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About this paper
Dean A. Pospisil, Brett W. Larsen, Sarah E. Harvey, Alex H. Williams
An investigation into shape distance estimation for high-dimensional neural representations uncovers that conventional "plug-in" methods introduce upward bias and converge slowly in data-limited settings. The study introduces a novel method-of-moments estimator, which offers substantially reduced bias and explicit control over the bias-variance tradeoff, thereby enhancing the reliability of representational comparisons by providing quantifiable uncertainty.
Key insights
- Standard plug-in estimators for shape distances, particularly the nuclear norm of cross-covariance, exhibit a substantial upward bias and slow convergence in high-dimensional, low-sample scenarios, overestimating similarity.
- The bias in plug-in estimators can correlate with nuisance variables such as the effective dimensionality of neural populations, potentially leading to confounded or erroneous scientific conclusions.
- A method-of-moments approach can effectively mitigate this bias and provide more accurate, statistically robust estimates of shape distances, complete with quantifiable uncertainty.
Summary by alphaXiv.
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