# Parametric Machine Learning Algorithms

Assumptions can greatly simplify the learning process, but can also limit what can be learned. Algorithms that simplify the function to a known form are called parametric machine learning algorithms.

A learning model that summarizes data with a set of parameters of fixed size (independent of the number of training examples) is called a parametric model. No matter how much data you throw at a parametric model, it won’t change its mind about how many parameters it needs.
The algorithms involve two steps:

1. Select a form for the function.
2. Learn the coefficients for the function from the training data.

An easy to understand functional form for the mapping function is a line, as is used in linear regression:

b0 + b1x1 + b2x2 = 0

Where b0, b1 and b2 are the coefficients of the line that control the intercept and slope, and x1 and x2 are two input variables.

Assuming the functional form of a line greatly simplifies the learning process. Now, all we need to do is estimate the coefficients of the line equation and we have a predictive model for the problem.

Often the assumed functional form is a linear combination of the input variables and as such parametric machine learning algorithms are often also called “linear machine learning algorithms“.

The problem is, the actual unknown underlying function may not be a linear function like a line. It could be almost a line and require some minor transformation of the input data to work right. Or it could be nothing like a line in which case the assumption is wrong and the approach will produce poor results.

Some more examples of parametric machine learning algorithms include:

• Logistic Regression
• Linear Discriminant Analysis
• Perceptron
• Naive Bayes
• Simple Neural Networks

Benefits of Parametric Machine Learning Algorithms:

• Simpler: These methods are easier to understand and interpret results.
• Speed: Parametric models are very fast to learn from data.
• Less Data: They do not require as much training data and can work well even if the fit to the data is not perfect.

Limitations of Parametric Machine Learning Algorithms:

• Constrained: By choosing a functional form these methods are highly constrained to the specified form.
• Limited Complexity: The methods are more suited to simpler problems.
• Poor Fit: In practice the methods are unlikely to match the underlying mapping function.