As I was preparing my (new) lectures for a PhD short course “at” Warwick (meaning on Teams!), I read a few surveys and other papers on all these acronyms. It included the massive Guttmann and Hyvärinen 2012 NCE JMLR paper, Goodfellow’s NIPS 2016 tutorial on GANs, and Kingma and Welling 2019 introduction to VAEs. Which I found a wee bit on the light side, maybe missing the fundamentals of the notion… As well as the pretty helpful 2019 survey on normalising flows by Papamakarios et al., although missing on the (statistical) density estimation side. And also a nice (2017) survey of GANs by Shakir Mohamed and Balaji Lakshminarayanan with a somewhat statistical spirit, even though convergence issues are not again not covered. But misspecification is there. And the many connections between ABC and GANs, if definitely missing on the uncertainty aspects. While Deep Learning by Goodfellow, Bengio and Courville adresses both the normalising constant (or partition function) and GANs, it was somehow not deep enough (!) to use for the course, offering only a few pages on NCE, VAEs and GANs. (And also missing on the statistical references addressing the issue, incl. [or excl.] Geyer, 1994.) Overall, the infinite variations offered on GANs leave me uncertain about their statistical relevance, as it is unclear how good the regularisation therein is for handling overfitting and consistent estimation. (And if I spot another decomposition of the Kullback-Leibler divergence, I may start crying…)
Archive for deep learning
NCE, VAEs, GANs & even ABC…
Posted in Statistics with tags ABC, Bayesian GANs, CDT, deep learning, energy based model, generative adversarial networks, noise contrasting estimation, normalising constant, normalising flow, partition function, PhD course, Teams, University of Warwick, variational autoencoders on May 14, 2021 by xi'ansampling with neural networks [seminar]
Posted in Statistics with tags deep learning, Flatiron Institute, generative model, neural network sampling, New York, webinar on March 29, 2021 by xi'an
Tomorrow (30 March, 11am ET, 16 GMT, 17 CET) Grant Rotskoff will give a webinar on Sampling with neural networks: prospects and perils, with links to developments in generative modeling to sample distributions that are challenging to sample with local dynamics, and the perils of neural network driven sampling to accelerate sampling.
Metropolis-Hastings via classification
Posted in pictures, Statistics, Travel, University life with tags ABC, ABC consistency, Chicago, Chicago Booth School of Business, deep learning, discriminant analysis, GANs, logistic regression, seminar, summary statistics, synthetic likelihood, University of Oxford, webinar, winter running on February 23, 2021 by xi'an
Veronicka Rockova (from Chicago Booth) gave a talk on this theme at the Oxford Stats seminar this afternoon. Starting with a survey of ABC, synthetic likelihoods, and pseudo-marginals, to motivate her approach via GANs, learning an approximation of the likelihood from the GAN discriminator. Her explanation for the GAN type estimate was crystal clear and made me wonder at the connection with Geyer’s 1994 logistic estimator of the likelihood (a form of discriminator with a fixed generator). She also expressed the ABC approximation hence created as the actual posterior times an exponential tilt. Which she proved is of order 1/n. And that a random variant of the algorithm (where the shift is averaged) is unbiased. Most interestingly requiring no calibration and no tolerance. Except indirectly when building the discriminator. And no summary statistic. Noteworthy tension between correct shape and correct location.
poems that solve puzzles [book review]
Posted in Books, Kids, University life with tags ACM Turing Award, Ada Lovelace, Alan Turing, algorithms, AlphaGo, book cover, book review, CHANCE, Charles Babbage, checkers, deep learning, difference engine, Dublin, Fourier transform, John Tukey, machine learning, Oxford University Press, puzzle, University College Dublin on January 7, 2021 by xi'an
Upon request, I received this book from Oxford University Press for review. Poems that Solve Puzzles is a nice title and its cover is quite to my linking (for once!). The author is Chris Bleakley, Head of the School of Computer Science at UCD.
“This book is for people that know algorithms are important, but have no idea what they are.”
These is the first sentence of the book and hence I am clearly falling outside the intended audience. When I asked OUP for a review copy, I was more thinking in terms of Robert Sedgewick’s Algorithms, whose first edition still sits on my shelves and which I read from first to last page when it appeared [and was part of my wife’s booklist]. This was (and is) indeed a fantastic book to learn how to build and optimise algorithms and I gain a lot from it (despite remaining a poor programmer!).
