a pen for ABC

Among the flury of papers arXived around the ICML 2019 deadline, I read on my way back from Oxford a paper by Wiqvist et al. on learning summary statistics for ABC by neural nets. Pointing out at another recent paper by Jiang et al. (2017, Statistica Sinica) which constructed a neural network for predicting each component of the parameter vector based on the input (raw) data, as an automated non-parametric regression of sorts. Creel (2017) does the same but with summary statistics. The current paper builds up from Jiang et al. (2017), by adding the constraint that exchangeability and partial exchangeability features should be reflected by the neural net prediction function. With applications to Markovian models. Due to a factorisation theorem for d-block invariant models, the authors impose partial exchangeability for order d Markov models by combining two neural networks that end up satisfying this factorisation. The concept is exemplified for one-dimension g-and-k distributions, alpha-stable distributions, both of which are made of independent observations, and the AR(2) and MA(2) models, as in our 2012 ABC survey paper. Since the later is not Markovian the authors experiment with different orders and reach the conclusion that an order of 10 is most appropriate, although this may be impacted by being a ble to handle the true likelihood.

troubling trends in machine learning

This morning, in Coventry, while having an n-th cup of tea after a very early morning run (light comes early at this time of the year!), I spotted an intriguing title in the arXivals of the day, by Zachary Lipton and Jacob Steinhard. Addressing the academic shortcomings of machine learning papers. While I first thought little of the attempt to address poor scholarship in the machine learning literature, I read it with growing interest and, although I am pessimistic at the chances of inverting the trend, considering the relentless pace and massive production of the community, I consider the exercise worth conducting, if only to launch a debate on the excesses found in the literature.

“…desirable characteristics:  (i) provide intuition to aid the reader’s understanding, but clearly distinguish it from stronger conclusions supported by evidence; (ii) describe empirical investigations that consider and rule out alternative hypotheses; (iii) make clear the relationship between theoretical analysis and intuitive or empirical claims; and (iv) use language to empower the reader, choosing terminology to avoid misleading or unproven connotations, collisions with other definitions, or conflation with other related but distinct concepts”

The points made by the authors are (p.1)

1. Failure to distinguish between explanation and speculation
2. Failure to identify the sources of empirical gains
3. Mathiness
4. Misuse of language

Again, I had misgiving about point 3., but this is not an anti-maths argument, rather about the recourse to vaguely connected or oversold mathematical results as a way to support a method.

Most interestingly (and living dangerously!), the authors select specific papers to illustrate their point, picking from well-established authors and from their own papers, rather than from junior authors. And also include counter-examples of papers going the(ir) right way. Among the recommendations for emerging from the morass of poor scholarship papers, they suggest favouring critical writing and retrospective surveys (provided authors can be found for these!). And mention open reviews before I can mention these myself. One would think that published anonymous reviews are a step in the right direction, I would actually say that this should be the norm (plus or minus anonymity) for all journals or successors of journals (PCis coming strongly to mind). But requiring more work from the referees implies rewards for said referees, as done in some biology and hydrology journals I refereed for (and PCIs of course).

ABC with kernelised regression

The exact title of the paper by Jovana Metrovic, Dino Sejdinovic, and Yee Whye Teh is DR-ABC: Approximate Bayesian Computation with Kernel-Based Distribution Regression. It appeared last year in the proceedings of ICML.  The idea is to build ABC summaries by way of reproducing kernel Hilbert spaces (RKHS). Regressing such embeddings to the “optimal” choice of summary statistics by kernel ridge regression. With a possibility to derive summary statistics for quantities of interest rather than for the entire parameter vector. The use of RKHS reminds me of Arthur Gretton’s approach to ABC, although I see no mention made of that work in the current paper.

In the RKHS pseudo-linear formulation, the prediction of a parameter value given a sample attached to this value looks like a ridge estimator in classical linear estimation. (I thus wonder at why one would stop at the ridge stage instead of getting the full Bayes treatment!) Things get a bit more involved in the case of parameters (and observations) of interest, as the modelling requires two RKHS, because of the conditioning on the nuisance observations. Or rather three RHKS. Since those involve a maximum mean discrepancy between probability distributions, which define in turn a sort of intrinsic norm, I also wonder at a Wasserstein version of this approach.

What I find hard to understand in the paper is how a large-dimension large-size sample can be managed by such methods with no visible loss of information and no explosion of the computing budget. The authors mention Fourier features, which never rings a bell for me, but I wonder how this operates in a general setting, i.e., outside the iid case. The examples do not seem to go into enough details for me to understand how this massive dimension reduction operates (and they remain at a moderate level in terms of numbers of parameters). I was hoping Jovana Mitrovic could present her work here at the 17w5025 workshop but she sadly could not make it to Banff for lack of funding!

a day for comments

As I was flying over Skye (with [maybe] a first if hazy perspective on the Cuillin ridge!) to Iceland, three long sets of replies to some of my posts appeared on the ‘Og:

• Dan Simpson replied to my comments of last Tuesday about his PC  construction;
• Arnaud Doucet precised some issues about his adaptive subsampling paper;
• Amandine Schreck clarified why I had missed some points in her Bayesian variable selection paper;
• Randal Douc defended the efficiency of using Carlin and Chib (1995) method for mixture simulation.

Thanks to them for taking the time to answer my musings…

 

adaptive subsampling for MCMC

“At equilibrium, we thus should not expect gains of several orders of magnitude.”

As was signaled to me several times during the MCqMC conference in Leuven, Rémi Bardenet, Arnaud Doucet and Chris Holmes (all from Oxford) just wrote a short paper for the proceedings of ICML on a way to speed up Metropolis-Hastings by reducing the number of terms one computes in the likelihood ratio involved in the acceptance probability, i.e.

The observations appearing in this likelihood ratio are a random subsample from the original sample. Even though this leads to an unbiased estimator of the true log-likelihood sum, this approach is not justified on a pseudo-marginal basis à la Andrieu-Roberts (2009). (Writing this in the train back to Paris, I am not convinced this approach is in fact applicable to this proposal as the likelihood itself is not estimated in an unbiased manner…)

In the paper, the quality of the approximation is evaluated by Hoeffding’s like inequalities, which serves as the basis for a stopping rule on the number of terms eventually evaluated in the random subsample. In fine, the method uses a sequential procedure to determine if enough terms are used to take the decision and the probability to take the same decision as with the whole sample is bounded from below. The sequential nature of the algorithm requires to either recompute the vector of likelihood terms for the previous value of the parameter or to store all of them for deriving the partial ratios. While the authors adress the issue of self-evaluating whether or not this complication is worth the effort, I wonder (from my train seat) why they focus so much on recovering the same decision as with the complete likelihood ratio and the same uniform. It would suffice to get the same distribution for the decision (an alternative that is easier to propose than to create of course). I also (idly) wonder if a Gibbs version would be manageable, i.e. by changing only some terms in the likelihood ratio at each iteration, in which case the method could be exact… (I found the above quote quite relevant as, in an alternative technique we are constructing with Marco Banterle, the speedup is particularly visible in the warmup stage.) Hence another direction in this recent flow of papers attempting to speed up MCMC methods against the incoming tsunami of “Big Data” problems.