Add robust inverse of a FI matrix in CBMR inference

[yifan0330]

Closes # .

Changes proposed in this pull request:

• For CBMR inference, add robust inverse of a Fisher information matrix using SVD and a thresholding approach to ignore small singular values

Summary by Sourcery

Add a robust inverse function for Fisher information matrices using SVD thresholding and integrate it into CBMR inference to replace direct matrix inversion for enhanced numerical stability, and update CBMR tests accordingly.

New Features:

• Introduce robust_inverse function in utils to compute Fisher information matrix inverses via SVD with thresholding.

Enhancements:

• Use robust_inverse in CBMR inference to replace np.linalg.inv for spatial and moderator coefficient covariance computations.

Documentation:

• Add documentation for the robust_inverse function detailing its parameters and behavior.

Tests:

• Skip CBMR import error test when Torch is installed to avoid false negatives.

[sourcery-ai]

Reviewer's Guide

This PR adds a numerically stable inverse function for Fisher information matrices via SVD thresholding and integrates it into the CBMR inference pipeline, replacing direct matrix inversions and updating related imports, docs, and tests.

Class diagram for robust_inverse utility function

classDiagram
    class robust_inverse {
        +robust_inverse(FI: np.ndarray, eps: float = 1e-8) np.ndarray
    }
    class np.linalg {
        +svd()
    }
    robust_inverse ..> np.linalg : uses

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Class diagram for CBMREstimator changes with robust_inverse integration

classDiagram
    class CBMREstimator {
        _glh_con_group()
        _glh_con_moderator()
    }
    class robust_inverse {
        +robust_inverse(FI: np.ndarray, eps: float = 1e-8) np.ndarray
    }
    CBMREstimator ..> robust_inverse : uses in _glh_con_group, _glh_con_moderator

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File-Level Changes

Change	Details	Files
Implement robust inverse for Fisher information matrices	Added robust_inverse definition Symmetrize input matrix before inversion Apply SVD, threshold small singular values, and reconstruct inverse	nimare/utils.py
Integrate robust_inverse into CBMR inference	Imported robust_inverse and updated dependencies Replaced np.linalg.inv calls with robust_inverse in spatial and moderator covariance calculations Added footcite reference in CBMREstimator docstring	nimare/meta/cbmr.py
Adjust CBMR tests for Torch import error	Decorated test_cbmr_importerror with skipif when Torch is installed	nimare/tests/test_meta_cbmr.py

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[sourcery-ai]

Hey @yifan0330 - I've reviewed your changes - here's some feedback:

• In robust_inverse, you’re only zeroing out small singular vectors (via U * M), but you still invert all singular values in S_inv; you should mask S_inv too (e.g. S_inv = np.where(S > eps, 1/S, 0)) to avoid amplifying tiny values.
• Consider adding targeted unit tests for robust_inverse (e.g., on singular or ill-conditioned matrices) to ensure it behaves as expected and thresholds values properly.

Prompt for AI Agents

Please address the comments from this code review:
## Overall Comments
- In `robust_inverse`, you’re only zeroing out small singular vectors (via `U * M`), but you still invert all singular values in `S_inv`; you should mask `S_inv` too (e.g. `S_inv = np.where(S > eps, 1/S, 0)`) to avoid amplifying tiny values.
- Consider adding targeted unit tests for `robust_inverse` (e.g., on singular or ill-conditioned matrices) to ensure it behaves as expected and thresholds values properly.

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[sourcery-ai]

suggestion (code-quality): Inline variable that is immediately returned (inline-immediately-returned-variable)

Suggested change

	FI_inv = U @ np.diag(S_inv) @ U.T
	return FI_inv
	return U @ np.diag(S_inv) @ U.T