Principal whitened gradient for information geometry.

Area of Science:

• Information Geometry
• Machine Learning
• Statistical Inference

Background:

• Optimization is crucial in information geometry for density model fitting.
• Existing methods can be computationally intensive and may lack robustness.
• Efficient parameter updates and accurate Fisher information matrix estimation are key challenges.

Purpose of the Study:

• To propose novel strategies for improving optimization in information geometry.
• To enhance the convergence speed and robustness of learning algorithms.
• To reduce computational costs associated with parameter estimation.

Main Methods:

• Identifying a local Euclidean embedding via tangent space whitening for additive parameter updates.
• Removing minor gradient components to improve Fisher information matrix estimation and reduce computational load.
• Proving the necessity of dimensionality reduction for learning multidimensional linear transformations.

Main Results:

• The proposed local Euclidean embedding approximates geodesic flow for optimal density models.
• Gradient component removal enhances Fisher information matrix estimation and decreases computational cost.
• Optimization using principal whitened gradients shows faster and more robust convergence in simulations.

Conclusions:

• The developed methods offer significant improvements in information geometry optimization.
• These strategies are effective for unsupervised learning with synthetic data and discriminant analysis of real-world datasets like breast cancer data.
• The findings pave the way for more efficient and reliable statistical inference and machine learning models.