to forty years ago, in case they need a song as well as a logo! (Note that BayesANT is also used for a robot using Bayesian optimisation!) And more generally a wide variety in the themes. Thanks to the j-organisers of this 100% live session!

The next session was on PDMPs, which I helped organise, with Manon Michel speaking from Marseille, exploiting the symmetry around the gradient, which is distribution-free! Then, remotely, Kengo Kamatani, speaking from Tokyo, who expanded the high-dimensional scaling limit to the Zig-Zag sampler, exhibiting an argument against small refreshment rates, and Murray Pollock, from Newcastle, who exposed quite clearly the working principles of the Restore algorithm, including why coupling from the past was available in this setting. A well-attended session despite the early hour (in the USA).

Another session of interest for me [which I attended by myself as everyone else was at lunch in CIRM!] was the contributed C16 on variational and scalable inference that included a talk on hierarchical Monte Carlo fusion (with my friends Gareth and Murray as co-authors), Darren’s call to adopt functional programming in order to save Bayesian computing from extinction, normalising flows for modularisation, and Dennis’ adversarial solutions for Bayesian design, avoiding the computation of the evidence.

Wes Johnson’s lecture was about stories with setting prior distributions based on experts’ opinions. Which reminded me of the short paper Kaniav Kamary and myself wrote about ten years ago, in response to a paper on the topic in the American Statistician. And could not understand the discrepancy between two Bayes factors based on Normal versus Cauchy priors, until I was told they were mistakenly used repeatedly.

Rushing out of dinner, I attended both the non-parametric session (live with Marta and Antonio!) and the high-dimension computational session on Bayesian model choice (mute!). A bit of a schizophrenic moment, but allowing to get a rough picture in both areas. At once. Including an adaptive MCMC scheme for selecting models by Jim Griffin. Which could be run directly over the model space. With my ever-going wondering at the meaning of neighbour models.

ISBA 20.2.21

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , on June 30, 2021 by xi'an

A second day which started earlier and more smoothly with a 100% local j-ISBA session. (Not counting the invigorating swim in Morgiou!) With talks by junior researchers from master to postdoc level, as this ISBA mirror meeting was primarily designed for them, so that they could all present their work, towards gaining more visibility for their research and facilitating more interactions with the participants. CIRM also insisted on this aspect of the workshop, which was well-attended.

I alas had to skip the poster session [and the joys of] despite skipping lunch [BND], due to organisational constraints. Then attended the Approximate Bayesian computation section, including one talk by Geoff Nicholls on confidence estimation for ABC, following upon the talk given by Kate last evening. And one by Florian Maire on learning the bound in accept-reject algorithms on the go, as in Caffo et al. (2002), which I found quite exciting and opening new possibilities, esp. if the Markov chain thus produced can be recycled towards unbiasedness without getting the constant right! For instance, by Rao-Blackwellisation, multiple mixtures, black box importance sampling, whatever. (This also reminded me of the earlier Goffinet et al. 1996.)

Followed by another Bayesian (modeling and) computation session. With my old friend Peter Müller talking about mixture inference with dependent priors (and a saturated colour scheme!), Matteo Ruggieri [who could not make it to CIRM!] on computable Bayesian inference for HMMs. Providing an impressive improvement upon particle filters for approximating the evidence. Also bringing the most realistic Chinese restaurant with conveyor belt! And Ming Yuan Zhou using optimal transport to define distance between distributions. With two different conditional distributions depending on which marginal is first fixed. And a connection with GANs (of course!).

And it was great to watch and listen to my friend Alicia Carriquiry talking on forensic statistics and the case for (or not?!) Bayes factors. And remembering Dennis Lindley. And my friend Jim Berger on frequentism versus Bayes! Consistency seems innocuous as most Bayes procedures are. Empirical coverage is another kind of consistency, isn’t it?

A remark I made when re-typing the program for CIRM is that there are surprisingly few talks about COVID-19 overall, maybe due to the program being mostly set for ISBA 2020 in Kunming. Maybe because we are more cautious than the competition…?!

And, at last, despite a higher density of boars around the CIRM facilities, no one got hurt yesterday! Unless one counts the impact of the French defeat at the Euro 2021 on the football fans here…

interdependent Gibbs samplers

Posted in Books, Statistics, University life with tags , , , , , , on April 27, 2018 by xi'an

Mark Kozdoba and Shie Mannor just arXived a paper on an approach to accelerate a Gibbs sampler. With title “interdependent Gibbs samplers“. In fact, it presents rather strong similarities with our SAME algorithm. More of the same, as Adam Johanssen (Warwick) entitled one of his papers! The paper indeed suggests multiplying replicas of latent variables (e.g., an hidden path for an HMM) in an artificial model. And as in our 2002 paper, with Arnaud Doucet and Simon Godsill, the focus here is on maximum likelihood estimation (of the genuine parameters, not of the latent variables). Along with argument that the resulting pseudo-posterior is akin to a posterior with a powered likelihood. And a link with the EM algorithm. And an HMM application.

