# Difference between Parametric vs Non-Parametric Models

When working with machine learning models, data scientists often come across a fundamental question: What sets parametric and non-parametric models apart? This is also one of the most frequent questions asked in the interviews.

Machine learning models can be parametric or non-parametric. Parametric models are those that require the specification of some parameters before they can be used to make predictions, while non-parametric models do not rely on any specific parameter settings and therefore often produce more accurate results. These two distinct approaches play a crucial role in predictive modeling, each offering unique advantages and considerations. This blog post discusses parametric vs non-parametric machine learning models with examples along with the key differences.

## What are parametric and non-parametric models?

Training machine learning models is about finding a function approximation built using input or predictor variables, and whose output represents the response variable. The reason why it is called function approximation is that there is always an error in relation to the value of function output vs actual or real-world value. And, an aspect of this error is reducible in the sense that further features/techniques can be used to improve upon the accuracy. Another aspect of this error is irreducible which represents the random error that can’t be dealt with. Learn greater details on basic concepts of machine learning in my other post – What is machine learning? Concepts and examples.

When estimating the function (called function approximation), the following two steps are followed:

• Identifying the function: The first step is to identify the function such as linear or non-linear function.
• Identifying the parameters of the function in case this is a linear function.

In case, the function identified is a linear function (model), the training or fitting of the machine learning models boils down to estimating the parameters. Here is an example of the linear model also called as linear regression model and related parameters (coefficients).

Such models are called parametric machine learning models. The parametric models are linear models which include determining the parameters such as that shown above. The most common approach to fitting the above model is referred to as the ordinary least squares (OLS) method. However, least squares are one of many possible ways to fit the linear model.

Parametric models require the prior specification of a set of parameters that define the underlying distribution of the data. This predetermined structure allows parametric models to make predictions based on a fixed number of parameters, regardless of the size of the training dataset. Common examples of parametric models include linear regression, Lasso regression, Ridge regression, logistic regression, etc.

Building non-parametric models do not make explicit assumptions about the functional form such as a linear model in the case of parametric models. Instead, non-parametric models can be seen as the function approximation that gets as close to the data points as possible. Non-parametric models do not rely on predefined parameter settings, enabling them to adapt to complex and irregular patterns within the data. The advantage over parametric approaches is that by avoiding the assumption of a particular functional form such as a linear model, non-parametric models have the potential to accurately fit a wider range of possible shapes for the actual or true function. Any parametric approach brings with it the possibility that the functional form (linear model) which is very different from the true function, in which case the resulting model will not fit the data well. Examples of non-parametric models include fully non-linear algorithms such as bagging, boosting, support vector machines, decision trees, random forests, etc.

## What’s the difference between parametric and non-parametric models?

The following is the list of differences between parametric and non-parametric machine learning models.

• In the case of parametric models, the assumption related to the functional form is made and a linear model is considered. In the case of non-parametric models, the assumption about the functional form is not made.
• Parametric models are much easier to fit than non-parametric models because parametric machine learning models only require the estimation of a set of parameters as the model is identified prior to a linear model. In the case of a non-parametric model, one needs to estimate some arbitrary function which is a much more difficult task.
• Parametric models often do not match the unknown function we are trying to estimate. The model performance is comparatively lower than the non-parametric models. The estimates done by the parametric models will be farther from being true.
• Parametric models are interpretable, unlike non-parametric models. This essentially means that one can go for parametric models when the goal is to find an inference. Instead, one can choose to go for non-parametric models when the goal is to make predictions with higher accuracy and interpretability or inference is not the key ask.

Here are the differences in the tabular form:

   Parametric Models Non-Parametric Models Definition Require predefined parameter settings Do not rely on specific parameters Flexibility Less flexible, assume fixed data structure Highly flexible, adapt to complex patterns Assumptions Make strong assumptions about data distribution Fewer assumptions about data distribution Complexity Simpler model structure More complex model structure Interpretability More interpretable Less interpretable Performance Efficient for large datasets with limited features Perform well with high-dimensional data

## When to use parametric vs non-parametric algorithms/methods for building machine learning models?

When the goal is to achieve models with high-performance prediction accuracy, one can go for non-linear methods such as bagging, boosting, support vector machines bagging boosting with non-linear kernels, and neural networks (deep learning). When the goal is to achieve modeling for making inferences, one can go for parametric methods such as lasso regression, linear regression, etc which have high interpretability. You may want to check a related post on the difference between prediction and inference – Machine learning: Prediction & Inference Difference

The parametric vs. non-parametric machine learning models debate is a longstanding one and it’s not easy to find an answer that satisfies everyone. What we can say for sure is this: parametric models are easier to work with but they don’t always produce the most accurate results, whereas non-parametric models require more time and effort upfront but will give you better accuracy in your predictions if done correctly. Whether you should use parametric or non-parametric depends on what your goals are as well as how comfortable your team members feel about working with them – hopefully now that we’ve given some insight into both sides of the argument, you’ll be able to make up your own mind!

## Ajitesh Kumar

I have been recently working in the area of Data analytics including Data Science and Machine Learning / Deep Learning. I am also passionate about different technologies including programming languages such as Java/JEE, Javascript, Python, R, Julia, etc, and technologies such as Blockchain, mobile computing, cloud-native technologies, application security, cloud computing platforms, big data, etc. I would love to connect with you on Linkedin. Check out my latest book titled as First Principles Thinking: Building winning products using first principles thinking.
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