Statistics Postdoc Tames Decades-Old Geometry Problem

https://www.quantamagazine.org/statistics-postdoc-tames-decades-old-geometry-problem-20210301/

by rbanffy • 5 years ago

188 38 5 years ago

tovej2• 5 years ago

As far as I can tell, this is a relevant proof when searching through high-dimensional parameter spaces (e.g. machine learning).

This would mean that overall geometry is not a (big) factor when it comes to getting stuck on local optima. Depending on how a random walk is implemented however, the conditions might create a practically concave search space.

scythmic_waves2• 5 years ago

This would mean that overall geometry is not a (big) factor when it comes to getting stuck on local optima.

I thought the results only applied to convex shapes. Search spaces in ML need not be convex, right? Or am I missing something?

tovej2• 5 years ago

I assume they are convex, typically cuboid. This is the type of space you get when each parameter is searched for a certain range.

Surely there could be search spaces that aren't convex. In that case the range of a variable would depend on the values of other variables. If you have an example of such a case I'd be interested in knowing about it.

6gvONxR4sf7o• 5 years ago

When it comes to getting stuck at a local optimum, I think it’s the convexity of the loss function that matters, not just the convexity of the parameter space. As I understand it, this result says that for convex losses, some simpler samplers work near enough to ideally.

zellyn• 5 years ago

The final paragraph was beautiful…

OmicronCeti• 5 years ago

Basically everything quanta writes is so good. They have some of the best science writers around in my opinion, and their efforts to make science and discovery accessible to non-experts and the public is admirable. I highly recommend their podcast that breaks down some of the popular stories, as well as "The Joy of X" which are long-form interviews with leading scientists.

strangeloops853• 5 years ago

Completely agree! I’ve really enjoyed Erica Klarreich’s writing in particular. I think she may very well be one of the most gifted and capable writers today on math in particular.

angry-tempest2• 5 years ago

She interviewed just the right people too! She is like the equivalent of Ed Yong for math

melling• 5 years ago

Funded by billionaire mathematician and hedge fund founder, where the algorithms make all the decisions

https://m.youtube.com/watch?v=QNznD9hMEh0

1976 winner of the Oswald Veblen Prize in Geometry

https://en.m.wikipedia.org/wiki/Oswald_Veblen_Prize_in_Geome...

thechao• 5 years ago

The person referenced above is “James Simon”.

tobmlt• 5 years ago

Aka, the Simons in Chern-Simons theory.

(Albert Schwarz formulated Chern–Simons theory, a topological quantum field theory, using the Chern-Simons form)

thomasahle• 5 years ago

They're entertaining to read, but I've never come away from one with any sort of understanding of the actual math and how I might use it. It would help if they at least defined the problem and the new theorem.

MaxBarraclough• 5 years ago

I figure this is because they're trying to make it accessible. As a somewhat mathematically literate non-mathematician I doubt I'd get much out of the real formulae that stump today's researchers. Quanta do a good job at dumbing it down enough to make sense to someone like me without making it completely empty. More specifically, Erica Klarreich does a good job of it - she seems to write most if not all of the Quanta articles that end up on the HN front page.

mcguire• 5 years ago

Did they define "substantial area" and I just missed it?

btilly2• 5 years ago

They actually did a better job of that with this problem than I usually see.

But if you don't have a substantial background, it may be hard to track.

revel• 5 years ago

Aside from being a wonderful achievement and advancement, this is a really excellent article. It's very impressive to read such technical material presented in such a beautiful way.

leafmeal• 5 years ago

Quanta is free, and virtually all of their articles read like this.

paulpauper• 5 years ago

It seems like unsolved problems in math are being solved at an increasingly fast rate. I think a combination of the internet making information more readily accessible combined with having more people alive to work on such problems, are contributing factors to this.

tpoacher3• 5 years ago

"To the surprise of experts in the field, a postdoctoral statistician has solved ..."

Wth? Am I the only one bothered by this opening statement? A post-doc IS an expert in the field. One who has spent a significant number of years doing a PhD to become THE expert in their own particular subfield, and presumably many more years after that diving into even greater detail.

Since when have we grown so accustomed to postdocs that we're treating them as on par with undergraduates in terms of academic value, and are so super surprised when they make an important discovery?

ttymck• 5 years ago

Is it not referring to the fact that they are a postdoctoral _statistician_ and not a "geometrician" or something of that nature?

omaranto• 5 years ago

Geometer, not geometrician, but yes, you're right.

strangeloops853• 5 years ago

I think you may be misunderstanding the implication. It's not that he's a postdoc that's surprising, but that he's a statistician who happens to have solved a major problem in convex geometry. The following quote sums it up:

"Chen is not a convex geometer by training — instead, he is a statistician who became interested in the KLS conjecture because he wanted to get a handle on random sampling. “No one knows Yuansi Chen in our community,” Eldan said. “It’s pretty cool that you have this guy coming out of nowhere, solving one of [our] most important problems.”"

The great thing is, the reaction of the community working on these type of problems was to understand and verify the result. And once it was, all credit to him.

tpoacher3• 5 years ago

Thanks for this explanation. That makes it slightly better I guess. It still sounds subtly presumptive though, when placed as the subheading. It feels a bit like when journalists report female scientists and feel the need to report their marital status in the first paragraph.

necubi• 5 years ago

The surprising thing is not that he's a post-doc, it's that he's a statistician.

Fomite• 5 years ago

As others have mentioned, and as someone who does statistics, I think you're putting the emphasis on the wrong word in "postdoctoral statistician".

If I solved a major open problem in geometry, Quanta could easily write "To the surprise of experts in the field, a professor of epidemiology has solved..." and they'd be correct in doing so.

ska• 5 years ago

Others have pointed out the misread here, but I'll add that typically the thing you are actually expert in after this amount of study is typically very narrow. So when they say "the surprise of experts in the field" on many topics "the experts" they are referring to is often a few dozen people.

a1369209993• 5 years ago

A post-doc IS an expert in the field.

Other people have already mentioned it, but to phrase it another way: he's a expert in a different field.

Statistics Postdoc Tames Decades-Old Geometry Problem

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