“The generative model consist of simply sampling the parameters ,  and then sampling m independent copies of the paths”

If anything this proposal is less appealing than SAME because it aims directly at the powered likelihood, rather than utilising an annealed sequence of powers that allows for a primary exploration of the whole parameter space before entering the trapping vicinity of a mode. Which makes me fail to catch the argument from the authors that this improves Gibbs sampling, as a more acute mode has on the opposite the dangerous feature of preventing visits to other modes. Hence the relevance to resort to some form of annealing.

As already mused upon in earlier posts, I find it most amazing that this technique has been re-discovered so many times, both in statistics and in adjacent fields. The idea of powering the likelihood with independent copies of the latent variables is obviously natural (since a version pops up every other year, always under a different name), but earlier versions should eventually saturate the market!

Sampling latent states for high-dimensional non-linear state space models with the embedded HMM method

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , on March 17, 2016 by xi'an

IMG_19390Previously, I posted a comment on a paper by Alex Shestopaloff and Radford Neal, after my visit to Toronto two years ago, using a particular version of ensemble Monte Carlo. A new paper by the same authors was recently arXived, as an refinement of the embedded HMM paper of Neal (2003), in that the authors propose a new and more efficient way to generate from the (artificial) embedded hidden Markov sampler that is central to their technique of propagating a set of pool states. The method exploits both forward and backward representations of HMMs in an alternating manner. And propagates the pool states from one observation time to the next. The paper also exploits latent Gaussian structures to make autoregressive proposals, as well as flip proposals from x to -x [which seem to only make sense when 0 is a central value for the target, i.e. when the observables y only depend on |x|]. All those modifications bring the proposal quite close to (backward) particle Gibbs, the difference being in using Metropolis rather than importance steps. And in an improvement brought by the embedded HMM approach, even though it is always delicate to generalise those comparisons when some amount of calibration is required by both algorithms under comparison. (Especially delicate when it is rather remote from my area of expertise!) Anyway, I am still intrigued [in a positive way] by the embedded HMM idea as it remains mysterious that a finite length HMM simulation can improve the convergence performances that much. And wonder at a potential connection with an earlier paper of Anthony Lee and Krys Latuszynski using a random number of auxiliary variables. Presumably a wrong impression from a superficial memory…

¼th i-like workshop in St. Anne’s College, Oxford

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on March 27, 2014 by xi'an

IMG_0153Due to my previous travelling to and from Nottingham for the seminar and back home early enough to avoid the dreary evening trains from Roissy airport (no luck there, even at 8pm, the RER train was not operating efficiently!, and no fast lane is planed prior to 2023…), I did not see many talks at the i-like workshop. About ¼th, roughly… I even missed the poster session (and the most attractive title of Lazy ABC by Dennis Prangle) thanks to another dreary train ride from Derby to Oxford.

IMG_0150As it happened I had already heard or read parts of the talks in the Friday morning session, but this made understanding them better. As in Banff, Paul Fearnhead‘s talk on reparameterisations for pMCMC on hidden Markov models opened a wide door to possible experiments on those algorithms. The examples in the talk were mostly of the parameter duplication type, somewhat creating unidentifiability to decrease correlation, but I also wondered at the possibility of introducing frequent replicas of the hidden chain in order to fight degeneracy. Then Sumeet Singh gave a talk on the convergence properties of noisy ABC for approximate MLE. Although I had read some of the papers behind the talk, it made me realise how keeping balls around each observation in the ABC acceptance step was not leading to extinction as the number of observations increased. (Summet also had a good line with his ABCDE algorithm, standing for ABC done exactly!) Anthony Lee covered his joint work with Krys Łatuszyński on the ergodicity conditions on the ABC-MCMC algorithm, the only positive case being the 1-hit algorithm as discussed in an earlier post. This result will hopefully get more publicity, as I frequently read that increasing the number of pseudo-samples has no clear impact on the ABC approximation. Krys Łatuszyński concluded the morning with an aggregate of the various results he and his co-authors had obtained on the fascinating Bernoulli factory. Including constructive derivations.

After a few discussions on and around research topics, it was too soon time to take advantage of the grand finale of a March shower to walk from St. Anne’s College to Oxford Station, in order to start the trip back home. I was lucky enough to find a seat and could start experimenting in R the new idea my trip to Nottingham had raised! While discussing a wee bit with my neighbour, a delightful old lady from the New Forest travelling to Coventry, recovering from a brain seizure, wondering about my LaTeX code syntax despite the tiny fonts, and who most suddenly popped a small screen from her bag to start playing Candy Crush!, apologizing all the same. The overall trip was just long enough for my R code to validate this idea of mine, making this week in England quite a profitable one!!! IMG_0145