Archive for University of Oxford

a journal of the plague year [almost gone]

Posted in Books, Kids, Mountains, pictures, Travel with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , on January 23, 2021 by xi'an

Read The stars are legion, by Kameron Hurley, which I brought back from Gainesville last year. Although I cannot remember why I bought the book, it must have been a “recommendation” on Amazon… The story is part unusual, part classical, with a constant switch between the two major characters [viewpoint].  And between different times. The style is complex, maybe too complex, as the universe is slowly revealing itself, through the perception biases of the characters. Including (spoiler!) one with multiple memory erasures and two attempts at recycling. Stars are actually (spoiler!) space-ships with some possibly organic elements that are decomposing (and showing the steel skeletons), with also apparently organic smaller vessels to travel between ships or fight between clans. Some of the ship inhabitants are mutants, possibly for being unprotected from space or ship radiations (although the control and propulsion of these ships is never mentioned), possibly because they are perceived as such by different groups in the ships, à la Huxley’s Brave New World? And there seem to be only females on-board, with all of them getting (mysteriously) pregnant at one time or another, rarely giving birth to children (associated with driving the ships? creating new ships?) but rather to other organic entities, apparently contributing to keeping the ship alive. All this is quite creative, with a powerful theme of power versus motherhood, but the story-telling is just too messy for me to have enjoyed it. The more because the type of subterranean universe where characters wander from one level to the next and discover supremely different ecosystems at each level never appealed to me. Since I read Verne’s Voyage au Centre de la Terre. (And I suddenly remembered dropping out of an earlier Hurley’s book.)

Cooked (the last remaining) pumpkin risotto with (legal) Lapsang tea, which worked out rather nicely, albeit loosing most of the Lapsang flavour. Had a week of (pleasant) cookie flavour home fragrance while my wife was preparing cookies for the entire family. Cooked a brunch with my son on the last Sunday of 2020, once again with Lapsang as drink. And had a Michelin take-away with my mom in Caen, since all restaurants remain closed till an unknown date. Which proved a great choice as it was surprisingly good, once out of the (potato starch) package.

Watched Season 2 of the BBC His Dark Materials series. Still impressed by the high level of the show (and enjoying it even more as I had forgotten basically everything about The Subtle Knife!) Except for the dark matter physicist turning to I Ching to understand her empirical experiment… But it remains a great series (esp. when mostly avoiding bears.) Also rewatched a Harry Potter film with my daughter, The Order of the Phoenix, which I found rather poor on the whole, despite a few great scenes (like the Wesley twins’ departure) and the fabulous rendering of the petty bureaucratic evil of Mrs. Umbridge throughout the film. And a part of The Half Blood Prince. Which sounded much better by comparison.

“It slowly dawned on me that it’s possible for the wise men who run your life for you to see disaster coming and not have a plan for dealing with it”

Read another K.J. Parker’s book, “How to rule an empire and get away with it“, sequel to “Sixteen ways &tc.” Light (mind-candy) but enjoyable bedside reading. Somewhat of a classical trick where a double becomes the real thing, if not in a Kagemusha tragic style.

simulating the pandemic

Posted in Books, Statistics with tags , , , , , , , , , , , on November 28, 2020 by xi'an

Nature of 13 November has a general public article on simulating the COVID pandemic as benefiting from the experience gained by climate-modelling methodology.

“…researchers didn’t appreciate how sensitive CovidSim was to small changes in its inputs, their results overestimated the extent to which a lockdown was likely to reduce deaths…”

The argument is essentially Bayesian, namely rather than using a best guess of the parameters of the model, esp. given the state of the available data (and the worse for March). When I read

“…epidemiologists should stress-test their simulations by running ‘ensemble’ models, in which thousands of versions of the model are run with a range of assumptions and inputs, to provide a spread of scenarios with different probabilities…”

it sounds completely Bayesian. Even though there is no discussion of the prior modelling or of the degree of wrongness of the epidemic model itself. The researchers at UCL who conducted the multiple simulations and the assessment of sensitivity to the 940 various parameters found that 19 of them had a strong impact, mostly

