Regularized free deconvolution for spectral repair of resampling distortion in high-dimensional particle filters
Resampling is the standard remedy for weight degeneracy in particle filters, but in high dimensions it distorts the spectrum of the ensemble covariance in a way that is computable from the importance weights. This paper studies the inverse problem: recovering the pre-resampling spectrum from the observed weights and the empirical spectrum alone, and using it without biasing the filter. We first show that the forward spectral law extends to random importance weights once one conditions on the weights together with the realized offspring counts, rather than on the weights alone. We then construct a regularized free-deconvolution estimator, prove its consistency with an explicit error budget...
| Authors | Deming Song, Chi-Kin Lam, Kefeng Li et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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