Compressed Empirical Measures
1 hour 3 mins,
116.61 MB,
MP3
44100 Hz,
252.72 kbits/sec
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About this item
| Description: |
Grunewalder, S
Thursday 29th March 2018 - 11:00 to 12:00 |
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| Created: | 2018-03-29 13:08 |
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| Collection: | Statistical scalability |
| Publisher: | Isaac Newton Institute |
| Copyright: | Grunewalder, S |
| 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: | I will present results on compressed representations of expectation operators with a particular emphasis on expectations with respect to empirical measures. Such expectations are a cornerstone of non-parametric statistics and compressed representations are of great value when dealing with large sample sizes and computationally expensive methods. I will focus on a conditional gradient like algorithm to generate such representations in infinite dimensional function spaces. In particular, I will discuss extensions of classical convergence results to uniformly smooth Banach spaces (think Lp, 1 < p < 1, or various scales of Besov and Sobolev spaces); a counter example to fast rates of convergence in norm when compact sets are used for approximations; workarounds based on slicing compact sets in suitable ways and a result about fast convergence when the norm convergence is replaced with a weaker form of convergence; results about the location of the representer of a probability measure inside the approximation set using smoothness assumptions on the point-evaluators; and an application of these results to empirical processes.
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