“…the length of the latent period during which an infected person has no symptoms and can’t pass the virus on; the effectiveness of social distancing; and how long after getting infected a person goes into isolation…”

but this outcome is predictable (and interesting). Mentions of Bayesian methods appear at the end of the paper:

“…the uncertainty in CovidSim inputs [uses] Bayesian statistical tools — already common in some epidemiological models of illnesses such as the livestock disease foot-and-mouth.”

and

“Bayesian tools are an improvement, says Tim Palmer, a climate physicist at the University of Oxford, who pioneered the use of ensemble modelling in weather forecasting.”

along with ensemble modelling, which sounds a synonym for Bayesian model averaging… (The April issue on the topic had also Bayesian aspects that were explicitely mentionned.)

MCqMC 2020 live and free and online

Posted in pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , on July 27, 2020 by xi'an

The MCqMC 20202 conference that was supposed to take place in Oxford next 9-14 August has been turned into an on-line free conference since travelling remains a challenge for most of us. Tutorials and plenaries will be live with questions  on Zoom, with live-streaming and recorded copies on YouTube. They will probably be during 14:00-17:00 UK time (GMT+1),  15:00-18:00 CET (GMT+2), and 9:00-12:00 ET. (Which will prove a wee bit of a challenge for West Coast and most of Asia and Australasia researchers, which is why our One World IMS-Bernoulli conference we asked plenary speakers to duplicate their talks.) All other talks will be pre-recorded by contributors and uploaded to a website, with an online Q&A discussion section for each. As a reminder here are the tutorials and plenaries:

Invited plenary speakers:

Aguêmon Yves Atchadé (Boston University)
Jing Dong (Columbia University)
Pierre L’Écuyer (Université de Montréal)
Mark Jerrum (Queen Mary University London)
Peter Kritzer (RICAM Linz)
Thomas Muller (NVIDIA)
David Pfau (Google DeepMind)
Claudia Schillings (University of Mannheim)
Mario Ullrich (JKU Linz)

Tutorials:

Fred Hickernell (IIT) — Software for Quasi-Monte Carlo Methods
Aretha Teckentrup (Edinburgh) — Markov chain Monte Carlo methods

non-reversible jump MCMC

Posted in Books, pictures, Statistics with tags , , , , , , , on June 29, 2020 by xi'an

Philippe Gagnon and et Arnaud Doucet have recently arXived a paper on a non-reversible version of reversible jump MCMC, the methodology introduced by Peter Green in 1995 to tackle Bayesian model choice/comparison/exploration. Whom Philippe presented at BayesComp20.

“The objective of this paper is to propose sampling schemes which do not suffer from such a diffusive behaviour by exploiting the lifting idea (…)”

The idea is related to lifting, creating non-reversible behaviour by adding a direction index (a spin) to the exploration of the models, assumed to be totally ordered, as with nested models (mixtures, changepoints, &tc.).  As with earlier versions of lifting, the chain proceeds along one (spin) direction until the proposal is rejected in which case the spin spins. The acceptance probability in the event of a change of model (upwards or downwards) is essentially the same as the reversible one (meaning it includes the dreaded Jacobian!). The original difficulty with reversible jump remains active with non-reversible jump in that the move from one model to the next must produce plausible values. The paper recalls two methods proposed by Christophe Andrieu and his co-authors. One consists in buffering a tempering sequence, but this proves costly.  Pursuing the interesting underlying theme that both reversible and non-reversible versions are noisy approximations of the marginal ratio, the other one consists in marginalising out the parameter to approximate the marginal probability of moving between nearby models. Combined with multiple choice to preserve stationarity and select more likely moves at the same time. Still requiring a multiplication of the number of simulations but parallelisable. The paper contains an exact comparison result that non-reversible jump leads to a smaller asymptotic variance than reversible jump, but it is unclear to me whether or not this accounts for the extra computing time resulting from the multiple paths in the proposed algorithms. (Even though the numerical illustration shows an improvement brought by the non-reversible side for the same computational budget.)

scalable Metropolis-Hastings, nested Monte Carlo, and normalising flows

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , on June 16, 2020 by xi'an

Over a sunny if quarantined Sunday, I started reading the PhD dissertation of Rob Cornish, Oxford University, as I am the external member of his viva committee. Ending up in a highly pleasant afternoon discussing this thesis over a (remote) viva yesterday. (If bemoaning a lost opportunity to visit Oxford!) The introduction to the viva was most helpful and set the results within the different time and geographical zones of the Ph.D since Rob had to switch from one group of advisors in Engineering to another group in Statistics. Plus an encompassing prospective discussion, expressing pessimism at exact MCMC for complex models and looking forward further advances in probabilistic programming.

