typos in week 45

doc/src/week45/week45.do.txt

@@ -734,27 +734,9 @@ plt.show()
 !ec
 
 
-!split
-===== Additive boosting  for Regression =====
-
-Here we present "Drucker's AdaBoost":"https://pdfs.semanticscholar.org/8d49/e2dedb817f2c3330e74b63c5fc86d2399ce3.pdf" tailored for regression.
-
-In bagging, each training example is equally likely to be
-picked. In boosting, the probability of a particular
-example being in the training set of a particular machine
-depends on the performance of the prior machines on
-that example. The following is a modification of
-Adaboost by Drucker.
-
-Start by selecting a set of training data $n$ and assign to each entry a weight $w_i=1$ for $i=1,2,\dots,n$. As we have done earlier, we could pick say $80\%$ of the data set for training. The algorithm runs as follows:
-o We define the probability that the  training sample $i$ is in the set by $p_i = w_i/\sum_iw_i$. We pick $n$ samples (with replacement) to form our training set. We pick a number uniformly in the range $[0,\sum_iw_i]$.
-o We choose then a regression machine (for example plain linear regression or a simple decision tree). A given regression machine makes then a hypothesis.
-o Using every member of the training set with the chosen regression machine we obtain then a prediction $\tilde{y}_i$.
-o We calculate then the loss function $L_i$ for each training sample. We can use various types of loss function as long as we have a value
-$L_i\in [0,1]$. 
 
 !split
-===== Gradient boosting: Basics with Steepest Descent =====
+===== Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent =====
 
 Gradient boosting is again a similar technique to Adaptive boosting,
 it combines so-called weak classifiers or regressors into a strong
@@ -836,8 +818,8 @@ o Initialize our estimate $f_0(x)$.
 o For $m=1:M$, we
   o compute the negative gradient vector $\bm{u}_m = -\partial C(\bm{y},\bm{f})/\partial \bm{f}(x)$ at $f(x) = f_{m-1}(x)$;
   o fit the so-called base-learner to the negative gradient $h_m(u_m,x)$;
-  o update the estimate $f_m(x) = f_{m-1}(x)+\nu h_m(u_m,x)$;
-o The final estimate is then $f_M(x) = \sum_{m=1}^M\nu h_m(u_m,x)$.
+  o update the estimate $f_m(x) = f_{m-1}(x)+h_m(u_m,x)$;
+o The final estimate is then $f_M(x) = \sum_{m=1}^M h_m(u_m,x)$.