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Related Experiment Video

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Published on: March 1, 2022

Functional Horseshoe Priors for Subspace Shrinkage.

Minsuk Shin¹, Anirban Bhattachrya¹, Valen E Johnson¹

¹Department of Statistics, Texas A&M University.

Journal of the American Statistical Association

|March 15, 2021

Summary

We developed a new functional horseshoe prior (fHS) for flexible function space shrinkage. This method improves estimation and model selection accuracy in nonparametric additive models compared to existing approaches.

Keywords:

Bayesian shrinkage additive model nonparametric regression posterior contraction

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Area of Science:

Statistics
Machine Learning
Functional Data Analysis

Background:

Shrinkage priors are crucial for regularizing complex models.
Existing priors often induce sparsity on parameters, not function shape.
Parametric function classes offer interpretability but lack flexibility.

Purpose of the Study:

Introduce the functional horseshoe prior (fHS) for function spaces.
Develop a prior that shrinks towards parametric function classes.
Evaluate the performance of fHS in nonparametric additive models.

Main Methods:

Proposed the functional horseshoe prior (fHS).
Demonstrated adaptive posterior concentration properties.
Established consistency of model selection via shrinkage parameter thresholding.

Main Results:

fHS encourages shrinkage on function shape, not parameter sparsity.
The method shows adaptive posterior concentration.
Model selection procedure using fHS is consistent.
fHS outperformed standard horseshoe and penalized likelihood methods in simulations and real data.

Conclusions:

The functional horseshoe prior (fHS) offers a novel approach to function space shrinkage.
fHS provides improved estimation accuracy and model selection in nonparametric additive models.
This method enhances flexibility while retaining benefits of parametric structures.