Feature Transformations: Binning, Polynomials, and Interactions

Suppose you have already learned that binning, polynomial terms, and interactions can reshape a dataset in useful ways. The natural next question is whether you should apply these transformations to every model you train. The answer is no, and the reason reveals something important about how models differ. The same transformed dataset can produce a large improvement for one model and almost no change for another. Understanding which models are sensitive to these changes is the first step toward deciding when a transformation is worth the effort.

A linear model can only combine features in a straight-line fashion. If the relationship between a feature and the target is curved, or depends on the combination of two features, the model cannot capture it unless someone builds that structure into the input. Transformations are one way of doing exactly that. The model's own flexibility is limited, so the work of representing a richer relationship is handed to the features themselves.

Binning is one of the transformations that hands this work to the features. A continuous numeric feature is split into ranges, and each range becomes its own column. The original single value is replaced by several columns, and each column records whether the value falls inside its range. The diagram below shows one value being converted into bin indicator columns.

This is why binning changes the shape of a linear model's prediction. Without bins, the model can only draw a straight line through the single numeric feature. With bins, the model's prediction can rise or fall in steps, because each bin contributes its own amount. The model is still linear in the new indicator columns, but the combined effect on the original feature is no longer a single straight line.

Polynomial features add powers of an existing feature as new columns. A feature x can be supplemented with $x^{2}$ and $x^{3}$, which lets a linear model represent a curve, because the model still combines columns in a linear way while one of those columns bends with the data. Interaction features multiply two features together, creating a column such as $x_{1} \cdot x_{2}$. This column captures the case where the effect of one feature depends on the value of another, something a plain linear model cannot express from the raw features alone.

Not every model benefits in the same way. Tree-based models stand in contrast to linear models. According to the source, they are often able to discover important interactions on their own, and most of the time they do not require the data to be transformed explicitly. A tree-based model splits the data in a sequence of decisions, and through those decisions it can pick up combinations of features without an explicit interaction column. For a learner choosing a model, this means that spending effort on manual interactions may give little return when the chosen model is tree-based.

Some model families sit between these two extremes. The source names SVMs, nearest neighbors, and neural networks. These models might sometimes benefit from binning, interactions, or polynomials, but the implications are usually much less clear than they are for linear models. You should not expect a predictable gain from transformations with these models. Instead, treat a transformation as an experiment whose result has to be measured on held-out data.

Once you know how many new features transformations can create, it is tempting to keep creating them until the dataset has far more columns than it started with. The source warns against this. Adding more features makes all models more complex, and that increases the chance of overfitting. Overfitting means the model learns patterns that belong to the training data specifically, so its performance on new data suffers. A model with many features has more ways to fit noise, which is why the number of features is a real design decision rather than something to maximize.

The source also points to a practical remedy. When you add new features, or whenever you work with a high-dimensional dataset, it can be a good idea to reduce the number of features so that only the most useful ones remain. Discarding the rest tends to produce simpler models, and simpler models often generalize better, meaning they perform more reliably on data they were not trained on.

The obvious follow-up question is how to tell which features are good. The source names three basic strategies, and each answers that question in a different way. All three are supervised methods. That means they use the target values, the thing the model is trying to predict, to decide which features to keep. The three strategies are univariate statistics, model-based selection, and iterative selection.

Univariate statistics judges each feature separately, using a statistic that relates that single feature to the target. It does not consider how a feature behaves alongside the others. Model-based selection instead fits a model and uses the importance that model assigns to each feature to decide which ones to keep. Iterative selection works step by step: it adds or removes one feature at a time, and each change is judged by the results it produces. Because it repeatedly changes the feature set, iterative selection generally involves fitting many more models than the other two strategies.

Because all three strategies use the target, there is a trap to avoid. If you select features using the whole dataset and then evaluate the model on a test set, the test set has already influenced which features were kept. The correct order is to split the data into training and test sets first, and then fit the feature selection only on the training part. The test portion then remains a fair check of how the selected features generalize.

The diagram shows where leakage would enter. If the selection step received the test rows, information about the held-out data would flow back into the choice of features. The evaluation would then be optimistic, because the features had been picked partly to suit the rows that were supposed to be unseen. Keeping the test part out of selection preserves its role as an honest check.