Estimating Local Intrinsic Dimensionality

By Laurent Amsaleg, Oussama Chelly, Teddy Furon, Stéphane Girard, Michael E. Houle, Ken-ichi Kawarabayashi, Michael Nett. 2015

168 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

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Citations in the corpus

Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples (2018, background): “The Local Intrinsic Dimensionality (Amsaleg et al., 2015) “assesses the space-ﬁlling capability of the region surrounding a reference example, based on the distance distribution of the example to its neighbors” (Ma et al., 2018).”
Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality (2018, methodology): “LIDF describes the relative rate at which its cumulative distance function F (r) increases as the distance r increases from 0, and can be estimated using the distances of x to its k nearest neighbors within the sample (Amsaleg et al., 2015).”
Density‐based clustering (2019, background): “However, this behavior can be locally very different for different areas of the data space, so the concept of local intrinsic dimensionality has been developed by Houle (2013, 2017a, 2017b) and associated measures have been studied by Amsaleg et al. (2015, 2018, 2019).”
The vulnerability of learning to adversarial perturbation increases with intrinsic dimensionality (2017, methodology): “Practical methods that have been developed for the estimation of the EVT index, including expansion-based estimators [6] and the well-known Hill estimator and its variants [23], can all be applied to LID (for a survey, see [24]).”
Dimensionality-Driven Learning with Noisy Labels (2018, background): “Several estimators of LID were developed in (Amsaleg et al., 2015; Levina & Bickel, 2005), of which the Maximum Likelihood Estimator (MLE) exhibited the best trade-off between statistical efﬁciency and complexity: Here, r i ( x ) denotes the distance between x and its i -th nearest neighbor, and r…”
Intrinsic dimension of data representations in deep neural networks (2019, background): “ﬁcant loss in classiﬁcation performance [4, 5]. Linear estimates of the ID in DNNs have been computed theoretically and numerically in simpliﬁed models [6], and local estimates of the ID developed in [7] have been related to robustness properties of deep networks to adversarial attacks [8, 9], showi”