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Small fixes to notation in documentation (#2903)

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* make every theta lowercase

* use uniform font and capitalization for function name
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Viraj Navkal 2017-11-28 13:32:35 -08:00 committed by Tianqi Chen
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doc/model.md
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@ -31,7 +31,7 @@ to measure the performance of the model given a certain set of parameters.
A very important fact about objective functions is they ***must always*** contain two parts: training loss and regularization. A very important fact about objective functions is they ***must always*** contain two parts: training loss and regularization.
```math ```math
Obj(\Theta) = L(\theta) + \Omega(\Theta) \text{obj}(\theta) = L(\theta) + \Omega(\theta)
``` ```
where ``$ L $`` is the training loss function, and ``$ \Omega $`` is the regularization term. The training loss measures how *predictive* our model is on training data. where ``$ L $`` is the training loss function, and ``$ \Omega $`` is the regularization term. The training loss measures how *predictive* our model is on training data.
@ -188,7 +188,7 @@ By defining it formally, we can get a better idea of what we are learning, and y
Here is the magical part of the derivation. After reformalizing the tree model, we can write the objective value with the ``$ t$``-th tree as: Here is the magical part of the derivation. After reformalizing the tree model, we can write the objective value with the ``$ t$``-th tree as:
```math ```math
Obj^{(t)} &\approx \sum_{i=1}^n [g_i w_{q(x_i)} + \frac{1}{2} h_i w_{q(x_i)}^2] + \gamma T + \frac{1}{2}\lambda \sum_{j=1}^T w_j^2\\ \text{obj}^{(t)} &\approx \sum_{i=1}^n [g_i w_{q(x_i)} + \frac{1}{2} h_i w_{q(x_i)}^2] + \gamma T + \frac{1}{2}\lambda \sum_{j=1}^T w_j^2\\
&= \sum^T_{j=1} [(\sum_{i\in I_j} g_i) w_j + \frac{1}{2} (\sum_{i\in I_j} h_i + \lambda) w_j^2 ] + \gamma T &= \sum^T_{j=1} [(\sum_{i\in I_j} g_i) w_j + \frac{1}{2} (\sum_{i\in I_j} h_i + \lambda) w_j^2 ] + \gamma T
``` ```