Archive for Harvard

Hands-On Differential Privacy [book review]

Posted in Books, R, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , on October 2, 2024 by xi'an

Hands-On Differential Privacy was published just a few months ago (from September  2024!) by (the US publisher) O’Reilly, famous for its programming and technical books with animal covers! A slate pencil sea urchin in the present case. The book is indeed classical O’Reilly’s, with lots of notes, little theory (or maths!) and symbols, a loose structuring of the chapters (no section numbers) and highly detailed examples, and of course plenty of OpenDP code inserts. For instance, in the present case, a case study about the privatization of a sample average x̄ that takes about ten pages. Terrible equation rendering btw (what’s wrong with LATEX?!).  Overall, I am quickly lost in most of the chapters due to a lack of a driving narrative, facing instead a catalogue of possible scenari and procedures, appearing one after the other as in a fashion show.

Hands-On Differential Privacy is written by Ethan Cowan, Michael Shoemate, and Mayana Pereira. I came across the book during the OpenDP workshop at Harvard [that took place right after my return from the Pacific Northwest] and it is definitely linked with OpenDP, all authors being  actually involved at one stage or another in the OpenDP Team. The style of the book is once again in tune with the O’Reilly manuals, which sort of clashes with my preferences. For instance, the introduction of differential privacy (Chapter 2) is quite extensive. Chapter 3 proceeds to teach about private data transform(ation)s, stability (a rewording of Lipschitz-ianity), with code illustrations, often repeating the earlier derivation (see eg p203), while Chapter 4 is its equivalent for private mechanisms. (With the diagrams Figures 3-1 and 4-1 differing only in highlighting/bolding different functions in a privatized data processing pipeline.) Returning to differential privacy with a privacy loss parameter and to Laplace and exponential mechanisms, Chapter 5 proposes several notions of privacy, all closed under post-processing. This includes Wasserman and Zhou (2010) interpretation of privacy as hypothesis testing, except it is not exploited further than connecting type I and type II with (ε,δ) parameters. Chapter 6 concludes Part I about concepts with a series of (fearless) combinators, keeping stability and privacy. With an increasing proportion of coding excerpts which I [imho] did not find particularly helpful.

Nothing about statistical loss of information or efficiency, bias, &tc. until Chapter 8 (p199) and even then so little. Part II is about practice, with a first Chapter  7 on setting a privacy unit (e.g., a person-month) before ensuring their privacy is protected. And discussing unbounded contributions (not unbounded data!). While Chapter 8 very thinly covers statistical modelling, while remaining agnostic about the choice of statistical procedures (Bayes being solely and naïvely mentioned for classification, furthermore with data-based evaluation of the class “prior” probabilities, p211). At this stage, procedures are often only defined through spinets of code, like the private Theil-Sen estimator (pp204-205). The continuous case boils to a Normality assumption, with its pmf being defined (p212) as

\text{Pr}(x=\mu)=\frac{1}{\sqrt{2\pi\sigma}}e^{-(x-\mu)/2\sigma^2}

which contains at least three errors! Chapter 9 is the equivalent of Chapter 8 for machine learning, mostly centred on private gradient descent. And a Pytorch section (pp232-235). Completed by a light Chapter 10 on synthetic data, which does not seem to broach upon the issue of large dimension covariates, providing instead a list of GAN synthetizers.

Part III (Deploying differential privacy) is even more about practice, with Chapter 11 on privacy attacks, Chapter 12 on calibrating a privacy mechanism (co-written with Jayshree Sarathy), and good practice (like codebooks and data annotations), with the appearance of contextual integrity I discovered if not perfectly understood last year at the BIRS workshop in Kelowna. And Chapter 13 on planning a privacy project, with an 11 step checklist, most of which are quite vague [imho] and do include strategies to make the data owners confident their privacy is safe.

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE]

unbiased HMC

Posted in Books, pictures, Statistics with tags , , , , , , , on September 25, 2017 by xi'an

Jeremy Heng and Pierre Jacob arXived last week a paper on unbiased Hamiltonian Monte Carlo by coupling, following the earlier paper of Pierre and co-authors on debiasing by coupling a few weeks ago. The coupling within the HMC amounts to running two HMC chains with common random numbers, plus subtleties!

“As with any other MCMC method, HMC estimators are justified in the limit of the number of iterations. Algorithms which rely on such asymptotics face the risk of becoming obsolete if computational power keeps increasing through the number of available processors and not through clock speed.”

The main difficulty here is to have both chains meet (exactly) with large probability, since coupled HMC can only bring these chain close to one another. The trick stands in using both coupled HMC and coupled Hastings-Metropolis kernels, since the coupled MH kernel allows for exact meetings when the chains are already close, after which they remain happily and forever together! The algorithm is implemented by choosing between the kernels at random at each iteration. (Unbiasedness follows by the Glynn-Rhee trick, which is eminently well-suited for coupling!) As pointed out from the start of the paper, the appeal of this unbiased version is that the algorithm can be (embarrassingly) parallelised since all processors in use return estimators that are iid copies of one another, hence easily merged into a better estimator.

on intelligent design…

Posted in Books, Kids, Travel with tags , , , , , , , on August 19, 2014 by xi'an

chicken In connection with Dawkins’ The God delusion, which review is soon to appear on the ‘Og, a poster at an exhibit on evolution in the Harvard Museum of Natural History, which illustrates one of Dawkins’ points on scientific agosticism. Namely, that refusing to take a stand on the logical and philosophical opposition between science and religion(s) is not a scientific position. The last sentence in the poster is thus worse than unnecessary…

estimating the measure and hence the constant

Posted in pictures, Running, Statistics, University life with tags , , , , , , , on December 6, 2012 by xi'an

Dawn in Providence, Nov. 30, 2012As mentioned on my post about the final day of the ICERM workshop, Xiao-Li Meng addresses this issue of “estimating the constant” in his talk. It is even his central theme. Here are his (2011) slides as he sent them to me (with permission to post them!):

He therefore points out in slide #5 why the likelihood cannot be expressed in terms of the normalising constant because this is not a free parameter. Right! His explanation for the approximation of the unknown constant is then to replace the known but intractable dominating measure—in the sense that it cannot compute the integral—with a discrete (or non-parametric) measure supported by the sample. Because the measure is defined up to a constant, this leads to sample weights being proportional to the inverse density. Of course, this representation of the problem is open to criticism: why focus only on measures supported by the sample? The fact that it is the MLE is used as an argument in Xiao-Li’s talk, but this can alternatively be seen as a drawback: I remember reviewing Dankmar Böhning’s Computer-Assisted Analysis of Mixtures and being horrified when discovering this feature! I am currently more agnostic since this appears as an alternative version of empirical likelihood. There are still questions about the measure estimation principle: for instance, when handling several samples from several distributions, why should they all contribute to a single estimate of μ rather than to a product of measures? (Maybe because their models are all dominated by the same measure μ.) Now, getting back to my earlier remark, and as a possible answer to Larry’s quesiton, there could well be a Bayesian version of the above, avoiding the rough empirical likelihood via Gaussian or Drichlet process prior modelling.