Archive for NeurIPS 2019

riddle on a circle

Posted in Books, Kids, R, Travel with tags , , , , , , , on December 22, 2019 by xi'an

The Riddler’s riddle this week provides another opportunity to resort to brute-force simulated annealing!

Given a Markov chain defined on the torus {1,2,…,100} with only moves a drift to the right (modulo 100) and a uniformely random jump, find the optimal transition matrix to reach 42 in a minimum (average) number of moves.

Which I coded in my plane to Seattle, under the assumption that there is nothing to do when the chain is already in 42. And the reasoning that there is not gain (on average) in keeping the choice between right shift and random jump random.

dure=min(c(41:0,99:42),50)
temp=.01
for (t in 1:1e6){
  i=sample((1:100)[-42],1)
  dura=1+mean(dure)
  if (temp*log(runif(1))<dure[i]-dura) dure[i]=dura
  if(temp*log(runif(1))<dure[i]-(dura<-1+dure[i*(i<100)+1])) 
    dure[i]=dura 
  temp=temp/(1+.1e-4*(runif(1)>.99))}

In all instances, the solution is to move at random for any position but those between 29 and 41, for an average 13.64286 number of steps to reach 42. (For values outside the range 29-42.)

no dichotomy between efficiency and interpretability

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , , , , on December 18, 2019 by xi'an

“…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).

AABI9 tidbits [& misbits]

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

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

Posted in Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , , , on December 7, 2019 by xi'an

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!)

label switching by optimal transport: Wasserstein to the rescue

Posted in Books, Statistics, Travel with tags , , , , , , , , , , , , , , on November 28, 2019 by xi'an

A new arXival by Pierre Monteiller et al. on resolving label switching by optimal transport. To appear in NeurIPS 2019, next month (where I will be, but extra muros, as I have not registered for the conference). Among other things, the paper was inspired from an answer of mine on X validated, presumably a première (and a dernière?!). Rather than picketing [in the likely unpleasant weather ]on the pavement outside the conference centre, here are my raw reactions to the proposal made in the paper. (Usual disclaimer: I was not involved in the review of this paper.)

“Previous methods such as the invariant losses of Celeux et al. (2000) and pivot alignments of Marin et al. (2005) do not identify modes in a principled manner.”

Unprincipled, me?! We did not aim at identifying all modes but only one of them, since the posterior distribution is invariant under reparameterisation. Without any bad feeling (!), I still maintain my position that using a permutation invariant loss function is a most principled and Bayesian approach towards a proper resolution of the issue. Even though figuring out the resulting Bayes estimate may prove tricky.

The paper thus adopts a different approach, towards giving a manageable meaning to the average of the mixture distributions over all permutations, not in a linear Euclidean sense but thanks to a Wasserstein barycentre. Which indeed allows for an averaged mixture density, although a point-by-point estimate that does not require switching to occur at all was already proposed in earlier papers of ours. Including the Bayesian Core. As shown above. What was first unclear to me is how necessary the Wasserstein formalism proves to be in this context. In fact, the major difference with the above picture is that the estimated barycentre is a mixture with the same number of components. Computing time? Bayesian estimate?

Green’s approach to the problem via a point process representation [briefly mentioned on page 6] of the mixture itself, as for instance presented in our mixture analysis handbook, should have been considered. As well as issues about Bayes factors examined in Gelman et al. (2003) and our more recent work with Kate Jeong Eun Lee. Where the practical impossibility of considering all possible permutations is processed by importance sampling.

An idle thought that came to me while reading this paper (in Seoul) was that a more challenging problem would be to face a model invariant under the action of a group with only a subset of known elements of that group. Or simply too many elements in the group. In which case averaging over the orbit would become an issue.