Introduction
When it comes to building a model for predicting continuous values, regression is the most popular choice. In supervised learning, the regression model is trained on the labeled dataset to predict output values based on input variables. However, there are two different approaches to regression: linear and isotonic. The choice of regression model depends on the nature of data and the problem you are solving. In this article, we will compare isotonic regression and linear regression and help you choose the best one for your data.
Isotonic Regression
Isotonic regression is a non-parametric regression technique that involves fitting a step-wise increasing function to the data. It is mainly used when the relationship between input variables and outputs is non-linear and monotonic (i.e., either strictly increasing or decreasing). This regression method is useful when dealing with noisy, non-linear data that does not fit a straight line.
The isotonic regression algorithm begins by sorting the input data in ascending order. Then, the algorithm iteratively assigns the weighted mean of all values less than or equal to the current input value to the output value at that point. The regression function can either be increasing or decreasing, and the fitting algorithm can adjust to the best option.
Linear Regression
Linear regression is a parametric regression technique that assumes a linear relationship between the input variables and the output. The model estimates the coefficients of the line that best describes the relationship between the input variables and the output.
The linear regression algorithm minimizes the sum of squared errors between the predicted output values and ground truth output values. It is a widely used regression technique because of its simplicity and effectiveness. However, its strength lies in its assumption of a linear relationship between the input variables and the output values.
Comparison of Isotonic Regression and Linear Regression
Isotonic regression and linear regression differ in their approach and assumptions. Isotonic regression does not assume a specific relationship between input variables and outputs, making it more flexible than linear regression. Additionally, isotonic regression is robust to outliers and noise in the data.
In contrast, linear regression assumes a linear relationship between input variables and output values. This assumption makes it more restrictive than isotonic regression. Moreover, linear regression can be sensitive to outliers, and it does not perform well when the data does not follow the linear relationship between inputs and outputs.
To decide which one to use, you should consider the type of data and any relationships that may exist between input variables and output values. If the relationship is monotonic and non-linear, then isotonic regression may be more appropriate. However, if you suspect that there is a linear relationship between input variables and outputs, then linear regression may be the better choice.
Conclusion
To summarize, isotonic regression and linear regression are both regression techniques used to predict continuous values. Isotonic regression is best suited for non-linear monotonic data, while linear regression is ideal for linear relationships. When choosing a regression model, the nature of data must be considered to ensure that the best model is selected.
References
- Muller, A. (2019). “Isotonic regression for monotonic relationships in data.” Retrieved from https://towardsdatascience.com/isotonic-regression-in-data-science-1f6da325b466
- Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT press.