Fix negative log-likelihood gradient

Author: brentyi

neural-networks-2.md

@@ -264,7 +264,7 @@ $$
 L_i = -\sum_j y_{ij} \log(\sigma(f_j)) + (1 - y_{ij}) \log(1 - \sigma(f_j))
 $$
 
-where the labels \\(y_{ij}\\) are assumed to be either 1 (positive) or 0 (negative), and \\(\sigma(\cdot)\\) is the sigmoid function. The expression above can look scary but the gradient on \\(f\\) is in fact extremely simple and intuitive: \\(\partial{L_i} / \partial{f_j} = y_{ij} - \sigma(f_j)\\) (as you can double check yourself by taking the derivatives).
+where the labels \\(y_{ij}\\) are assumed to be either 1 (positive) or 0 (negative), and \\(\sigma(\cdot)\\) is the sigmoid function. The expression above can look scary but the gradient on \\(f\\) is in fact extremely simple and intuitive: \\(\partial{L_i} / \partial{f_j} = \sigma(f_j) - y_{ij}\\) (as you can double check yourself by taking the derivatives).
 
 **Regression** is the task of predicting real-valued quantities, such as the price of houses or the length of something in an image. For this task, it is common to compute the loss between the predicted quantity and the true answer and then measure the L2 squared norm, or L1 norm of the difference. The L2 norm squared would compute the loss for a single example of the form: