Archive for Helsinki

deep and embarrassingly parallel MCMC

Posted in Books, pictures, Statistics with tags , , , , , , , on April 9, 2019 by xi'an

Diego Mesquita, Paul Blomstedt, and Samuel Kaski (from Helsinki, like the above picture) just arXived a paper on embarrassingly parallel MCMC. Following a series of papers discussed on this ‘og in the past. They use a deep learning approach of Dinh et al. (2017) to the computation of the probability density of a convoluted and non-volume-preserving transform of a given random variable to turn multiple samples from sub-posteriors [corresponding to the k k-th roots of the true posterior] into a sample from the true posterior. If I understand correctly the argument [on page 4], the deep neural network provides a density estimate that apparently does better than traditional non-parametric density estimates. Maybe by being more efficient than a Parzen-Rosenblat estimator which is of order the number of simulations… For any value of θ, the estimate of the true target is the product of these estimates and for a value of θ simulated from one of the subposteriors an importance weight naturally ensues. However, for a one-dimensional transform of θ, h(θ), I would prefer estimating first the density of h(θ) for each sample and then construct an importance weight. If only to avoid the curse of dimension.

On various benchmarks, like the banana-shaped 2D target above, the proposed method (NAP) does better. Even in relatively high dimensions. Given that the overall computing times are not produced, with only the calibration that the same number of subsamples were produced for all methods, it would be interesting to test the same performances on even higher dimensions and larger population sizes.

a new rule for adaptive importance sampling

Posted in Books, Statistics with tags , , , , , , , , , on March 5, 2019 by xi'an

Art Owen and Yi Zhou have arXived a short paper on the combination of importance sampling estimators. Which connects somehow with the talk about multiple estimators I gave at ESM last year in Helsinki. And our earlier AMIS combination. The paper however makes two important assumptions to reach optimal weighting, which is inversely proportional to the variance:

  1. the estimators are uncorrelated if dependent;
  2. the variance of the k-th estimator is of order a (negative) power of k.

The later is puzzling when considering a series of estimators, in that k appears to act as a sample size (as in AMIS), the power is usually unknown but also there is no reason for the power to be the same for all estimators. The authors propose to use ½ as the default, both because this is the standard Monte Carlo rate and because the loss in variance is then minimal, being 12% larger.

As an aside, Art Owen also wrote an invited discussion “the unreasonable effectiveness of Monte Carlo” of ” Probabilistic Integration: A Role in Statistical Computation?” by François-Xavier Briol, Chris  Oates, Mark Girolami (Warwick), Michael Osborne and Deni Sejdinovic, to appear in Statistical Science, discussion that contains a wealth of smart and enlightening remarks. Like the analogy between pseudo-random number generators [which work unreasonably well!] vs true random numbers and Bayesian numerical integration versus non-random functions. Or the role of advanced bootstrapping when assessing the variability of Monte Carlo estimates (citing a paper of his from 1992). Also pointing out at an intriguing MCMC paper by  Michael Lavine and Jim Hodges to appear in The American Statistician.

StanCon in Helsinki [29-31 Aug 2018]

Posted in Books, pictures, R, Statistics, Travel, University life with tags , , , , , , , , on March 7, 2018 by xi'an

As emailed to me by Aki Vehtari, the next StanCon will take place this summer in the wonderful city of Helsinki, at the end of August. On Aalto University Töölö Campus precisely. The list of speakers and tutorial teachers is available on the webpage. (The only “negative point” is that the conference does not include a Tuesday, the night of the transcendence 2 miles race!) Somewhat concluding this never-ending summer of Bayesian conferences!

ABC gas

Posted in pictures, Running, Travel with tags , , , , , , , on August 9, 2017 by xi'an

European statistics in Finland [EMS17]

Posted in Books, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on August 2, 2017 by xi'an

While this European meeting of statisticians had a wide range of talks and topics, I found it to be more low key than the previous one I attended in Budapest, maybe because there was hardly any talk there in applied probability. (But there were some sessions in mathematical statistics and Mark Girolami gave a great entry to differential geometry and MCMC, in the spirit of his 2010 discussion paper. Using our recent trip to Montréal as an example of geodesic!) In the Bayesian software session [organised by Aki Vetahri], Javier Gonzáles gave a very neat introduction to Bayesian optimisation: he showed how optimisation can be turned into Bayesian inference or more specifically as a Bayesian decision problem using a loss function related to the problem of interest. The point in following a Bayesian path [or probabilist numerics] is to reduce uncertainty by the medium of prior measures on functions, although resorting [as usual] to Gaussian processes whose arbitrariness I somehow dislike within the infinity of priors (aka stochastic processes) on functions! One of his strong arguments was that the approach includes the possibility for design in picking the next observation point (as done in some ABC papers of Michael Guttman and co-authors, incl. the following talk at EMS 2017) but again the devil may be in the implementation when looking at minimising an objective function… The notion of the myopia of optimisation techniques was another good point: only looking one step ahead in the future diminishes the returns of the optimisation and an alternative presented at AISTATS 2016 [that I do not remember seeing in Càdiz] goes against this myopia.

Umberto Piccini also gave a talk on exploiting synthetic likelihoods in a Bayesian fashion (in connection with the talk he gave last year at MCqMC 2016). I wondered at the use of INLA for this Gaussian representation, as well as at the impact of the parameterisation of the summary statistics. And the session organised by Jean-Michel involved Jimmy Olson, Murray Pollock (Warwick) and myself, with great talks from both other speakers, on PaRIS and PaRISian algorithms by Jimmy, and on a wide range of exact simulation methods of continuous time processes by Murray, both managing to convey the intuition behind their results and avoiding the massive mathematics at work there. By comparison, I must have been quite unclear during my talk since someone interrupted me about how Owen & Zhou (2000) justified their deterministic mixture importance sampling representation. And then left when I could not make sense of his questions [or because it was lunchtime already].

Helsingin satama ja katedraali [jatp]

Posted in pictures, Running, Travel, University life with tags , , , , , , , , on July 27, 2017 by xi'an

Self-Transcendence 2 mile races in Helsinki

Posted in Running, Travel, University life with tags , , , , , , , , , , , on July 26, 2017 by xi'an

Upon our arrival in Helsinki for EMS 2017, Jean-Michel Marin pointed out to me the existence of a 2 miles race the next day [as every Tuesday], indicated on the webpage of the conference. And encouraged me to run it. As I had brought my running gear and did not need preparation for a 2 miles [a mere loop in the parc!], I decided to try the race and we took a tram all the way to a faraway suburb where a few other runners had gathered. It was very relaxed and friendly, with recyclable cloth bibs and free juice available. Against all odds, I managed to win the race, with a first mile under six minutes thanks to another runner rushing me. And got a tee shirt as a reward. (Checking on Wikipedia later, I found that Sri Chinmoy was an Indian guru advocating running as a form of meditation, which I find rather absurd as I am anything but meditating when running a race..!)