arXiv:2608.21466v1 Announce Type: new
Abstract: We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For...
By Michael C. H. Choi, Youjia Wang
arXiv:2603.19657v2 Announce Type: replace-cross
Abstract: We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matr...
By Xinyu Liu, Hai Zhang
The paper introduces a new dimensionality reduction technique that enhances nearest‑neighbour relationships to estimate high‑information projections. It constructs a matrix encoding local covariance via nearest‑neighbour pairs and shows that, under standard regularity conditions, this matrix consistently estimates the Density Information Matrix (DIM), a non‑parametric analogue of the Fisher Information Matrix. The authors also demonstrate the method’s practical usefulness for clustering and outlier detection.
By David P. Hofmeyr
arXiv:2604.02535v2 Announce Type: replace
Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....
By Zeyang Huang, Angelos Chatzimparmpas, Thomas H\"ollt, Takanori Fujiwara
The paper introduces a geometry‑aware graph construction method that adaptively selects Gaussian kernel bandwidths per node to align the kernel’s spectral complexity with the intrinsic dimensionality of the underlying manifold. By matching the kernel’s effective rank to a local intrinsic dimension estimate derived from a minimum spanning tree, the method operates within a manifold‑consistent log‑log scaling regime. Experiments on CIFAR‑100 demonstrate that this adaptive bandwidth approach consistently improves leave‑one‑out classification and label propagation accuracy compared to fixed‑bandwidth and other adaptive techniques.
By Ecem Bozkurt, Antonio Ortega
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
By Yuga Iguchi, Paul Fearnhead