- Email spam detection (spam or not).
- Churn prediction (churn or not).
- Conversion prediction (buy or not).

University of Michigan - Ann Arbor

Binary classification is the simplest form of classification problem where there are exactly two possible classes or categories to predict. A common example is designing a classifier that takes an image as input and outputs the predicted class assignment from a set of two options, such as $$\textrm{\{cat, dog\}}$$.

Binary Classification

Developers need to know what works and how to use it. This site uses less math and more tutorials with working code.
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Logistic regression is used to model discontinuous output choices - for example, when a variable is 'yes' or 'no' rather than a continuous value. In this case, logistic regression calculates the probability of a given categorical output, and decides on a threshold at which the model decides between categories to select for output. 

Logistic Regression

Logistic regression is a statistical model that forces the output of an otherwise unbounded function to the interval (0, 1). $$p(y=1 | x;\theta) = \sigma(\theta^\top x)$$ $$\sigma(x) = \frac{e^x}{e^x + 1}$$ $$p(y=0 | x;\theta) = 1 - p(y=1 | x;\theta)$$ Where $$\theta$$ is the parameter vector. For binary classification problems, logistic regression can be used instead of linear regression to handle the discontinuous nature of the target output. However, the sigmoid function $$\sigma$$ has no local minimum or maximum, so an optimization technique like gradient descent must be used instead.

Logistic Regression Model

For binary classification tasks, an easier task generally requires fewer labeled training examples than a harder task to reach a comparable performance level. Here, task difficulty is an informal comparison rather than a precisely defined quantity.

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