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Analysis of SEC-SAXS data via EFA deconvolution and Scatter

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Published on: January 28, 2021

Sampling Spiked Wishart Eigenvalues.

Thomas G Brooks¹

¹Institute for Translational Medicine and Therapeutics, University of Pennsylvania, Philadelphia, Pennsylvania, USA.

Communications in Statistics: Simulation and Computation

|November 21, 2025

Summary

This summary is machine-generated.

New efficient sampling schemes are introduced for the eigenvalues of the spiked Wishart distribution with multiple spikes. This method also applies to spiked pseudo-Wishart distributions and aids in fitting eigenvalue distributions.

Keywords:

Wishart distribution eigenvalues simulation singular values stochastic gradient descent

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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.