New directions in solving structured nonconvex problems in multivariate statistics
1 hour 7 mins,
123.88 MB,
MP3
44100 Hz,
252.43 kbits/sec
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About this item
| Description: |
Mazumder, R
Tuesday 6th March 2018 - 11:00 to 12:00 |
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| Created: | 2018-03-12 11:12 |
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| Collection: | Statistical scalability |
| Publisher: | Isaac Newton Institute |
| Copyright: | Mazumder, R |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Nonconvex problems arise frequently in modern applied statistics and machine learning, posing outstanding challenges from a computational and statistical viewpoint. Continuous especially convex optimization, has played a key role in our computational understanding of (relaxations or approximations of) these problems. However, some other well-grounded techniques in mathematical optimization (for example, mixed integer optimization) have not been explored to their fullest potential. When the underlying statistical problem becomes difficult, simple convex relaxations and/or greedy methods have shortcomings. Fortunately, many of these can be ameliorated by using estimators that can be posed as solutions to structured discrete optimization problems. To this end, I will demonstrate how techniques in modern computational mathematical optimization (especially, discrete optimization) can be used to address the canonical problem of best-subset selection and cousins. I will describe how recent algorithms based on local combinatorial optimization can lead to high quality solutions in times comparable to (or even faster than) the fastest algorithms based on L1-regularization. I will also discuss the relatively less understood low Signal to Noise ratio regime, where usual subset selection performs unfavorably from a statistical viewpoint; and propose simple alternatives that rely on nonconvex optimization. If time permits, I will outline problems arising in the context robust statistics (least median squares/least trimmed squares), low-rank factor analysis and nonparametric function estimation where, these techniques seem to be promising.
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