Understanding Feature Importance in Linear Models: Key Considerations
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Chapter 1: Introduction to Linear Models
The realm of linear models encompasses various types, including ordinary linear regression, Ridge regression, Lasso regression, and SGD regression. In these models, coefficients are often interpreted as indicators of feature importance, which reflects how effectively a feature can predict a target variable. For instance, we might assess how the age of a house influences its price.
This article outlines four commonly overlooked yet essential pitfalls in interpreting coefficients of linear models as feature importance:
- Standardization of the Dataset
- Variability Across Different Models
- Issues with Highly Correlated Features
- Stability Assessment through Cross-Validation
Section 1.1: The Structure of Linear Regression
Linear regression is expressed in the form:
y = w * x
where ( y ) represents the predicted value, ( w ) are the coefficients, and ( x ) refers to the features.
To illustrate, let's consider a simple example: estimating the price of a house based on three features: the age of the house, the number of rooms, and the total square footage.
Assuming we input this dataset into a linear model and train it, we will obtain certain coefficient values. At this juncture, we need to determine the feature importance for the age of the house, the number of rooms, and the square footage: can we equate their importance to the coefficients [20, 49, 150]?
Subsection 1.1.1: Importance of Standardization
The answer is straightforward: coefficients can only be interpreted as feature importance if the dataset has been standardized prior to training. For example, applying a standard scaler to the raw data before fitting the model allows us to claim that the feature importance of the age of the house is 20.
This requirement arises because features may exist on different scales; for instance, the number of rooms might range from 1 to 10, while square footage could vary from 500 to 4000. Therefore, scaling is necessary to ensure that coefficients accurately represent feature importance.
Section 1.2: The Variability Among Linear Models
Different linear models may yield significantly different opinions on feature importance. In our earlier example, an ordinary linear model might produce coefficients of [20, 49, 150], whereas Ridge regression could generate [1820, 23, 90]. As a best practice, consider employing an ensemble approach to amalgamate insights from various models.