# Differences Between Parametric and Nonparametric Algorithms: Which One You Need To Pick

If you are a **data scientist**, you might have heard about parametric and nonparametric algorithms. But do you really know what the key difference between them and what are popular algorithms will fall under both these categories ?

If the answer is right, then let’s deep dive to know the hidden truth’s about parametric and nonparametric algorithms.

Let’s begin with assumptions first.

Strong assumptions are made about the underlying distribution of the data by parametric algorithms. They erroneously assume that the data adheres to a particular probability distribution.

Such as the normal distribution, and that the distribution's parameters are either known or can be inferred from the data. ANOVA, **logistic regression,** and linear regression are a few examples of parametric algorithms.

On the other hand, nonparametric algorithms place the least amount of reliance on the data's underlying distribution. Nonparametric algorithms estimate the distribution directly from the data rather than assuming a particular distribution. Few nonparametric algorithm examples are

**Random forests**,- decision trees,
- k-nearest neighbors

Differences Between Parametric and Nonparametric Algorithms

The type of data you have, the size of the dataset, the difficulty of the problem, and the desired level of accuracy are just a few of the variables that must be considered when selecting the best algorithm for your **data analysis **needs.

Generally speaking, parametric algorithms are more suitable when the underlying data distribution is known or can be estimated, and when the dataset is large enough to estimate the distribution's parameters accurately.

Nonparametric algorithms, on the other hand, are more appropriate when the underlying distribution of the data is unknown or cannot be estimated, and when the dataset is small or noisy. Nonparametric algorithms are also more flexible and can handle a wider range of data types and distributions than parametric algorithms.

In this article, we will delve deeper into the world of parametric and nonparametric algorithms and provide a comprehensive guide to understanding their differences, applications, advantages, and disadvantages.

We will cover various topics such as the basics of parametric and nonparametric algorithms, their applications in different fields, and their strengths and limitations. We will also discuss how to choose the right algorithm for your data analysis needs based on the specific characteristics of your data and problem.

## Definition of Parametric and Nonparametric Algorithms

The Machine Learning Algorithms are trained on the available data and used to predict future or unknow target data. Sometimes used get the glean insights from data. These algorithms can be divided into two main categories:

**Parametric Algorithms:**Parametric algorithms operate under predefined assumptions regarding the distribution and relationships in the underlying data, utilizing a fixed number of parameters to predict new data points based on these assumptions.

**Nonparametric Algorithms:**Nonparametric algorithms do not make explicit assumptions about the data distribution or the predictor function, allowing for more flexibility and adaptability to the structure of the data, often at the expense of requiring more data and computational resources.

Effective data analysis depends on knowing how these two categories of algorithms differ from one another. We will define parametric and nonparametric algorithms in this article, go over their significance, and contrast their advantages and disadvantages.

Inferences are made by parametric algorithms regarding the data's underlying distribution. These presumptions are frequently founded on a predetermined set of variables, like the mean and variance of a normal distribution.

The algorithm then uses these parameters to make predictions by estimating them from the data. Common examples of parametric algorithms include linear regression and logistic regression.

On the other hand, nonparametric algorithms don't make any assumptions regarding the fundamental distribution of the data. Instead, they base their predictions on the data itself.

The relationship between the predictors and the outcome variable need not take a specific functional form in order to be used with nonparametric algorithms. Common examples of nonparametric algorithms include decision trees and random forests.

It is crucial to comprehend the differences between parametric and nonparametric algorithms for a number of reasons. It first enables data analysts to choose the best algorithm for their unique problem.

A parametric algorithm may be the best option if the underlying distribution of the data is known or assumed to take a particular form. However, a nonparametric algorithm might be more appropriate if the data does not follow a particular distribution.

Second, knowing the distinctions between parametric and nonparametric algorithms can aid analysts in better understanding the meaning of their findings. Estimates of the underlying parameters are provided by parametric algorithms, and these estimates can be used to draw conclusions about the population.

Estimates of the relationships between variables are provided by nonparametric algorithms, which can be used to make predictions or identify significant

## What Are Parametric Algorithms

Parametric algorithms are a type of machine learning algorithm that makes assumptions about the underlying distribution of the data. They are based on a fixed set of parameters that are learned from the training data and used to make predictions on new, unseen data.

Parametric algorithms can be applied to a wide range of data types, including continuous and categorical variables. Some examples of parametric algorithms include

Linear regression is a parametric algorithm used to model the relationship between a dependent variable and one or more independent variables. It assumes that the relationship between the variables is linear and uses a set of coefficients to determine the slope and intercept of the line.

Logistic regression is a parametric algorithm used for binary classification tasks. It models the probability of an event occurring based on the values of the input variables. Naive Bayes is a probabilistic algorithm used for classification tasks. It assumes that the input variables are independent of each other and calculates the probability of each class given the input variables.

