diff --git a/doc/model.md b/doc/model.md index 6c39fd345..973ec8df5 100644 --- a/doc/model.md +++ b/doc/model.md @@ -113,11 +113,11 @@ Instead, we use an additive strategy: fix what we have learned, add a new tree a We note the prediction value at step `t` by ``$ \hat{y}_i^{(t)}$``, so we have ```math -\hat{y}_i^{(0)} = 0\\ -\hat{y}_i^{(1)} = f_1(x_i) = \hat{y}_i^{(0)} + f_1(x_i)\\ -\hat{y}_i^{(2)} = f_1(x_i) + f_2(x_i)= \hat{y}_i^{(1)} + f_2(x_i)\\ -\dots\\ -\hat{y}_i^{(t)} = \sum_{k=1}^t f_k(x_i)= \hat{y}_i^{(t-1)} + f_t(x_i) +\hat{y}_i^{(0)} &= 0\\ +\hat{y}_i^{(1)} &= f_1(x_i) = \hat{y}_i^{(0)} + f_1(x_i)\\ +\hat{y}_i^{(2)} &= f_1(x_i) + f_2(x_i)= \hat{y}_i^{(1)} + f_2(x_i)\\ +&\dots\\ +\hat{y}_i^{(t)} &= \sum_{k=1}^t f_k(x_i)= \hat{y}_i^{(t-1)} + f_t(x_i) ``` It remains to ask Which tree do we want at each step? A natural thing is to add the one that optimizes our objective.