causality
The posterior at web scale
It is 2008, and the sampling revolution has hit a wall of its own: MCMC is exact in the limit but the limit never arrives when the model has millions of latent variables and the corpus has billions of words — the chain would need geological time. Trade exactness for reach: recast posterior inference as optimization, fitting the closest tractable distribution to the true posterior and bounding what the approximation gives up. Make it stream, so the fit updates from minibatches without revisiting the archive. Then be honest about the known sin — variational approximations understate uncertainty. Get it wrong and every large-scale probabilistic model reports intervals systematically too narrow, a whole literature of overconfidence dressed in Bayesian clothing.
Who this problem belongs to
The two figures whose methods fit it best, out of 67 in contention.
Blei is the central figure the problem is describing. His work through the 2000s, especially latent Dirichlet allocation with Ng and Jordan in 2003 and his subsequent development of stochastic variational inference around 2008-2013, is precisely the move the problem asks for: recast posterior inference as optimization, fitting the closest tractable distribution to the true posterior rather than sampling it, and make the fit update from minibatches without revisiting the full corpus. His papers are explicit about the honest cost, variational approximations understate posterior uncertainty, and he spent much of his career characterizing and partially correcting that bias. This is not adjacent expertise applied sideways; it is the actual named contribution, streaming variational Bayes for web-scale text corpora, which is why the score sits at the ceiling.
Jordan, together with Ghahramani, Jaakkola, and Saul, wrote the 1999 paper that established variational methods as a general framework for graphical models, the foundational move from which Blei's later web-scale work directly descends. His decades mentoring the Berkeley lineage that produced much of the modern computational Bayes and machine learning toolkit put him at the literal center of the field the problem describes, and his own research bridged the statistics of exact graphical-model inference with the optimization-based approximations that made million-variable models tractable. The only reason this sits fractionally below Blei is that the specific streaming, web-corpus-scale engineering, minibatches, stochastic gradients on the variational objective, was Blei's more targeted 2008-era contribution built on top of Jordan's earlier general framework.
Fought here
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
67 figures are scored on this problem. Draw it in a battle to see where you land.