When training a machine learning algorithm, how can you handle non-linear variable relationships?

1 What are non-linear variable relationships?

Non-linear variable relationships are when the output or target variable does not change in a proportional or constant way with the input or predictor variables. For example, the relationship between temperature and pressure in a gas is non-linear, as it follows the ideal gas law. Non-linearities can arise from complex interactions, feedback loops, thresholds, or other factors that affect the data generation process.

2 Why are non-linear variable relationships important?

Non-linear variable relationships are important because they can affect the accuracy and generalizability of your machine learning algorithm. If you ignore or miss non-linearities, you might end up with a model that is too simple or too complex for the data. A too simple model might underfit the data, meaning that it cannot capture the patterns and variations in the data. A too complex model might overfit the data, meaning that it learns the noise and outliers in the data and cannot generalize well to new or unseen data.

3 How to detect non-linear variable relationships?

One way to detect non-linear variable relationships is to visualize the data using scatter plots, histograms, box plots, or other graphical tools. You can plot the output variable against each input variable or against combinations of input variables to see if there is any curvature, heteroscedasticity, or outliers in the data. You can also use correlation coefficients, such as Pearson's or Spearman's, to measure the strength and direction of the linear relationship between variables. However, correlation does not imply causation, and it might not capture non-linear relationships well.

4 How to transform non-linear variable relationships?

Another way to handle non-linear variable relationships is to transform the variables using mathematical functions, such as logarithms, exponentials, polynomials, or trigonometric functions. These transformations can help to linearize the relationship between variables or to reduce the skewness or variance of the variables. For example, you can use a log transformation to reduce the effect of outliers or to model multiplicative relationships. You can also use a polynomial transformation to model quadratic or cubic relationships. However, you need to be careful not to over-transform the variables or lose the interpretability of the model.

5 How to model non-linear variable relationships?

A third way to handle non-linear variable relationships is to use machine learning models that can capture non-linearities inherently, such as decision trees, random forests, neural networks, or support vector machines. These models can learn complex functions that map the input variables to the output variable without relying on linear assumptions or transformations. For example, you can use a decision tree to split the data into regions based on rules or thresholds, or you can use a neural network to learn hidden layers of features that represent non-linear combinations of the input variables. However, you need to be careful not to overfit the data or lose the explainability of the model.

6 How to evaluate non-linear variable relationships?

A final way to handle non-linear variable relationships is to evaluate the performance of your machine learning algorithm using appropriate metrics and methods, such as mean squared error, R-squared, cross-validation, or learning curves. These metrics and methods can help you to compare different models or transformations and to assess how well they fit the data and generalize to new data. You can also use residual plots, which show the difference between the actual and predicted values, to check for any patterns or problems in the model fit. You can also use feature importance or partial dependence plots to understand the effect of each variable on the output variable.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?