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Pairwise Distortion Distribution with Graph-Based Importance Sampling for Quantization Error and Intrinsic Dimension Estimation — arXiv:2611.04341

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04341
License (as archived): CC0-1.0
Archived: 2026-11-04T18:57:47.293Z
SHA-256 of the archived text: aa2335ce33296b9a157f3905c6389fb99c51b4c062471913d8ea16f4cdd294ca
Stable URL of this page: https://metraipolis.com/documento/dc_ebbf65946bb2

How to cite

Pairwise Distortion Distribution with Graph-Based Importance Sampling for Quantization Error and Intrinsic Dimension Estimation — arXiv:2611.04341 — arXiv (en), https://arxiv.org/abs/2611.04341 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ebbf65946bb2 (Metraipolis archive dc_ebbf65946bb2, sha256 aa2335ce33296b9a157f3905c6389fb99c51b4c062471913d8ea16f4cdd294ca)

BibTeX

@misc{dcebbf65946bb2,
  title = {Pairwise Distortion Distribution with Graph-Based Importance Sampling for Quantization Error and Intrinsic Dimension Estimation — arXiv:2611.04341},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04341},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ebbf65946bb2; sha256 aa2335ce33296b9a157f3905c6389fb99c51b4c062471913d8ea16f4cdd294ca},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04341. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Quantifying the dimensionality of data is a fundamental need in machine learning and signal processing applications such as representation learning, data compression, and inverse problems, where the extrinsic dimension in which the data is presented can be very different from the intrinsic dimension that determines the operational performance. Various concepts, such as Rényi information dimension, rate-distortion dimension, and quantization dimension are useful here. Despite their theoretical significance, estimating these measures are challenging given their asymptotic definitions. Recent research has shown that analyzing the pairwise distortion distribution (PDD) of a data source can provide a tractable lower bound on the distortion of random codebook quantization, from which a tractable notion of intrinsic dimension can be derived. In this paper we extend this line of research in three main ways. First, we develop a related upper bound on distortion of random codebook quantization. Second, we improve the computability of both the lower and upper bounds, using a graph-based adaptive importance sampling approach. Third, we leverage the bounds to define new notions of intrinsic dimension which form upper and lower bounds on the Rényi information dimension, rate-distortion dimension, and quantization dimension, and which can be empirically estimated from unknown data sources. We illustrate the concepts by analyzing several artificial and empirical distributions.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ML, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2611.04341 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T18:36:22.149Z dalla pagina https://arxiv.org/list/stat.ML/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).