Bayesian cumulative shrinkage for infinite factorizations.

Area of Science:

• Statistics
• Machine Learning
• Psychometrics

Background:

• Determining the dimensionality of parameter spaces is challenging in models relying on factorizations, such as factor analysis.
• Classical shrinkage priors offer some utility, but increasing shrinkage priors provide a more effective way to penalize model complexity.

Purpose of the Study:

• To propose a novel increasing shrinkage prior, the cumulative shrinkage process, for parameters governing dimension in overcomplete models.
• To demonstrate the broad applicability and advantages of this new prior, particularly in factor analysis.

Main Methods:

• The cumulative shrinkage process utilizes an interpretable sequence of spike-and-slab distributions.
• Increasing mass is assigned to the spike as model complexity grows, effectively controlling dimensionality.
• An adaptive Markov chain Monte Carlo algorithm is developed for efficient implementation.

Main Results:

• The proposed cumulative shrinkage process shows theoretical and practical advantages over existing methods.
• It demonstrates an improved ability to accurately recover the true model dimension.
• Simulations and a personality data application confirm the performance gains.

Conclusions:

• The cumulative shrinkage process offers a powerful and flexible approach for dimension inference in factor analysis and other complex models.
• This method provides a principled way to handle model complexity and improve parameter estimation.
• The proposed algorithm facilitates practical application and further research in Bayesian nonparametrics.