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Single and Multiple Index Models
Published on Jan 16, 20134627 Views
Statistical estimation in the high-dimensional setting, with more variables than samples, has been the focus of considerable research over the last decade. It is now well understood that consisten
Chapter list
Single and Multiple Index Models00:00
Modern Data00:28
High-dimensional Data (1)01:42
Examples of Structure Subspaces02:31
High-dimensional Data (2)03:48
High-dimensional Data (3)04:14
Semi-parametric Models04:52
Example: Additive Models (1)05:38
Example: Additive Models (2)07:21
Example: Sparse Additive Models08:12
Semi-parametric story only goes so far09:53
Sparse Models10:07
Sparse Nonparametric Models (1)10:42
Sparse Nonparametric Models (2)11:13
Block-sparse Models13:19
Low-rank Models14:23
Nonparametric Low-Rank Models (1)15:15
Nonparametric Low-Rank Models (2)16:11
"A unified story for non-parametric structure ..."16:36
Multiple Index Model (1)17:40
Multiple Index Model (2)17:58
Multiple Index Model (3)18:20
Multiple Index Model (4)19:10
Multiple Index Model (5)19:31
Occurrences in the wild19:49
Application: Neural Coding22:41
Application: Responses in early visual cortex (V1)24:37
Application: Retinal Modeling26:41
Multiple Index Models28:38
Index Models and Projections29:12
On Index Models and Projections32:13
Projection Pursuit Regression33:22
Backfitting34:05
Multiple Index Model Backfitting (1)35:00
Multiple Index Model Backfitting (2)36:27
Candidate Method for SIM Estimation36:40
Step II in SIM estimation: Fitting the Proj. Weights38:30
Single Index Model Loss (1)39:27
Single Index Model Loss (2)39:45
Single Index Model Loss (3)40:10
A surrogate loss40:25
Bergman Divergence41:13
Surrogate Bregman Los42:00
SIM Estimation using Surrogate Bregman Loss42:59
Application: Retinal Modeling45:39
Parameter and Prediction Error47:37
Function Recovery: Exponential48:33
Function Recovery: Sigmoidal48:58
Function Recovery: Rectifying49:04
Summary49:11
Thank You!50:18