Supervised learning (SL) is a paradigm in machine learning where input objects (for example, a vector of predictor variables) and a desired output value (also known as human-labeled supervisory signal) train a model. The training data is processed, building a function that maps new data on expected output values.^[1] An optimal scenario will allow for the algorithm to correctly determine output values for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way (see inductive bias). This statistical quality of an algorithm is measured through the so-called generalization error.

Tendency for a task to employ supervised vs. unsupervised methods. Task names straddling circle boundaries is intentional. It shows that the classical division of imaginative tasks (left) employing unsupervised methods is blurred in today's learning schemes.

Steps to follow

To solve a given problem of supervised learning, one has to perform the following steps:

1. Determine the type of training examples. Before doing anything else, the user should decide what kind of data is to be used as a training set. In the case of handwriting analysis, for example, this might be a single handwritten character, an entire handwritten word, an entire sentence of handwriting or perhaps a full paragraph of handwriting.
2. Gather a training set. The training set needs to be representative of the real-world use of the function. Thus, a set of input objects is gathered and corresponding outputs are also gathered, either from human experts or from measurements.
3. Determine the input feature representation of the learned function. The accuracy of the learned function depends strongly on how the input object is represented. Typically, the input object is transformed into a feature vector, which contains a number of features that are descriptive of the object. The number of features should not be too large, because of the curse of dimensionality; but should contain enough information to accurately predict the output.
4. Determine the structure of the learned function and corresponding learning algorithm. For example, the engineer may choose to use support-vector machines or decision trees.
5. Complete the design. Run the learning algorithm on the gathered training set. Some supervised learning algorithms require the user to determine certain control parameters. These parameters may be adjusted by optimizing performance on a subset (called a validation set) of the training set, or via cross-validation.
6. Evaluate the accuracy of the learned function. After parameter adjustment and learning, the performance of the resulting function should be measured on a test set that is separate from the training set.

Algorithm choice

A wide range of supervised learning algorithms are available, each with its strengths and weaknesses. There is no single learning algorithm that works best on all supervised learning problems (see the No free lunch theorem).

There are four major issues to consider in supervised learning:

How supervised learning algorithms work

Given a set of ${\displaystyle N}$ training examples of the form ${\displaystyle \{(x_{1},y_{1}),...,(x_{N},\;y_{N})\}}$ such that ${\displaystyle x_{i}}$ is the feature vector of the ${\displaystyle i}$-th example and ${\displaystyle y_{i}}$ is its label (i.e., class), a learning algorithm seeks a function ${\displaystyle g:X\to Y}$, where ${\displaystyle X}$ is the input space and ${\displaystyle Y}$ is the output space. The function ${\displaystyle g}$ is an element of some space of possible functions ${\displaystyle G}$, usually called the hypothesis space. It is sometimes convenient to represent ${\displaystyle g}$ using a scoring function ${\displaystyle f:X\times Y\to \mathbb {R} }$ such that ${\displaystyle g}$ is defined as returning the ${\displaystyle y}$ value that gives the highest score: ${\displaystyle g(x)={\underset {y}{\arg \max }}\;f(x,y)}$. Let ${\displaystyle F}$ denote the space of scoring functions.

Although ${\displaystyle G}$ and ${\displaystyle F}$ can be any space of functions, many learning algorithms are probabilistic models where ${\displaystyle g}$ takes the form of a conditional probability model ${\displaystyle g(x)={\underset {y}{\arg \max }}\;P(y|x)}$, or ${\displaystyle f}$ takes the form of a joint probability model ${\displaystyle f(x,y)=P(x,y)}$. For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

There are two basic approaches to choosing ${\displaystyle f}$ or ${\displaystyle g}$: empirical risk minimization and structural risk minimization.^[6] Empirical risk minimization seeks the function that best fits the training data. Structural risk minimization includes a penalty function that controls the bias/variance tradeoff.

