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k-NN Regression Adapts to Local Intrinsic Dimension
Published on Jan 25, 20125501 Views
Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional da
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k-NN Regression adapts to local intrinsic dimension00:00
k-NN Regression - 100:10
k-NN Regression - 200:33
k-NN Regression - 301:07
Curse of dimension - 101:21
Curse of dimension - 201:49
Fortunately, high dimensional data often has low intrinsic complexity - 101:55
Fortunately, high dimensional data often has low intrinsic complexity - 202:09
Fortunately, high dimensional data often has low intrinsic complexity - 302:15
Fortunately, high dimensional data often has low intrinsic complexity - 402:22
Main result - 102:40
Main result - 202:59
Other work on adaptivity to intrinsic dimension - 103:13
Other work on adaptivity to intrinsic dimension - 204:37
Outline - 104:51
Intrinsic dimension - 105:36
Intrinsic dimension - 206:03
Intrinsic dimension - 306:40
Intrinsic dimension - 406:59
Given a query x - 107:47
Given a query x - 208:23
Given a query x - 308:36
Given a query x - 408:47
Outline - 209:06
Adaptivity for k - General intuition - 109:21
Adaptivity for k - General intuition - 209:58
Adaptivity for k - General intuition - 310:06
Adaptivity for k - General intuition - 410:34
Adaptivity for k - General intuition - 510:54
Adaptivity for k - Result - 111:12
Adaptivity for k - Result - 211:54
Outline - 312:10
Choosing k(x) - Best possible rate in terms of d - 112:29
Choosing k(x) - Best possible rate in terms of d - 212:41
Choosing k locally at x - Intuition13:22
Choosing k(x) - Result - 114:37
Choosing k(x) - Result - 215:08
Results likely extend to:15:29
Take home message - 116:03
Take home message - 216:23
Thank you16:47