Feature-space selection with banded ridge regression.

Area of Science:

• Neuroscience
• Machine Learning
• Computational Biology

Background:

• Encoding models predict brain activity from stimulus representations.
• Existing methods often use single feature spaces or struggle with multiple complementary spaces.
• Regularization is key for fitting these models.

Purpose of the Study:

• To develop a method for decomposing variance explained by banded ridge regression across feature spaces.
• To demonstrate how banded ridge regression performs automatic feature-space selection.
• To address computational challenges in fitting these models for large datasets.

Main Methods:

• Extended ridge regression to banded ridge regression, optimizing regularization per feature space.
• Developed a method to decompose explained variance over multiple feature spaces.
• Proposed computational strategies for large-scale applications.

Main Results:

• Banded ridge regression effectively performs feature-space selection, ignoring non-predictive or redundant spaces.
• This selection enhances prediction accuracy and model interpretability.
• The method is mathematically linked to other feature selection techniques.

Conclusions:

• Banded ridge regression offers a powerful approach for analyzing complex brain data by selecting optimal feature spaces.
• The proposed methods improve the efficiency and interpretability of encoding models.
• An open-source Python package, Himalaya, is released to facilitate implementation.