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I am trying to use Logistic Regression to make a spam filter, but I am having trouble understanding the weight update part. I have processed my email dataset, and I have an attribute vector of the top n words that are most likely to be contained within a spam.

From my understanding, during training, I will have to implement an optimization formula after each training example in order to update the weights.

$$ w_l \leftarrow w_l + \eta \cdot \sum_{i=1}^m [ y^{(i)} - P(c_+ \mid \vec{x}^{(i)} )] \cdot x_l^{(i)} $$

How does a formula such as this work? How can it be implemented in Python?

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