Back to poems, this one reads much more like an history of computer science for newbies than a deep entry into the “science of algorithms”, with imho too little on the algorithms themselves and their connections with computer languages and too much emphasis on the pomp and circumstances of computer science (like so-and-so got the ACM A.M. Turing Award in 19… and retired in 19…). Beside the antique algorithms for finding primes, approximating π, and computing the (fast) Fourier transform (incl. John Tukey), the story moves quickly to the difference engine of Charles Babbage and Ada Lovelace, then to Turing’s machine, and artificial intelligence with the first checkers codes, which already included some learning aspects. Some sections on the ENIAC, John von Neumann and Stan Ulam, with the invention of Monte Carlo methods (but no word on MCMC). A bit of complexity theory (P versus NP) and then Internet, Amazon, Google, Facebook, Netflix… Finishing with neural networks (then and now), the unavoidable AlphaGo, and the incoming cryptocurrencies and quantum computers. All this makes for pleasant (if unsurprising) reading and could possibly captivate a young reader for whom computers are more than a gaming console or a more senior reader who so far stayed wary and away of computers. But I would have enjoyed much more a low-tech discussion on the construction, validation and optimisation of algorithms, namely a much soft(ware) version, as it would have made it much more distinct from the existing offer on the history of computer science.
[Disclaimer about potential self-plagiarism: this post or an edited version of it will eventually appear in my Books Review section in CHANCE.]
frontier of simulation-based inference
Posted in Books, Statistics, University life with tags ABC, Bayesian deep learning, classification, deep learning, GANs, kernel density estimator, National Academy of Science, neural network, neural networks and learning machines, PNAS, simulation-based inference, Statistics, summary statistics, Wasserstein distance on June 11, 2020 by xi'an
“This paper results from the Arthur M. Sackler Colloquium of the National Academy of Sciences, `The Science of Deep Learning,’ held March 13–14, 2019, at the National Academy of Sciences in Washington, DC.”
A paper by Kyle Cranmer, Johann Brehmer, and Gilles Louppe just appeared in PNAS on the frontier of simulation-based inference. Sounding more like a tribune than a research paper producing new input. Or at least like a review. Providing a quick introduction to simulators, inference, ABC. Stating the shortcomings of simulation-based inference as three-folded:
- costly, since required a large number of simulated samples
- loosing information through the use of insufficient summary statistics or poor non-parametric approximations of the sampling density.
- wasteful as requiring new computational efforts for new datasets, primarily for ABC as learning the likelihood function (as a function of both the parameter θ and the data x) is only done once.
And the difficulties increase with the dimension of the data. While the points made above are correct, I want to note that ideally ABC (and Bayesian inference as a whole) only depends on a single dimension observation, which is the likelihood value. Or more practically that it only depends on the distance from the observed data to the simulated data. (Possibly the Wasserstein distance between the cdfs.) And that, somewhat unrealistically, that ABC could store the reference table once for all. Point 3 can also be debated in that the effort of learning an approximation can only be amortized when exactly the same model is re-employed with new data, which is likely in industrial applications but less in scientific investigations, I would think. About point 2, the paper misses part of the ABC literature on selecting summary statistics, e.g., the culling afforded by random forests ABC, or the earlier use of the score function in Martin et al. (2019).
The paper then makes a case for using machine-, active-, and deep-learning advances to overcome those blocks. Recouping other recent publications and talks (like Dennis on One World ABC’minar!). Once again presenting machine-learning techniques such as normalizing flows as more efficient than traditional non-parametric estimators. Of which I remain unconvinced without deeper arguments [than the repeated mention of powerful machine-learning techniques] on the convergence rates of these estimators (rather than extolling the super-powers of neural nets).
“A classifier is trained using supervised learning to discriminate two sets of data, although in this case both sets come from the simulator and are generated for different parameter points θ⁰ and θ¹. The classifier output function can be converted into an approximation of the likelihood ratio between θ⁰ and θ¹ (…) learning the likelihood or posterior is an unsupervised learning problem, whereas estimating the likelihood ratio through a classifier is an example of supervised learning and often a simpler task.”
The above comment is highly connected to the approach set by Geyer in 1994 and expanded in Gutmann and Hyvärinen in 2012. Interestingly, at least from my narrow statistician viewpoint!, the discussion about using these different types of approximation to the likelihood and hence to the resulting Bayesian inference never engages into a quantification of the approximation or even broaches upon the potential for inconsistent inference unlocked by using fake likelihoods. While insisting on the information loss brought by using summary statistics.
“Can the outcome be trusted in the presence of imperfections such as limited sample size, insufficient network capacity, or inefficient optimization?”
Interestingly [the more because the paper is classified as statistics] the above shows that the statistical question is set instead in terms of numerical error(s). With proposals to address it ranging from (unrealistic) parametric bootstrap to some forms of GANs.
