Polynomial Regression vs Neural Network

In this article, we are going to compare polynomial regression and neural networks.

What is Polynomial Regression?

Polynomial regression is a technique used to model the relationship between a dependent variable (what you’re trying to predict) and an independent variable (what you’re basing your prediction on) when that relationship isn’t straight line. Polynomial regressions are capable to fit curves by leveraging polynomial equations. Hence, the complexity of the curve is dependent on the degree of polynomial.

Advantages of Polynomial Regression

1. Ability to capture relationships between variables by fitting higher-degree polynomial functions
2. They do not assume linear relationship between the independent and dependent variables.

Limitations of Polynomial Regression

1. There is a risk of overfitting, when the model captures noise in the data leading to poor performance on test set.
2. Can produce unbounded predictions, particularly when extrapolating beyond the range of the observed data.

What are Neural Network?

Neural Networks are brain inspired machine learning models. The basic structure of neural network includes layers and activation functions.

• Neural networks are built up of interconnected nodes called artificial neurons. These are loosely based on biological neurons in our brains.
• These artificial neurons are organized in layers, typically consisting of an input layer, one or more hidden layers, and an output layer.

The neural network adjust the weights of the connections between neurons to minimize the difference between predicted output and actual target values during training.

Advantages of Neural Network

1. Neural networks are able to handle structured as well as unstructured data.
2. Capable of learning and extracting relevant features from the raw data.

Limitations of Neural Network

1. Complex model are difficult to understand and the black box layer hinder the transparency of the model’s predictions.
2. Computationally expensive.

Polynomial Regression vs Neural Network: Flexibility and Complexity

In terms of complexity, neural network offer more flexibility in comparison to polynomial regression. The neural networks are capable of capturing complex nonlinear relationships in the data and polynomial regression is much simpler hence, struggles to capture the patterns.

Polynomial Regression vs Neural Network: Performance

Neural Networks tend to outperform Polynomial Regression, especially when dealing with large datasets and complex relationships. They have the ability to learn from data hierarchically and adapt to diverse patterns.

Polynomial Regression vs Neural Network: Interpretability

Polynomial Regression provides straightforward interpretation due to its linear nature. It’s easier to understand the impact of each feature on the target variable. Neural Networks, however, are often considered black-box models, making it challenging to interpret the learned parameters.

Difference between Polynomial Regression and Neural Network

Feature/Aspect	Polynomial Regression	Neural Network
Structure	Single equation (polynomial)	Multi-layered (input, hidden, output layers)
Flexibility	Limited to polynomial functions	High flexibility; handles complex non-linear relationships
Complexity	Simple	Complex
Interpretability	Easily interpretable	Less interpretable (black-box model)
Training	Requires finding polynomial coefficients	Requires adjusting weights and biases through optimization
Overfitting	Prone with higher-degree polynomials	Prone, especially with complex architectures
Computational Needs	Less computational resources	More computational resources, especially for deep networks
Data Requirements	Moderate	High; requires large labeled datasets
Generalization	May not generalize well, especially with high-degree polynomials	Can generalize well with proper regularization and tuning
Applicability	Suitable for simpler, non-linear data	Suitable for complex, high-dimensional data
Versatility	Limited to regression problems	Versatile; applicable to various ML tasks
Feature Engineering	May require manual feature selection for polynomial terms	Can automatically learn features from data

When to Use Polynomial Regression Instead of Neural Networks

There are certain scenarios where polynomial regression are a better option over neural network.

1. When the relationship between variables is relatively simple and can be approximated by a polynomial function without the need for complex transformations.
2. When interpretability of the model is crucial, and stakeholders require a clear understanding of the relationships between variables.
3. When computational resources are limited
4. When the dataset already contains polynomial features or the relationship between variables can be easily captured by adding polynomial terms to the regression model.
5. When we are dealing with a low dimension dataset.