Archive for NeurIPS 2021

day two at ISBA 22

Posted in Mountains, pictures, Running, Statistics, Travel with tags , , , , , , , , , , , , , , , , , , , on June 30, 2022 by xi'an

Still woke up early too early, which let me go for a long run in Mont Royal (which felt almost immediately familiar from earlier runs at MCM 2017!) at dawn and at a pleasant temperature (but missed the top bagel bakery on the way back!). Skipped the morning plenary lectures to complete recommendation letters and finishing a paper submission. But had a terrific lunch with a good friend I had not seen in Covid-times, at a local branch of Kinton Ramen which I already enjoyed in Vancouver as my Airbnb was located on top of it.

I chaired the afternoon Bayesian computations session with Onur Teymur presenting the general spirit of his Neurips 21 paper on black box probabilistic numerics. Mentioning that a new textbook on the topic by Phillip Henning, Michael Osborne, and Hans Kersting had appeared today! The second talk was by Laura Bondi who discussed an ABC model choice approach to assess breast cancer screening. With enough missing data (out of 78051 women followed over 12 years) to lead to an intractable likelihood. Starting with vanilla ABC using 32 summaries and moving to our random forest approach. Unsurprisingly concluding with different top models, but not characterising the identifiability provided by the choice of the summaries. The third talk was by Ryan Chan (fresh Warwick PhD recipient), about a Fusion divide-and-conquer approach that avoids the approximation of earlier approaches. In particular he uses a clever accept-reject algorithm to generate a product of densities using the component densities. A nice trick that Murray explained to me while visiting in Paris lg ast month. (The approach appears to be parameterisation dependent.) The final talk was by Umberto Picchini and in a sort the synthetic likelihood mirror of Massi’s talk yesterday, in the sense of constructing a guided proposal relying on observed summaries. If not comparing both approaches on a given toy like the g-and-k distribution.

posterior collapse

Posted in Statistics with tags , , , , , , on February 24, 2022 by xi'an

The latest ABC One World webinar was a talk by Yixin Wang about the posterior collapse of auto-encoders, of which I was completely unaware. It is essentially an identifiability issue with auto-encoders, where the latent variable z at the source of the VAE does not impact the likelihood, assumed to be an exponential family with parameter depending on z and on θ, through possibly a neural network construct. The variational part comes from the parameter being estimated as θ⁰, via a variational approximation.

“….the problem of posterior collapse mainly arises from the model and the data, rather than from inference or optimization…”

The collapse means that the posterior for the latent satisfies p(z|θ⁰,x)=p(z), which is not a standard property since θ⁰=θ⁰(x). Which Yixin Wang, David Blei and John Cunningham show is equivalent to p(x|θ⁰,z)=p(x|θ⁰), i.e. z being unidentifiable. The above quote is then both correct and incorrect in that the choice of the inference approach, i.e. of the estimator θ⁰=θ⁰(x) has an impact on whether or not p(z|θ⁰,x)=p(z) holds. As acknowledged by the authors when describing “methods modify the optimization objectives or algorithms of VAE to avoid parameter values θ at which the latent variable is non-identifiable“. They later build a resolution for identifiable VAEs by imposing that the conditional p(x|θ,z) is injective in z for all values of θ. Resulting in a neural network with Brenier maps.

From a Bayesian perspective, I have difficulties to connect to the issue, the folk lore being that selecting a proper prior is a sufficient fix for avoiding non-identifiability, but more fundamentally I wonder at the relevance of inferring about the latent z’s and hence worrying about their identifiability or lack thereof.

%d bloggers like this: