parallel tempering on optimised paths

Saifuddin Syed, Vittorio Romaniello, Trevor Campbell, and Alexandre Bouchard-Côté, whom I met and discussed with on my “last” trip to UBC, on December 2019, just arXived a paper on parallel tempering (PT), making the choice of tempering path an optimisation problem. They address the touchy issue of designing a sequence of tempered targets when the starting distribution π⁰, eg the prior, and the final distribution π¹, eg the posterior, are hugely different, eg almost singular.

“…theoretical analysis of reversible variants of PT has shown that adding too many intermediate chains can actually deteriorate performance (…) [while] on non reversible regime adding more chains is guaranteed to improve performances.”

The above applies to geometric combinations of π⁰ and π¹. Which “suffers from an arbitrarily suboptimal global communication barrier“, according to the authors (although the counterexample is not completely convincing since π⁰ and π¹ share the same variance). They propose a more non-linear form of tempering with constraints on the dependence of the powers on the temperature t∈(0,1).  Defining the global communication barrier as an average over temperatures of the rejection rate, the path characteristics (e.g., the coefficients of a spline function) can then be optimised in terms of this objective. And the temperature schedule is derived from the fact that the non-asymptotic round trip rate is maximized when the rejection rates are all equal. (As a side item, the technique exposed in the earlier tempering paper by Syed et al. was recently exploited for a night high resolution imaging of a black hole from the M87 galaxy.)

no dichotomy between efficiency and interpretability

“…there are actually a lot of applications where people do not try to construct an interpretable model, because they might believe that for a complex data set, an interpretable model could not possibly be as accurate as a black box. Or perhaps they want to preserve the model as proprietary.”

One article I found quite interesting in the second issue of HDSR is “Why are we using black box models in AI when we don’t need to? A lesson from an explainable AI competition” by Cynthia Rudin and Joanna Radin, which describes the setting of a NeurIPS competition last year, the Explainable Machine Learning Challenge, of which I was blissfully unaware. The goal was to construct an operational black box predictor fpr credit scoring and turn it into something interpretable. The authors explain how they built instead a white box predictor (my terms!), namely a linear model, which could not be improved more than marginally by a black box algorithm. (It appears from the references that these authors have a record of analysing black-box models in various setting and demonstrating that they do not always bring more efficiency than interpretable versions.) While this is but one example and even though the authors did not win the challenge (I am unclear why as I did not check the background story, writing on the plane to pre-NeuriPS 2019).

I find this column quite refreshing and worth disseminating, as it challenges the current creed that intractable functions with hundreds of parameters will always do better, if only because they are calibrated within the box and have eventually difficulties to fight over-fitting within (and hence under-fitting outside). This is also a difficulty with common statistical models, but having the ability to construct error evaluations that show how quickly the prediction efficiency deteriorates may prove the more structured and more sparsely parameterised models the winner (of real world competitions).

emergence [jatp]

 

 

 

AABI9 tidbits [& misbits]

Today’s Advances in Approximate Bayesian Inference symposium, organised by Thang Bui, Adji Bousso Dieng, Dawen Liang, Francisco Ruiz, and Cheng Zhang, took place in front of Vancouver Harbour (and the tentalising ski slope at the back) and saw more than 400 participants, drifting away from the earlier versions which had a stronger dose of ABC and much fewer participants. There were students’ talks in a fair proportion, as well (and a massive number of posters). As of below, I took some notes during some of the talks with no pretense at exhaustivity, objectivity or accuracy. (This is a blog post, remember?!) Overall I found the day exciting (to the point I did not suffer at all from the usal naps consecutive to very short nights!) and engaging, with a lot of notions and methods I had never heard about. (Which shows how much I know nothing!)

