Archive for Bayesian inference

OWAB [season] I

Posted in Statistics, University life with tags , , , , , , , , , , , , on November 23, 2024 by xi'an

Our “new” seminar series, the One World Approximate Bayesian Inference (OWABI) Seminar, will see its second OWABI talk given on Thursday 28 November at 11am UK time. The speaker is Jeremias Knoblauch (University College London), who will talk about

Post-Bayesian machine learning

Abstract: In this talk, I provide my perspective on the machine learning community’s efforts to develop inference procedures with Bayesian characteristics that go beyond Bayes’ Rule as an epistemological principle. I will explain why these efforts are needed, as well as the forms which they take. Focusing on some of my own contributions to the field, I will trace out some of the community’s most important milestones, as well as the challenges that lie ahead. Throughout, I will provide success stories of the field, and emphasise the new opportunities that open themselves up to us once we dare to go beyond orthodox Bayesian procedures.

Keywords: Generalised Bayes; robustness; Bayesian machine learning.

filogenesi della pasta ripiena

Posted in Books, pictures, R, Statistics, University life with tags , , , , , , , , , , , , , , , , , , , , , on November 13, 2024 by xi'an

Bayesian Inference: Theory, Methods, Computations [book review]

Posted in Statistics with tags , , , , , , , , , , , , , , , , , , , , , on November 12, 2024 by xi'an

Bayesian Inference: Theory, Methods, Computations by Silvelyn Zwanzig and Rauf Ahmad, both from Uppsala University, is a recent book published by Chapman & Hall / CRC Press. About 300p long (plus appendices), it covers the core aspects of Bayesian inference, namely the decision theoretic motivations, its asymptotic validation, the specifics of estimation and testing, and the computational approximations (MC, MCMC, ABC, VB), with entries on prior specification and Normal linear models. And some R codes. It is (and feels like) constructed from Master and PhD courses (at Uppsala University), with a rigorous mathematical presentation and many examples, some related to biostatistics. Drawings from the first author’s daughter are included in most chapters, to this reviewer’s bemusement. From a further personal viewpoint, the book also reads rather close to my (Bayesian) choice of a Bayesian textbook, which proves rather accurate since several chapters are inspired by my own Bayesian Choice. as acknowledged therein. As well as by the more recent Statistical Decision Theory: Estimation, Testing, and Selection by Liese & Miescke (2008) and Introduction to the Theory of Statistical Inference by Liero & Zwanzig (2011). Witness, for instance, an example of prior construction for capture-recapture experiments on lizards as analysed by my PhD student Dupuis (1995) [with a curious switch to the authors on p.263] and  also included in The Bayesian Choice (with drawing 2.9 incorrect in that the lizards there have marks on their backs, instead of the code adopted by the ecologists, namely cutting one specific phalange for each capture).

Other minor quandaries: The usual issue of quoting the wrong edition for creating a method, as when citing Jeffreys (1946) for inventing non-informative priors [p.53], failing to point out the parameterisation invariance of intrinsic losses [p.95]considering that Bayes factors are only relevant for obtaining evidence against the null hypothesis [p.216], recommending BIC and DIC (!) [pp.232-6], advocating sampling importance resampling (SIR) for approximate sampling from the target (omitting infinite variance issues) [p.253], defining annealing as using “several trial distributions” [p.261], a mistake in ABC-MCMC [p.274] since the case when the simulated data is too far from the actual data should lead to a repetition rather than a pure rejection.

All in all, a reasonable textbook with some recent input, but still lacking in originality, if I may subjectively say so.

[Disclaimer about potential self-plagiarism: this post or an edited version of it could possibly appear in my Books Review section in CHANCE.]

OWAB [season] I

Posted in Statistics, University life with tags , , , , , , , , , , , , , , , , , , on October 28, 2024 by xi'an

OWABC is dead, long life OWABI! After 5 seasons of the One World Approximate Bayesian Computation (ABC) Seminar, launched in April 2020 (!) to gather members and disseminate results and innovation during those weeks and months under lockdown, the organisers (incl. yours truly) have now decided to launch a “new” seminar series, the One World Approximate Bayesian Inference (OWABI) Seminar, to better reflect the broader interest and scope of this series, which goes beyond ABC. With Bluesky, X, and Linkedin accountsWith Bluesky, X, and Linkedin accounts. In particular, simulation-based inference and ML related techniques will play a crucial role. We are also pleased to announce that Stefan Radev has joined the OWABI Organiser Team.

The first OWABI talk will be given on Thursday the 31st October at 11am UK time. The speaker is Ullrich Koethe (University of Heidelberg), who will talk about

“Free-form flows for physics-informed generative modeling”

Abstract: The talk first introduces a useful categorization of the (sometimes confusing) “generative model zoo” in terms of different change-of-variables formulas. It then shows how normalizing flows, a major architecture for generative neural networks, can be used for simulation-based Bayesian inference in the sciences. Finally, it proposes free-form flows to simplify the incorporation of physical prior knowledge, e.g. rotation and translation invariance or the restriction of the distribution to a manifold, into generative models.
Keywords: normalizing flows; physical-informed neural networks; simulation-based inference

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]