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High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity
Published on Jan 25, 20126781 Views
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving d
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Chapter list
High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity00:00
Introduction00:16
Sparse linear regression - 100:41
Sparse linear regression - 201:12
Corrupted variables - 101:34
Corrupted variables - 201:58
Corrupted variables - 302:42
Corrupted variables - 403:28
Corrupted variables - 503:38
Corrupted variables - 603:59
Lasso as plug-in estimator - 104:37
Lasso as plug-in estimator - 204:56
Lasso as plug-in estimator - 305:04
Lasso as plug-in estimator - 405:53
Example: Additive noise - 106:14
Example: Additive noise - 206:40
Example: Additive noise - 306:57
Example: Missing data - 107:03
Example: Missing data - 207:06
High-dimensional consistency? - 107:51
High-dimensional consistency? - 207:55
Theoretical guarantees: canonical Lasso08:39
Theoretical guarantees: modified Lasso - 109:11
Theoretical guarantees: modified Lasso - 209:48
High-dimensional consistency? - 110:13
High-dimensional consistency? - 210:21
Optimization of objective - 110:50
Optimization of objective - 211:43
Projected gradient descent - 111:59
Projected gradient descent - 212:16
Projected gradient descent - 312:36
Projected gradient descent - 412:53
Global linear convergence observed in practice13:08
Theoretical guarantees: modified Lasso - 113:32
Theoretical guarantees: modified Lasso - 213:57
Illustration of statistical and optimization error14:17
Application: Gaussian graphical models - 114:58
Application: Gaussian graphical models - 215:29
Application: Gaussian graphical models - 316:24
Gaussian inverse covariance estimation16:45
Summary17:10
Open questions17:48