[docs] Fix formula in path smoothing docs (fixes #5139)(#5154)

microsoft · Apr 15, 2022 · fc0c8fd · fc0c8fd
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diff --git a/docs/Parameters.rst b/docs/Parameters.rst
@@ -594,7 +594,7 @@ Learning Control Parameters
 
    -  larger values give stronger regularization
 
-      -  the weight of each node is ``(n / path_smooth) * w + w_p / (n / path_smooth + 1)``, where ``n`` is the number of samples in the node, ``w`` is the optimal node weight to minimise the loss (approximately ``-sum_gradients / sum_hessians``), and ``w_p`` is the weight of the parent node
+      -  the weight of each node is ``w * (n / path_smooth) / (n / path_smooth + 1) + w_p / (n / path_smooth + 1)``, where ``n`` is the number of samples in the node, ``w`` is the optimal node weight to minimise the loss (approximately ``-sum_gradients / sum_hessians``), and ``w_p`` is the weight of the parent node
 
       -  note that the parent output ``w_p`` itself has smoothing applied, unless it is the root node, so that the smoothing effect accumulates with the tree depth
 

diff --git a/include/LightGBM/config.h b/include/LightGBM/config.h
@@ -531,7 +531,7 @@ struct Config {
   // desc = if set to zero, no smoothing is applied
   // desc = if ``path_smooth > 0`` then ``min_data_in_leaf`` must be at least ``2``
   // desc = larger values give stronger regularization
-  // descl2 = the weight of each node is ``(n / path_smooth) * w + w_p / (n / path_smooth + 1)``, where ``n`` is the number of samples in the node, ``w`` is the optimal node weight to minimise the loss (approximately ``-sum_gradients / sum_hessians``), and ``w_p`` is the weight of the parent node
+  // descl2 = the weight of each node is ``w * (n / path_smooth) / (n / path_smooth + 1) + w_p / (n / path_smooth + 1)``, where ``n`` is the number of samples in the node, ``w`` is the optimal node weight to minimise the loss (approximately ``-sum_gradients / sum_hessians``), and ``w_p`` is the weight of the parent node
   // descl2 = note that the parent output ``w_p`` itself has smoothing applied, unless it is the root node, so that the smoothing effect accumulates with the tree depth
   double path_smooth = 0;