Compressed Empirical Measures
1 hour 3 mins,
912.99 MB,
MPEG-4 Video
640x360,
29.97 fps,
44100 Hz,
1.93 Mbits/sec
Share this media item:
Embed this media item:
Embed this media item:
About this item
Description: |
Grunewalder, S
Thursday 29th March 2018 - 11:00 to 12:00 |
---|
Created: | 2018-03-29 13:08 |
---|---|
Collection: | Statistical scalability |
Publisher: | Isaac Newton Institute |
Copyright: | Grunewalder, S |
Language: | eng (English) |
Distribution: | World (downloadable) |
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.
|
---|
Available Formats
Format | Quality | Bitrate | Size | |||
---|---|---|---|---|---|---|
MPEG-4 Video * | 640x360 | 1.93 Mbits/sec | 912.99 MB | View | Download | |
WebM | 640x360 | 632.25 kbits/sec | 291.74 MB | View | Download | |
iPod Video | 480x270 | 496.41 kbits/sec | 229.06 MB | View | Download | |
MP3 | 44100 Hz | 252.72 kbits/sec | 116.61 MB | Listen | Download | |
Auto | (Allows browser to choose a format it supports) |