The first talk was by Michalis Titsias, Gradient-based Adaptive Markov Chain Monte Carlo (jointly with Petros Dellaportas) involving as its objective function the multiplication of the variance of the move and of the acceptance probability, with a proposed adaptive version merging gradients, variational Bayes, neurons, and two levels of calibration parameters. The method advocates using this construction in a burnin phase rather than continuously, hence does not require advanced Markov tools for convergence assessment. (I found myself less excited by adaptation than earlier, maybe because it seems like switching one convergence problem for another, with additional design choices to be made.)The second talk was by Jakub Swiatkowsk, The k-tied Normal Distribution: A Compact Parameterization of Gaussian Mean Field Posteriors in Bayesian Neural Networks, involving mean field approximation in variational inference (loads of VI at this symposium!), meaning de facto searching for a MAP estimator, and reminding me of older factor analysis and other analyse de données projection methods, except it also involved neural networks (what else at NeurIPS?!)The third talk was by Michael Gutmann, Robust Optimisation Monte Carlo, (OMC) for implicit data generated models (Diggle & Graton, 1982), an ABC talk at last!, using a formalisation through the functional representation of the generative process and involving derivatives of the summary statistic against parameter, in that sense, with the (Bayesian) random nature of the parameter sample only induced by the (frequentist) randomness in the generative transform since a new parameter “realisation” is obtained there as the one providing minimal distance between data and pseudo-data, with no uncertainty or impact of the prior. The Jacobian of this summary transform (and once again a neural network is used to construct the summary) appears in the importance weight, leading to OMC being unstable, beyond failing to reproduce the variability expressed by the regular posterior or even the ABC posterior. It took me a while to wonder `where is Wally?!’ (the prior) as it only appears in the importance weight.

The fourth talk was by Sergey Levine, Reinforcement Learning, Optimal , Control, and Probabilistic Inference, back to Kullback-Leibler as the objective function, with linkage to optimal control (with distributions as actions?), plus again variational inference, producing an approximation in sequential settings. This sounded like a type of return of the MaxEnt prior, but the talk pace was so intense that I could not follow where the innovations stood.

The fifth talk was by Iuliia Molchanova, on Structured Semi-Implicit Variational Inference, from BAyesgroup.ru (I did not know of a Bayesian group in Russia!, as I was under the impression that Bayesian statistics were under-represented there, but apparently the situation is quite different in machine learning.) The talk brought an interesting concept of semi-implicit variational inference, exploiting some form of latent variables as far as I can understand, using mixtures of Gaussians.

The sixth talk was by Rianne van den Berg, Normalizing Flows for Discrete Data, and amounted to covering three papers also discussed in NeurIPS 2019 proper, which I found somewhat of a suboptimal approach to an invited talk, as it turned into a teaser for following talks or posters. But the teasers it contained were quite interesting as they covered normalising flows as integer valued controlled changes of variables using neural networks about which I had just became aware during the poster session, in connection with papers of Papamakarios et al., which I need to soon read.

The seventh talk was by Matthew Hoffman: Langevin Dynamics as Nonparametric Variational Inference, and sounded most interesting, both from title and later reports, as it was bridging Langevin with VI, but I alas missed it for being “stuck” in a tea-house ceremony that lasted much longer than expected. (More later on that side issue!)

After the second poster session (with a highly original proposal by Radford Neal towards creating  non-reversibility at the level of the uniform generator rather than later on), I thus only attended Emily Fox’s Stochastic Gradient MCMC for Sequential Data Sources, which superbly reviewed (in connection with a sequence of papers, including a recent one by Aicher et al.) error rate and convergence properties of stochastic gradient estimator methods there. Another paper I need to soon read!

The one before last speaker, Roman Novak, exposed a Python library about infinite neural networks, for which I had no direct connection (and talks I have always difficulties about libraries, even without a four hour sleep night) and the symposium concluded with a mild round-table. Mild because Frank Wood’s best efforts (and healthy skepticism about round tables!) to initiate controversies, we could not see much to bite from each other’s viewpoint.

off to Vancouver

Today I am flying to Vancouver for an ABC workshop, the second Symposium on Advances in Approximate Bayesian Inference, which is a pre-NeurIPS workshop following five earlier editions, to some of which I took part. With an intense and exciting programme. Not attending the following NeurIPS as I had not submitted any paper (and was not considering relying on a lottery!). Instead, I will give a talk at ABC UBC on Monday 4pm, as, coincidence, coincidence!, I was independently invited by UBC to the IAM-PIMS Distinguished Colloquium series. Speaking on ABC on a broader scale than in the workshop. Where I will focus on ABC-Gibbs. (With alas no time for climbing, missing an opportunity for a winter attempt at The Stawamus Chief!)