### Advantages and disadvantages of parametric algorithms

The simplicity of parametric algorithms is one of their main benefits. They are frequently simpler to understand and apply than nonparametric algorithms because they make assumptions about the underlying distribution of the data.

Additionally, they need less training data to learn the parameters, which is advantageous when there is a shortage of data.

The assumptions that parametric algorithms make, however, can also be a drawback. The resulting model might not accurately depict the data if the underlying distribution of the data does not concur with the assumptions made by the algorithm.

Furthermore, if the data contains outliers or **missing values,** a parametric algorithm's performance may be negatively impacted.

### Use cases for Parametric Algorithms

Parametric algorithms are commonly used in situations where the underlying distribution of the data is known or can be reasonably assumed. They are particularly effective in situations where the number of input variables is small relative to the size of the training data set.

Some common use cases for parametric algorithms include predicting housing prices based on features such as square footage and number of bedrooms, predicting the likelihood of customer churn based on demographic information, and identifying **spam emails** based on their content

### List Of Parametric Algorithms

1. Linear Regression

Logistic Regression

Perceptron

Naive Bayes

Multinomial Naive Bayes

Bernoulli Naive Bayes

Linear SVM

Ordinary Least Squares Regression (OLS)

Quadratic Discriminant Analysis (QDA)

Parametric

**Time Series**MethodsAR (AutoRegressive)

MA (Moving Average)

ARIMA (AutoRegressive Integrated Moving Average)

Mixtures of Gaussians

Multivariate Adaptive Regression Splines (MARS)

These are some of the most well-known parametric algorithms. It's important to understand the assumptions these models make about the underlying data, as these assumptions can greatly affect the **model's performance**.

If the assumptions are violated, the model might not perform well. In such cases, non-parametric methods might be more appropriate.

## What are Nonparametric Algorithms

When it comes to data analysis and machine learning, nonparametric algorithms are an alternative to their parametric counterparts. Unlike parametric algorithms, nonparametric algorithms do not make any assumptions about the underlying distribution of the data.

Instead, they rely on methods such as ranking, sorting, and order statistics to extract patterns and insights from the data.

Nonparametric algorithms are a class of** machine learning algorithms** that do not make assumptions about the underlying distribution of the data. These algorithms are useful when there is limited information about the data and when the data distribution is unknown.

Nonparametric algorithms do not have fixed numbers of parameters and the number of parameters grows with the size of the training data.

Examples of nonparametric algorithms include **decision trees**, k-nearest neighbors, and support vector machines. Decision trees are a popular nonparametric algorithm that recursively splits the data into subsets based on the value of an attribute until a stopping criterion is met.

**K-nearest neighbors** is another nonparametric algorithm that classifies a new data point based on the class of its k nearest neighbors in the training set. **Support vector machines** are nonparametric algorithms that find a hyperplane that separates the data into different classes

### Advantages and disadvantages of nonparametric algorithms

The main advantage of nonparametric algorithms is their flexibility and ability to handle complex and nonlinear relationships between variables. They can work well with small sample sizes and are less sensitive to outliers and assumptions about the underlying distribution of the data.

Nonparametric algorithms can also be easily adapted to different types of data and are less affected by the curse of dimensionality.

However, nonparametric algorithms may require larger sample sizes compared to parametric algorithms to achieve the same level of accuracy. They can also be computationally intensive and slower to train and evaluate. Nonparametric algorithms may also suffer from overfitting if the model is too complex or if the training data is not representative of the population.

### Use cases for nonparametric algorithms

Applications for nonparametric algorithms include speech and image recognition, natural language processing, and recommender systems. They are frequently used in ecological and environmental studies as well, where the underlying data distribution may be complicated and nonlinear.

When assumptions about the distribution of the data may not hold true or when there is little prior knowledge about the data, nonparametric algorithms can be especially helpful.

### List Of Nonparametric Algorithms

Here's a list of some popular nonparametric algorithms in machine learning:

#### Classification and Regression Algorithms

For classification and regression

Decision Trees

C4.5

ID3 (Iterative Dichotomiser 3)

With a non-linear kernel, such as Radial Basis Function (RBF) Kernel

#### Clustering Algorithms

Agglomerative Clustering

Divisive Clustering

k-Means Clustering

DBSCAN (Density-Based Spatial Clustering of Applications with Noise)

Mean Shift Clustering

#### Ensemble Algorithms

Random Forest

Random Forest Classification

Random Forest Regression

Bootstrap Aggregating (Bagging)

Bagged Decision Trees

Bagged Support Vector Machines

#### Dimensionality Reduction

Kernel

**Principal Component Analysis**(PCA)t-Distributed Stochastic Neighbor Embedding (t-SNE)

Uniform Manifold Approximation and Projection (UMAP)

