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

Examples of Binary Classification

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 a technique like gradient decent must be used instead.

Logistic Regression

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. 

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 $$\textrm{\{cat, dog\}}$$.

University of Michigan - Ann Arbor

Claude

In machine learning, classification refers to a predictive modeling problem where a class label is predicted for a given example of input data. There are three main types of classification tasks that you may encounter; they are:
- Binary Classification,
- Multi-Class Classification,
- Multi-Label Classification.


3 Types of Classification Tasks in Machine Learning

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.

An Introduction to Statistical Learning with Applications in R

Developers need to know what works and how to use it. This site uses less math and more tutorials with working code.
https://machinelearningmastery.com/

Machine Learning Mastery

Dive into Deep Learning

Multi-label classification is a machine learning problem focused on predicting classes that are not mutually exclusive, allowing a single example to be assigned to multiple categories simultaneously. This formulation is particularly useful for auto-tagging tasks, where an item (such as a blog post or an image) might be associated with several correlated tags at once.

Multi-Label Classification

Multiclass-multioutput classification (also known as multitask classification) is a classification task which labels each sample with a set of non-binary properties. Both the number of properties and the number of classes per property is greater than 2. A single estimator thus handles several joint classification tasks. This is both a generalization of the multilabel classification task, which only considers binary attributes, as well as a generalization of the multiclass classification task, where only one property is considered.

https://scikit-learn.org/stable/modules/multiclass.html

Multiclass-multioutput Classification

Binary Classification

Multiclass classification is a type of classification problem where the goal is to assign an example to one of more than two possible classes. A typical application is handwritten character recognition, which involves categorizing inputs into many distinct, mutually exclusive categories such as $$\textrm{\{0, 1, 2, ... 9, a, b, c, ...\}}$$.

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