Made of three papers, the thesis includes this ICML 2019 [remember the era when there were conferences?!] paper on scalable Metropolis-Hastings, by Rob Cornish, Paul Vanetti, Alexandre Bouchard-Côté, Georges Deligiannidis, and Arnaud Doucet, which I commented last year. Which achieves a remarkable and paradoxical O(1/√n) cost per iteration, provided (global) lower bounds are found on the (local) Metropolis-Hastings acceptance probabilities since they allow for Poisson thinning à la Devroye (1986) and  second order Taylor expansions constructed for all components of the target, with the third order derivatives providing bounds. However, the variability of the acceptance probability gets higher, which induces a longer but still manageable if the concentration of the posterior is in tune with the Bernstein von Mises asymptotics. I had not paid enough attention in my first read at the strong theoretical justification for the method, relying on the convergence of MAP estimates in well- and (some) mis-specified settings. Now, I would have liked to see the paper dealing with a more complex problem that logistic regression.

The second paper in the thesis is an ICML 2018 proceeding by Tom Rainforth, Robert Cornish, Hongseok Yang, Andrew Warrington, and Frank Wood, which considers Monte Carlo problems involving several nested expectations in a non-linear manner, meaning that (a) several levels of Monte Carlo approximations are required, with associated asymptotics, and (b) the resulting overall estimator is biased. This includes common doubly intractable posteriors, obviously, as well as (Bayesian) design and control problems. [And it has nothing to do with nested sampling.] The resolution chosen by the authors is strictly plug-in, in that they replace each level in the nesting with a Monte Carlo substitute and do not attempt to reduce the bias. Which means a wide range of solutions (other than the plug-in one) could have been investigated, including bootstrap maybe. For instance, Bayesian design is presented as an application of the approach, but since it relies on the log-evidence, there exist several versions for estimating (unbiasedly) this log-evidence. Similarly, the Forsythe-von Neumann technique applies to arbitrary transforms of a primary integral. The central discussion dwells on the optimal choice of the volume of simulations at each level, optimal in terms of asymptotic MSE. Or rather asymptotic bound on the MSE. The interesting result being that the outer expectation requires the square of the number of simulations for the other expectations. Which all need converge to infinity. A trick in finding an estimator for a polynomial transform reminded me of the SAME algorithm in that it duplicated the simulations as many times as the highest power of the polynomial. (The ‘Og briefly reported on this paper… four years ago.)

The third and last part of the thesis is a proposal [to appear in ICML 20] on relaxing bijectivity constraints in normalising flows with continuously index flows. (Or CIF. As Rob made a joke about this cleaning brand, let me add (?) to that joke by mentioning that looking at CIF and bijections is less dangerous in a Trump cum COVID era at CIF and injections!) With Anthony Caterini, George Deligiannidis and Arnaud Doucet as co-authors. I am much less familiar with this area and hence a wee bit puzzled at the purpose of removing what I understand to be an appealing side of normalising flows, namely to produce a manageable representation of density functions as a combination of bijective and differentiable functions of a baseline random vector, like a standard Normal vector. The argument made in the paper is that imposing this representation of the density imposes a constraint on the topology of its support since said support is homeomorphic to the support of the baseline random vector. While the supporting theoretical argument is a mathematical theorem that shows the Lipschitz bound on the transform should be infinity in the case the supports are topologically different, these arguments may be overly theoretical when faced with the practical implications of the replacement strategy. I somewhat miss its overall strength given that the whole point seems to be in approximating a density function, based on a finite sample.