#### Neural Networks and Deep Learning

Artificial

**Neural Networks**(ANN)Deep Learning Models

Generative Adversarial Networks (GAN)

#### Association Rule Learning

Eclat Algorithm

#### Others Algorithms

Local Outlier Factor (LOF)

One-Class Support Vector Machines

These **algorithms have various applications** and are used for classification, regression, clustering, and dimensionality reduction among other tasks in machine learning. Always choose an algorithm based on the specific requirements and nature of your data to achieve the best possible **model performance.**

## What Is the Differences Between Parametric and Nonparametric Algorithms

The two main categories of algorithms used in machine learning are parametric and nonparametric. These two types of algorithms differ primarily in the data assumptions they base those assumptions on.

### Comparison of assumptions made by parametric and nonparametric algorithms

The assumption made by parametric algorithms is that the data will follow a particular distribution, like the normal distribution. A predetermined number of parameters for these algorithms are determined by the data.

Since it relies on the assumption that there is a linear relationship between the input variables and the output variable, linear regression is a classic illustration of a parametric algorithm.

On the other hand, nonparametric algorithms don't make any presumptions regarding the fundamental distribution of the data. Instead, they rely on the data itself to determine how the input variables and output variables relate to one another.

The **k-nearest neighbors algorithm** is an illustration of a nonparametric algorithm; it measures the separation between an input data point and its k closest neighbors in order to forecast an outcome variable.

### Comparison of complexity and flexibility of parametric and nonparametric algorithms

Since they are limited by their underlying data assumptions, parametric algorithms are typically less flexible than nonparametric algorithms. They may, however, require less data to train and be more computationally effective.

Since they can accommodate any underlying data distribution, nonparametric algorithms are more adaptable than parametric ones. They may, however, cost more to compute and require more training data.

### Comparison of accuracy and performance of parametric and nonparametric algorithms

The particular problem at hand determines the precision and effectiveness of parametric and nonparametric algorithms. When the assumptions made by the parametric algorithm are accurate, parametric algorithms may generally outperform nonparametric algorithms. However, the parametric algorithm might not work well if the assumptions are off.

On the other hand, nonparametric algorithms may outperform parametric algorithms when the data's underlying distribution is complex or unknowable. However, they might cost more to compute and may need more data to train.

## Difference Between Parametric and Non-Parametric Algorithms in Tabular Form

Below is a table outlining some key differences between parametric and non-parametric algorithms:

Feature | Parametric Algorithms | Non-Parametric Algorithms |
---|---|---|

| Make assumptions about data distribution and structure. | Make minimal assumptions about data distribution and structure. |

| Fixed number of parameters. | Number of parameters grows with the data. |

| Less flexible due to predefined assumptions. | More flexible and can adapt to various data structures. |

| Typically lower. | Typically higher, especially with larger datasets. |

| Can work well even with smaller datasets. | May require larger datasets for accurate predictions. |

| Generally more interpretable. | Can be less interpretable due to their flexibility. |

| Typically faster and require less data. | Can be slower and data-intensive. |

| Faster due to fewer parameters. | May be slower, especially with larger datasets. |

| When data distribution is known and data is limited. | When no prior knowledge about data distribution and sufficient data is available. |

| Linear Regression, Logistic Regression, etc. | k-Nearest Neighbors, Decision Trees, etc. |

| Sensitive to outliers due to strict assumptions. | Often more robust to outliers due to their flexibility. |

Each approach, parametric and non-parametric, has its own set of advantages and is suitable for different kinds of data and problem types. Choosing between them depends on various factors including data size, data distribution, problem complexity, and computational resources.

## How to Choose the Right Algorithm

When it comes to choosing between parametric and nonparametric algorithms for your data analysis, there are several factors to consider. The choice ultimately depends on the nature of the data you are working with, the assumptions you are willing to make, and the specific problem you are trying to solve.

### Factors to consider when choosing between parametric and nonparametric algorithms

One of the main factors to consider is the distribution of the data. Parametric algorithms assume that the data follows a specific distribution, such as a normal distribution. If your data follows a known distribution, then a parametric algorithm may be more appropriate.

On the other hand, if your data is not normally distributed or the distribution is unknown, a nonparametric algorithm may be more suitable.

Another factor to consider is the sample size. Parametric algorithms generally require a larger sample size to be effective. If you have a small sample size, then a nonparametric algorithm may be a better choice.

The assumptions made by parametric algorithms also need to be considered. If the assumptions are not met, then the results may be inaccurate or unreliable. Nonparametric algorithms, on the other hand, make fewer assumptions and are more robust to violations of these assumptions.

