TIL about Logistic Regression permalink

\[\ h_{\theta}(x) = \frac{1}{ 1 + e^{ -{\theta}^{\intercal}x } } \]

Logistic regression is a form of machine learning used to determine a discrete, non-continuous value. Today, I started learning abaut binary classification which has two cases - negative (0) and positive (1) - that your prediction can result in. This is accomplished using a Sigmoid function; otherwise known as a logistic function - hence the name, logistic regression.

Examples include:

Like linear regression, logistic regression also has a cost function used to fit parameters to the algorithm based on training data:

\[\ J({\theta}) = \frac{1}{m} \cdot -y^{\intercal}log(h) - (1 - y)^{\intercal} log(1-h) \]

And since the cost function is convex, we can use a slightly modified version of gradient descent to learn the parameters:

\[\ \theta := \theta - \frac{\alpha}{m}X^{\intercal}( \frac{1}{1 + e^{ -{\theta}^{\intercal}x }} - \overset{\rarr}{y}) \]

There is a form of multiclass classification in which the prediction has more than two cases, but I get to learn that tomorrow!


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