Maximum Likelihood Estimation of Intrinsic Dimension

By Elizaveta Levina, Peter J. Bickel. 2004

1,050 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning

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In Representation & Self-Supervised Learning

Citations in the corpus

A Neural Scaling Law from the Dimension of the Data Manifold (2020, methodology): “The variance of this estimator was studied in [LB05].”
The Intrinsic Dimension of Images and Its Impact on Learning (2021, methodology): “Levina & Bickel (2005) propose to average the local estimates at each point to obtain a global estimate ¯ m k = where n is the number of samples.”
Hausdorff GAN: Improving GAN Generation Quality With Hausdorff Metric (2021, methodology): “Moreover, the sphere should contain sufﬁciently many data points [28].”
The dimensionality of discourse (2010, neutral): “Levina E, Bickel P (2005) Maximum likelihood estimation of intrinsic dimension.”
Topological Data Analysis (2016, background): “Some examples include Little et al. (2011); Lombardi et al. (2011); Hein & Audibert (2005); Levina & Bickel (2004); Kégl (2002); Costa & Hero (2004).”
Dimensionality-Driven Learning with Noisy Labels (2018, positive): “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…”
Riemannian Manifold Learning (2008, background): “Several estimates [54] for this data set are 4.”
Convergence of Laplacian Eigenmaps (2006, methodology): “Some of the recent work includes estimating geometric invariants of the manifold, such as homology [35, 27], dimensionality [ 24 , 20], geodesic distances [7], and comparing point clouds using Gromov-Hausdorff distance [22].”
Intrinsic dimension estimation: Advances and open problems (2016, methodology): “Examples of pointwise methods are Farahmand et al’s [29], Mordohai-Medioni’s [71], He et al’s [39] and Levina-Bickel’s algorithms [58].”
Hubs in Space: Popular Nearest Neighbors in High-Dimensional Data (2010, methodology): “To further support the above findings, we include the 6th column (dmle) to Table 1, corresponding to intrinsic dimensionality measured by the maximum likelihood estimator (Levina and Bickel, 2005).”
Local polynomial regression on unknown manifolds (2007, methodology): “Examples of this situation are given in all of these papers — see also [14].”
Nearest-Neighbor Searching and Metric Space Dimensions (2005, methodology): “A derivation of a similar estimator via maximum likelihood was given by Levina and Bickel [LB05].”