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Trees for Regression and Classification
Published on 2007-02-2510451 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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Presentation
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
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
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
Example: Image Denoising46:34
Theory of Complexity Regularization47:34
Learning from Data51:20
Approximation and Estimation52:14
Classifier Approximations53:12
Approximation Error54:29
Boundary Smoothness56:09
Transition Smoothness56:50
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
The Classifier Learning Problem01:09:50
Chernoff’s Bound01:11:52
Error Deviation Bounds01:14:41
Uniform Deviation Bound01:15:18
Setting Penalties01:16:29
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