In some cases, the problem itself may dictate the choice of algorithm. For example, if you are trying to classify images or text data, then a nonparametric algorithm may be more appropriate since the distribution of these types of data is often unknown.

### Parametric Vs. Nonparametric Algorithm Implementation In Python

Real-world examples of when to use parametric vs. nonparametric algorithms

- Sepal Width vs. Sepal Length linearity test r-value: 0.11756978413300208
- Linear regression R-squared: 0.725963770390784
- KNN R-squared: 0.8388

In this code, we first visualize the distribution of the data using a scatter plot, with the color of the points representing the class labels. We can see that there is some overlap between the classes, which suggests that a linear classifier may not be the best choice.

Next, we check the normality assumption for the Sepal Length feature using a histogram and a normality test. The p-value of the normality test is greater than 0.05, which suggests that we can assume normality for this feature.

We also check the linearity assumption for the Sepal Width vs. Sepal Length relationship using a scatter plot and a correlation coefficient. The correlation coefficient is close to 0, which suggests that there is no linear relationship between these two features.

Finally, we fit a linear regression model and a k-nearest neighbors model to the data, and compare their performance using the R-squared metric. In this case, the KNN model outperforms the linear regression model, which is consistent with our observation that a **linear classifier** may not be the best choice for this data.

## Conclusion

In conclusion, choosing between parametric and nonparametric algorithms requires careful consideration of several factors such as the distribution of the data, sample size, and assumptions made by the algorithms. Both types of algorithms have their advantages and disadvantages and can be used for different types of problems.

In the future, there is a growing trend towards the use of nonparametric algorithms due to their flexibility and robustness to assumptions. This is particularly evident in the field of **machine learning**, where nonparametric algorithms such as random forests and support vector machines have gained popularity.

However, parametric algorithms still have a role to play in data analysis, particularly in cases where the assumptions made by these algorithms are met and the data follows a known distribution.

Overall, the choice of algorithm ultimately depends on the specific problem and the nature of the data at hand. By understanding the differences between parametric and nonparametric algorithms and the factors that influence their choice, data analysts can make informed decisions and obtain accurate and reliable results.

## Frequently Asked Questions (FAQs) On Parametric and Nonparametric Algorithms

#### 1. What Are Parametric Algorithms in Machine Learning?

Parametric algorithms assume a specific functional form for the underlying distribution of data, characterized by a finite number of parameters (e.g., Linear Regression, Logistic Regression).

#### 2. What Are Nonparametric Algorithms?

Nonparametric algorithms do not assume a particular functional form for the data distribution and use data-driven approaches to model data, often resulting in more flexible models (e.g., Decision Trees, K-Nearest Neighbors).

#### 3. How Do Parametric and Nonparametric Algorithms Differ?

Parametric algorithms make strong assumptions about data and are characterized by simplicity and speed, while nonparametric algorithms offer flexibility and can model various data structures but might require more data and computational resources.

#### 4. When Should I Choose a Parametric Algorithm?

Consider parametric algorithms when you have limited data, need a quick and interpretable model, and when it's reasonable to make certain assumptions about the underlying data distribution.

#### 5. In Which Situations is a Nonparametric Algorithm More Suitable?

Nonparametric algorithms are typically chosen for their flexibility when dealing with complex and unknown data distributions and when having a larger dataset to mitigate overfitting.

#### 6. Can I Use Both Parametric and Nonparametric Algorithms for a Single Problem?

Yes, exploring both parametric and nonparametric algorithms for a single problem can provide diverse insights and it's common to compare various model types during the model selection process.

#### 7. Which Algorithm Type is More Prone to Overfitting?

Nonparametric algorithms, especially without appropriate **hyperparameter tuning** or regularization, can be more prone to overfitting due to their flexibility and data-driven approach.

#### 8. Are Parametric Models Always Less Accurate than Nonparametric Models?

Not necessarily. The suitability and accuracy of parametric versus nonparametric models often depend on the specific use-case, data availability, and the true underlying **data distribution**.

#### 9. What Are Common Parametric Algorithms?

Common parametric algorithms include Linear Regression, Logistic Regression, and Perceptron.

#### 10. What Are Examples of Nonparametric Algorithms?

Examples of nonparametric algorithms include K-Nearest Neighbors, Decision Trees, and Kernel Smoothing Methods.

#### 11. How Does Computational Complexity Compare Between the Two?

Parametric algorithms generally require less computational power due to their simplicity and predefined structure, whereas nonparametric algorithms can be computationally intensive, particularly with large datasets.

#### 12. How Does Data Size Impact Parametric and Nonparametric Models?

Parametric models can be advantageous with smaller datasets due to their simplicity, while nonparametric models, though requiring larger datasets to generalize well, can adeptly model complex patterns in large data.

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