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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

A recursive model-reduction method for approximate inference in Gaussian Markov random fields.

Jason K Johnson¹, Alan S Willsky

¹Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. jasonj@mit.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 31, 2008

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This study introduces recursive cavity modeling for efficient inference in large Gauss-Markov random fields. This method approximates complex fields using smaller, manageable models for accurate, scalable results in applications like remote sensing.

Area of Science:

Computational statistics
Machine learning
Signal processing

Background:

Large-scale Gauss-Markov random fields present significant inference challenges.
Existing methods often struggle with scalability and computational tractability.
Accurate approximation of marginal statistics is crucial for many applications.

Purpose of the Study:

To introduce recursive cavity modeling for approximate, near-optimal inference in large Gauss-Markov random fields.
To develop a scalable and computationally tractable approach for complex probabilistic models.
To demonstrate the effectiveness of the proposed method in large-scale remote sensing problems.

Main Methods:

Subdividing the random field into smaller subfields and constructing cavity models to approximate them.

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Employing a tree-structured algorithm with an upward pass for building cavity models and a downward pass for blanket models.

Utilizing model thinning and a maximum-entropy approach for tractable approximate inference.

Developing a fast preconditioner for iterative computation of optimal estimates.

Main Results:

Recursive cavity modeling provides a principled and tractable approach to approximate inference.
The method achieves near-optimal inference by approximating subfields with concise cavity models.
Demonstrated accuracy and scalability on challenging, large-scale remote sensing problems.
Integration of recursive inference, variational learning, and iterative estimation.

Conclusions:

Recursive cavity modeling offers an effective solution for inference in large Gauss-Markov random fields.
The approach is accurate, scalable, and computationally tractable.
This method has significant potential for applications in remote sensing and other complex data analysis domains.