Sampling Spiked Wishart Eigenvalues

Area of Science:

• Statistics
• Computational Statistics
• Machine Learning

Background:

• Efficient sampling methods are crucial for analyzing complex statistical distributions.
• Previous work addressed standard and single-spike Wishart distributions.
• Generalizing these methods is essential for broader applications.

Purpose of the Study:

• To generalize efficient eigenvalue sampling schemes for the spiked Wishart distribution to an arbitrary number of spikes.
• To extend these methods to the spiked pseudo-Wishart distribution.
• To enable fitting eigenvalue distributions to target distributions using stochastic gradient descent.

Main Methods:

• Generalization of existing efficient sampling schemes for Wishart eigenvalues.
• Application of the generalized schemes to spiked Wishart distributions with multiple spikes.
• Adaptation of the procedure for stochastic gradient descent.

Main Results:

• Development of efficient sampling schemes for eigenvalues of the multi-spike Wishart distribution.
• Successful application to the spiked pseudo-Wishart distribution.
• Demonstration of differentiability for stochastic gradient descent optimization.

Conclusions:

• The generalized sampling schemes provide efficient tools for analyzing multi-spike Wishart and spiked pseudo-Wishart distributions.
• The approach facilitates the fitting of eigenvalue distributions to target distributions.
• This work advances computational methods in statistical modeling and machine learning.