Information-Corrected Estimation: A Generalization Error Reducing Parameter Estimation Method

Area of Science:

• Machine Learning
• Statistical Learning Theory

Background:

• Supervised machine learning models are often universal approximators where parameter values are less important than out-of-sample performance.
• Traditional model estimation focuses on parameter bias/variance, which may not correlate with predictive accuracy.
• Ridge regression (L2 regularization) is common but requires hyperparameter tuning and can be sensitive to parameterization.

Purpose of the Study:

• To introduce a novel objective function, Information-Corrected Estimation (ICE), designed to minimize KL divergence-based generalization error in supervised learning.
• To provide a theoretically sound method for improving model generalization across a broad range of models.
• To experimentally validate ICE's effectiveness against established methods like Maximum Likelihood Estimation and L2 regularization.

Main Methods:

• Developed Information-Corrected Estimation (ICE) by defining a corrected likelihood function.
• Theoretically analyzed ICE for its effectiveness under mild regularity conditions.
• Experimentally compared ICE against Maximum Likelihood Estimation and L2 regularization on finite datasets.

Main Results:

• ICE is theoretically proven to be effective for a wide class of models.
• Experimental results demonstrate significant reductions in generalization error using ICE compared to Maximum Likelihood Estimation.
• ICE also showed superior performance over L2 regularization in reducing generalization error.

Conclusions:

• Information-Corrected Estimation (ICE) offers a theoretically grounded and experimentally validated approach to enhance supervised learning model generalization.
• ICE provides a direct method to minimize KL divergence, leading to improved out-of-sample predictive performance.
• The proposed method represents a significant advancement over traditional Maximum Likelihood Estimation and L2 regularization techniques.