Bayesian sparse partial least squares.

Area of Science:

• Machine Learning
• Statistical Modeling
• Computational Neuroscience

Background:

• Partial Least Squares (PLS) is a multivariate statistical method for modeling relationships between variable sets.
• Existing PLS methods vary in component computation, lacking inherent sparsity and automatic component selection.
• Bayesian inference offers a probabilistic framework for parameter estimation and model selection.

Purpose of the Study:

• To propose a novel Bayesian formulation of Partial Least Squares (PLS).
• To introduce extensions providing input space sparsity and automatic selection of latent components.
• To validate the proposed Bayesian PLS methods on synthetic and real-world neurophysiological data.

Main Methods:

• Developed a Bayesian framework for Partial Least Squares (PLS).
• Incorporated sparsity-inducing priors at the input space level.
• Utilized variational inference for efficient parameter distribution estimation.
• Introduced automatic relevance determination for selecting the optimal number of latent components.

Main Results:

• The proposed Bayesian PLS methods demonstrated effective performance on synthetic data.
• Successfully applied the methods to electrocorticogram (ECoG) data from monkeys.
• Achieved sparsity in the input space and automatic selection of latent components.
• The Bayesian approach provided a robust alternative to traditional PLS.

Conclusions:

• The Bayesian formulation of PLS offers significant advantages, including enhanced interpretability and automated component selection.
• The proposed methods are effective for analyzing complex datasets, such as neurophysiological recordings.
• This work advances the application of Bayesian methods in multivariate statistical modeling.