Today I learned that there are two fundamental ways to understand how Logistic Regression works and makes predictions:
In the Perceptron trick, we run the model through multiple iterations (epochs). In each iteration, we select a data point and update the weights based on the difference between the actual and predicted values.
The General Equation:
W_new = W_old + (Learning Rate) * (y - y_predicted) * Xi
This equation updates the weights of our decision boundary (W1x1 + W2x2 + W0 = 0). As the weights change, the position and orientation of the line shift until it effectively separates the classes.
The main limitation of the Perceptron trick is that it stops as soon as it finds a line that separates the data points correctly. It doesn't look for the best possible line—just any line that works.
Because it doesn't aim for the maximum margin or optimal separation, it often fails when classifying new, unseen data points that fall close to the boundary. This is where the Probability Method (used in libraries like Scikit-learn) comes in. It doesn't just look for a "pass/fail" separation; it optimizes for the highest probability of being correct.
Understanding the weakness of the Perceptron trick is the best way to appreciate why we use the Probabilistic approach in modern machine learning. I’ll be diving into the Probability Method in my next post!
Check out the full explanation here: youtube.com/watch
Feel free to leave a comment with your thoughts or questions!
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