What is the z-score standardization formula and what statistics does it target?

Decision-tree models do not require feature scaling because they split data based on feature conditions (thresholds) rather than absolute magnitudes. Monotonic rescaling of feature values does not change the branching structure or the order of splits.

Conditions: Model is a decision tree or an ensemble of trees (random forest, XGBoost, etc.).; Splitting logic is based on comparing feature values to thresholds.

Feature scaling is needed because raw features often differ in units and magnitudes, making them incomparable. Scaling brings them onto a common scale, which is necessary for many machine learning algorithms to function properly.

Conditions: Dataset contains multiple features with different units or ranges.; The model is sensitive to feature magnitudes (e.g., distance-based or gradient-based).

Import `MinMaxScaler` from `sklearn.preprocessing`, instantiate it, and call `fit_transform` on the selected DataFrame columns. This fits the scaler to the data (learning min/max) and transforms the values to the [0, 1] range.

Conditions: Input data is numerical.; Scikit-learn library is installed.

Import `StandardScaler` from `sklearn.preprocessing`, instantiate it, and call `fit_transform` on the selected DataFrame columns. This transforms the data to have mean 0 and standard deviation 1.

Conditions: Input data is numerical.; Scikit-learn library is installed.

Min-max normalization transforms a feature value $X$ into $X_{\text{norm}} = \frac{X - X_{\min}}{X_{\max} - X_{\min}}$, mapping the feature's observed range onto the interval $[0, 1]$.

Conditions: Applied per numerical feature.; Requires a finite minimum $X_{\min}$ and maximum $X_{\max}$ for the feature.; Assumes $X_{\max} \neq X_{min}$ to avoid division by zero.