Why does label encoding give different predictions from one-hot encoding

Label Encoding and One-Hot Encoding give different predictions because they represent categorical variables in fundamentally different ways.

• Label Encoding might cause issues by implying an ordinal relationship between categories, leading to biased predictions.
• One-Hot Encoding prevents this by treating categories independently, resulting in more accurate predictions when there’s no natural order among the categories.

Label Encoding:

• How It Works: Label Encoding assigns an integer value to each unique category in a feature. For example, if you have three towns: ['West Windsor', 'Robbinsville', 'Princeton'], Label Encoding would convert them into numerical values like this:
  • West Windsor → 0
  • Robbinsville → 1
  • Princeton → 2
• Interpretation in the Model: When you use Label Encoding, the model interprets the numbers as continuous values, meaning it sees a numeric relationship between them (i.e., “Princeton” might be considered numerically higher than “West Windsor” and closer to “Robbinsville”). This can cause issues if the numeric values don’t have any ordinal relationship.

One-Hot Encoding:

• How It Works: One-Hot Encoding creates a separate binary (0 or 1) column for each unique category. For example, the three towns would be represented as:
  • West Windsor → [1, 0, 0]
  • Robbinsville → [0, 1, 0]
  • Princeton → [0, 0, 1]
• Interpretation in the Model: One-Hot Encoding treats each category as a separate binary feature and does not impose any ordinal relationship between them. This means the model doesn’t assume that one category is greater or lesser than another. Each category is treated independently.

Key Differences in Predictions:

1. Ordinal vs. Non-Ordinal Data Representation:

   • With Label Encoding, the model might treat “Robbinsville” (encoded as 1) as closer to “West Windsor” (encoded as 0) than “Princeton” (encoded as 2), even though these categories don’t have any inherent numerical relationship. This can lead the model to incorrectly infer relationships based on these numeric values.
   • With One-Hot Encoding, no such relationship is assumed. Each category is represented as a vector of 0s and 1s, and the model treats them as distinct entities, preventing any assumptions about their order.

2. Model Interpretation:

   • Label Encoding introduces an implicit ordinal relationship (e.g., 0 < 1 < 2) that can influence the model, especially for linear models like Linear Regression, which assumes that the input features are on a similar scale. This may lead to inappropriate relationships in the regression model.
   • One-Hot Encoding avoids this issue by using binary columns for each category, effectively preventing the model from assuming an ordinal relationship between the categories.

3. Feature Space:

   • Label Encoding results in a single feature column for the categorical variable.
   • One-Hot Encoding expands the feature space, creating as many columns as there are categories. In the case of a categorical feature with many unique values, this can significantly increase the dimensionality of the model.

Why Predictions Differ:

• In Label Encoding, a linear regression model might learn that “Robbinsville” is numerically closer to “West Windsor” than “Princeton,” and this might distort the predictions.
• In One-Hot Encoding, the model treats each category independently, leading to different relationships being learned (if any) between the categories and the target variable.

Example:

Let’s assume you are predicting house prices, and you’re using a linear regression model where the town feature is the only predictor (along with some other features like area).

• With Label Encoding:

  • The model will interpret the encoded numeric values (0 for West Windsor, 1 for Robbinsville, and 2 for Princeton) and might incorrectly assume a relationship such as: “Princeton” (2) is somehow numerically “higher” than “West Windsor” (0), which doesn’t reflect any meaningful relationship.
  • This can lead to biased coefficients and, therefore, inaccurate predictions.

• With One-Hot Encoding:

  • The model will learn the effect of each category (West Windsor, Robbinsville, and Princeton) as a separate feature, with no assumption of ordinality.
  • This often results in more accurate predictions, especially when categorical features have no inherent order.