What is the meaning of a quantile regression model that predicts the conditional mean? What does that phrase "quantile regression model that predicts the conditional mean"  mean? How to interpret that?
I found it in Liu et al. (2020).
The authors have compared the results of linear regression, QRF conditional mean, QRF conditional median, QRF conditional first quantile, and QRF conditional third quantile. What confuses me is that for my little understanding, QRF predicting the conditional mean is exactly the same as Random forest, and the results for both should be identical, which is not the case in that paper! Note: the authors use R packages randomForest, and quantregForest.
 A: The article "A predictive analytics tool to provide visibility
into completion of work orders in supply chain
systems" that you refer to is not very clear about it.
At some point they actually say the following

As a generalization of Random Forest, Quantile Regression Forest predicts the conditional quantiles instead of the
conditional mean

So it is a bit odd that they speak about QRF predicting the conditional mean.
But indeed, in the results section of the article they suddenly introduce 'QRF conditional mean'. They only use this term in four places (only in the results) and do not explain it.

A wild guess might be that it relates to how they perform the bagging in the random forests algorithm.
They explain how they obtain several regression tree estimates $\hat{y}_m$ and as a final result use the average of $M$ trees
$$\hat{y}(\mathbf{x}^\prime) = \frac{1}{M} \sum_{m=1}^M \hat{y}_m(\mathbf{x}^\prime)$$
Then they explain quantile regression forest as using a different cost function (the absolute error). But in addition it seems that they also use a different bagging method with an additional equation. If we fill in their equation 6 into equation 3, then we get
$$Q_\alpha(\mathbf{x}) = \text{inf}\left\{ y: \frac{1}{M} \sum_{m=1}^M \mathbf{1}_{\hat{y}_m(\mathbf{x}^\prime)\leq y} \geq \alpha \right\}  $$
It could be that their 'QRF conditional mean', 'QRF conditional median', 'QRF conditional 1st quantile' and 'QRF conditional 3rd quantile', relate to the different bagging methods.
So it could be that this 'quantile regression model that predicts the conditional mean' relates to something like median of means or mean of medians.
