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Efficient Representations for High-Cardinality Categorical Variables in Machine Learning

Zixuan Liang

TL;DR

Novel encoding techniques, including means encoding, low-rank encoding, and multinomial logistic regression encoding, are introduced to address high-cardinality categorical variables and demonstrate significant improvements in model performance and computational efficiency compared to baseline methods.

Abstract

High\-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one\-hot encoding often results in high\-dimensional sparse feature spaces, increasing the risk of overfitting and reducing scalability. This paper introduces novel encoding techniques, including means encoding, low\-rank encoding, and multinomial logistic regression encoding, to address these challenges. These methods leverage sufficient representations to generate compact and informative embeddings of categorical data. We conduct rigorous theoretical analyses and empirical validations on diverse datasets, demonstrating significant improvements in model performance and computational efficiency compared to baseline methods. The proposed techniques are particularly effective in domains requiring scalable solutions for large datasets, paving the way for more robust and efficient applications in machine learning.

Efficient Representations for High-Cardinality Categorical Variables in Machine Learning

TL;DR

Novel encoding techniques, including means encoding, low-rank encoding, and multinomial logistic regression encoding, are introduced to address high-cardinality categorical variables and demonstrate significant improvements in model performance and computational efficiency compared to baseline methods.

Abstract

High\-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one\-hot encoding often results in high\-dimensional sparse feature spaces, increasing the risk of overfitting and reducing scalability. This paper introduces novel encoding techniques, including means encoding, low\-rank encoding, and multinomial logistic regression encoding, to address these challenges. These methods leverage sufficient representations to generate compact and informative embeddings of categorical data. We conduct rigorous theoretical analyses and empirical validations on diverse datasets, demonstrating significant improvements in model performance and computational efficiency compared to baseline methods. The proposed techniques are particularly effective in domains requiring scalable solutions for large datasets, paving the way for more robust and efficient applications in machine learning.
Paper Structure (43 sections, 4 theorems, 13 equations, 10 figures, 2 tables, 4 algorithms)

This paper contains 43 sections, 4 theorems, 13 equations, 10 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Related Work
  4. Alternative Clustering and Estimation Approaches
  5. Encoding High-Cardinality Categorical Data in Machine Learning
  6. Random Projections and Embeddings in Data Encoding
  7. Challenges with High-Dimensional Encoding
  8. Factorial Splits and Overfitting in Decision Trees
  9. Representing Groups with Sufficient Latent State
  10. Encoding Strategies for Categorical Variables
  11. Average Encoding
  12. Extension to High-Cardinality Categories
  13. Comparison with One-Hot Encoding
  14. Low-rank Encodings
  15. Multinomial Logistic Regression Encoding
  16. ...and 28 more sections

Key Result

Lemma 1

Let $L_i$ be a latent variable that is discrete and has $k$ distinct possible values. Under the assumption that the conditional dependencies between observed variables $X_i$ and $L_i$ are captured through a latent state model, I have the following:

Figures (10)

  • Figure 1: This causal graph shows the core assumption that $Y_i$ and $X_i$ are conditionally independent of group membership $G_i$ when conditioned on latent state $L_i$. Gray nodes denote observed variables.
  • Figure 2: Visualization of the average encoding method.
  • Figure 3: Example demonstrating the intuition behind average encoding. The categories $(A,B)$ and $(C,D)$ are associated with distinct latent groups.
  • Figure 4: Schematic of low-rank encoding via Singular Value Decomposition (SVD). Alternatively, Sparse PCA (SPCA) can be employed in place of SVD.
  • Figure 5: Illustration of the mnl encoding approach.
  • ...and 5 more figures

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • proof
  • proof
  • proof
  • proof