Kernel Logistic Regression
Explore kernel logistic regression to overcome the limits of linear models by applying the kernel trick. Understand how to optimize using BCE loss and gradient descent with Gram matrices to classify complex, nonlinear data.
We'll cover the following...
In the previous lessons, we mastered logistic regression, a powerful discriminative classifier, and understood how to optimize it using gradient descent on the BCE Loss. However, as a linear model, standard logistic regression is fundamentally limited to solving problems where the classes are linearly separable.
To overcome this limitation and enable logistic regression to tackle complex, non-linear data (like concentric circles or interlocking spirals), we must employ the kernel trick.
We can kernelize logistic regression just like other linear models by observing that the parameter vector is a linear combination of the feature vectors , that is:
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