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Trees for Regression and Classification
Published on Feb 25, 200710443 Views
Tree models are widely used for regression and classification problems, with interpretability and ease of implementation being among their chief attributes. Despite the widespread use tree models, a c
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Chapter list
Learning with Trees00:01
Basic Problem: Partitioning05:51
Classification06:36
Signal and Image Processing07:16
Partitioning Schemes07:58
Why Trees ?09:24
Example: Gamma-Ray Burst Analysis10:47
Trees and Partitions13:23
Estimation using Pruned Tree14:39
Gamma-Ray Burst 84514:58
Recursive Partitions16:04
Adapted Partition16:34
Image Denoising16:50
Decision (Classification) Trees17:26
Classification18:36
Image Partitions19:25
TITLE19:59
Image Coding20:15
Probabilistic Framework21:14
Prediction Problem23:12
Challenge24:27
Empirical Risk25:38
Empirical Risk Minimization26:25
Classification and Regression Trees26:59
Classification and Regression Trees27:57
Empirical Risk Minimization on Trees28:45
Overfitting Problem30:00
Bias/Variance Trade-off32:29
Estimation and Approximation Error33:22
Estimation Error in Regression35:13
Estimation Error in Classification36:00
Partition Complexity and Overfitting36:51
Controlling Overfitting38:22
Complexity Regularization39:12
Per-Cell Variance Bounds: Regression39:57
Per-Cell Variance Bounds: Classification40:59
Variance Bounds41:44
A Slightly Weaker Variance Bound44:15
Complexity Regularization44:51
Example: Image Denoising46:34
Theory of Complexity Regularization47:34
TITLE48:22
Classification49:45
Probabilistic Framework50:49
Learning from Data51:20
Approximation and Estimation52:14
Classifier Approximations53:12
Approximation Error54:29
Approximation Error55:45
Boundary Smoothness56:09
Transition Smoothness56:50
Transition Smoothness57:30
Fundamental Limit to Learning58:20
Related Work01:01:05
Box-Counting Class01:03:11
Box-Counting Sub-Classes01:04:31
Dyadic Decision Trees01:06:26
Dyadic Decision Trees01:07:34
The Classifier Learning Problem01:09:50
Empirical Risk01:10:34
Chernoff’s Bound01:11:52
Chernoff’s Bound01:13:27
Error Deviation Bounds01:14:41
Uniform Deviation Bound01:15:18
Setting Penalties01:16:29
Setting Penalties01:17:30
Uniform Deviation Bound01:19:20
Decision Tree Selection01:20:18
Rate of Convergence01:22:14
Balanced vs. Unbalanced Trees01:24:27
Spatial Adaptation01:25:22
Relative Chernoff Bound01:26:10
Designing Leaf Penalties01:27:15
Uniform Deviation Bound01:28:25