how prediction of xgboost correspond to leaves values I trained xgboost regressor. Now I want to see its fitted trees and to trace the prediction of an object. For simplicity I trained model with n_estimators = 1. But when I make a prediction for some object, I don't understand, how to get the same value with fitted trees.




So the prediction for object [0.92689...] is 0.334... (which is ok, according to the plot), but 0.334 doesn't seem to be one of the leaves values. So my question is, given the fitted xgboost (fitted trees of xgboost), how prediction of xgboost correspond to leaves values?
 A: Predictions of boosted models are sums of all the leaf weights $f_i(x)$ for some observation $x$. After $k$ rounds of boosting, the prediction $\hat{y}^{(k)}$ for a single observation is
$$
\hat{y}^{(0)} = f_0(x)\\
\hat{y}^{(1)} = \hat{y}^{(0)} + f_1(x) \\
\vdots \\
\hat{y}^{(k)} = \hat{y}^{(k-1)} + f_k(x) = \sum_{i=0}^k f_i(x)
$$
where $f_k$ is the prediction from the $k$th booster (tree). Note that $f_0$ is given ahead of time, not something learned by the xgboost model. Usually, $f_0$ is chosen to be some constant, such as the mean value of $y$.
In your regression model, $f_0 = 0.5$ for every observation. We know this because the printout of the model object says base_score=0.5. For the single sample you provide, we have $f_1(x)=-0.166 \dots$. This gives a prediction of $$\hat{y}^{(1)}=0.5 -0.166 \ldots = 0.334\dots$$
The xgboost documentation has a helpful introduction to how boosting works. https://xgboost.readthedocs.io/en/latest/tutorials/model.html
Other models (most notably classification models), will often predict some transformation of the sum of the leaf weights. For example: How does gradient boosting calculate probability estimates?