In both cases, it is assumed that the training set consists of a sample of independent and identically distributed pairs, ${\displaystyle (x_{i},\;y_{i})}$. In order to measure how well a function fits the training data, a loss function ${\displaystyle L:Y\times Y\to \mathbb {R} ^{\geq 0}}$ is defined. For training example ${\displaystyle (x_{i},\;y_{i})}$, the loss of predicting the value ${\displaystyle {\hat {y}}}$ is ${\displaystyle L(y_{i},{\hat {y}})}$.

The risk ${\displaystyle R(g)}$ of function ${\displaystyle g}$ is defined as the expected loss of ${\displaystyle g}$. This can be estimated from the training data as

${\displaystyle R_{emp}(g)={\frac {1}{N}}\sum _{i}L(y_{i},g(x_{i}))}$.

Generative training

The training methods described above are discriminative training methods, because they seek to find a function ${\displaystyle g}$ that discriminates well between the different output values (see discriminative model). For the special case where ${\displaystyle f(x,y)=P(x,y)}$ is a joint probability distribution and the loss function is the negative log likelihood ${\displaystyle -\sum _{i}\log P(x_{i},y_{i}),}$ a risk minimization algorithm is said to perform generative training, because ${\displaystyle f}$ can be regarded as a generative model that explains how the data were generated. Generative training algorithms are often simpler and more computationally efficient than discriminative training algorithms. In some cases, the solution can be computed in closed form as in naive Bayes and linear discriminant analysis.

Generalizations

There are several ways in which the standard supervised learning problem can be generalized:

• Semi-supervised learning or weak supervision: the desired output values are provided only for a subset of the training data. The remaining data is unlabeled or imprecisely labeled.
• Active learning: Instead of assuming that all of the training examples are given at the start, active learning algorithms interactively collect new examples, typically by making queries to a human user. Often, the queries are based on unlabeled data, which is a scenario that combines semi-supervised learning with active learning.
• Structured prediction: When the desired output value is a complex object, such as a parse tree or a labeled graph, then standard methods must be extended.
• Learning to rank: When the input is a set of objects and the desired output is a ranking of those objects, then again the standard methods must be extended.

Approaches and algorithms

• Analytical learning
• Artificial neural network
• Backpropagation
• Boosting (meta-algorithm)
• Bayesian statistics
• Case-based reasoning
• Decision tree learning
• Inductive logic programming
• Gaussian process regression
• Genetic programming
• Group method of data handling
• Kernel estimators
• Learning automata
• Learning classifier systems
• Learning vector quantization
• Minimum message length (decision trees, decision graphs, etc.)
• Multilinear subspace learning
• Naive Bayes classifier
• Maximum entropy classifier
• Conditional random field
• Nearest neighbor algorithm
• Probably approximately correct learning (PAC) learning
• Ripple down rules, a knowledge acquisition methodology
• Symbolic machine learning algorithms
• Subsymbolic machine learning algorithms
• Support vector machines
• Minimum complexity machines (MCM)
• Random forests
• Ensembles of classifiers
• Ordinal classification
• Data pre-processing
• Handling imbalanced datasets
• Statistical relational learning
• Proaftn, a multicriteria classification algorithm

Applications

• Bioinformatics
• Cheminformatics
  • Quantitative structure–activity relationship
• Database marketing
• Handwriting recognition
• Information retrieval
  • Learning to rank
• Information extraction
• Object recognition in computer vision
• Optical character recognition
• Spam detection
• Pattern recognition
• Speech recognition
• Supervised learning is a special case of downward causation in biological systems
• Landform classification using satellite imagery^[7]
• Spend classification in procurement processes^[8]

General issues

• Computational learning theory
• Inductive bias
• Overfitting (machine learning)
• (Uncalibrated) class membership probabilities
• Unsupervised learning
• Version spaces

See also

• List of datasets for machine learning research

References

External links

• Machine Learning Open Source Software (MLOSS)