added steepest descent boosting

This commit is contained in:
mhjensen
2019-11-11 23:49:53 +01:00
parent fb0906d974
commit 18239e1a21
69 changed files with 1665 additions and 1128 deletions
+15 -2
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@@ -1938,7 +1938,7 @@ plt.show()
!split
===== Gradient boosting: Basics =====
===== Gradient boosting: Basics with Steepest Descent =====
Gradient boosting is again a similar technique to Adaptive boosting,
it combines so-called weak classifiers or regressors into a strong
@@ -1948,7 +1948,20 @@ In order to understand the method, let us illustrate its basics by
bringing back the essential steps in linear regression, where our cost
function was the least squares function.
See discussion during lecture November 8.
!split
===== The Squared-Error again! Steepest Descent =====
We start again with our cost function ${\cal C}(\bm{y}m\bm{f})=\sum_{i=0}^{n-1}{\cal L}(y_i, f(x_i))$ where we want to minimize
This means that for every iteration, we need to optimize
!bt
\[
(\hat{\bm{f}}) \mathrm{argmin}_{\bm{f}}\hspace{0.1cm} \sum_{i=0}^{n-1}(y_i-f(x_i))^2.
\]
!et
!split
===== Gradient Boosting, algorithm =====