Boosting using depth$-$one trees $($or stumps$)$ leads to an additive model: that is$,$ a model of

the form

f$($X$)=$ X

p

j$=1$

fj $($Xj $),$

where X $=($X$1,,$ Xp$)$ is the feature vector and there are p features. Explain why this is the

case. Hint: start with the expression f$($X$)=$ PB

b$=1\backslash$lambda $$f

b

$($X$)$ and determine the function fj