DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
By V. Marčenko, Leonid A. Pastur. 1967
Subfields: Statistics and Probability, Probabilistic & Bayesian Methods
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Citations in the corpus
- The Full Spectrum of Deep Net Hessians At Scale: Dynamics with Sample Size (2018, background): “Leaning further on a random matrix theory analogy, the authors further suggested that the bulk might be modeled as a Marchenko-Pastur (MP) distribution [11].”
- Empirical Analysis of the Hessian of Over-Parametrized Neural Networks (2017, background): “The result dates back to sixties and can be found in [Marˇcenko and Pastur, 1967].”
- RUDDER: Return Decomposition for Delayed Rewards (2018, background): “The Marchenko-Pastur quarter circular law for rectangular matrices says that for n = m the maximal singular value is 2 √ m [71].”
- Ligand biological activity predicted by cleaning positive and negative chemical correlations (2019, methodology): “Under certain weak assumptions, if entries in R± are random and drawn from a Gaussian distribution with zero mean and unit variance, the probability of C± having an eigenvalue λ is given by the Marchenko–Pastur distribution (31)”
- Estimating the Spectral Density of Large Implicit Matrices (2018, background): “In particular, we consider A = BB T where B ∈ D × N and B ij ∼ N (0 , σ 2 N ). constant If both N and D are taken to infinity at the same rate, i.e., D, N → ∞ with D = φN for some φ , then the limiting spectral density can be shown to obey the Marchenko-Pastur distribution (Marˇcenko and Pastur, 1967”
- Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices (2007, background): “This function has an explicit expression (Marčenko and Pastur [5]), satisfying all properties to be investigated in this paper.”
- Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels Under Limited Feedback (2009, methodology): “by Marc̆enko and Pastur [25] to derive the limiting distribution of sample covariance matrices (w hich corresponds here to the case QN =RN =SN =IN ).”
- Generalization of Two-layer Neural Networks: An Asymptotic Viewpoint (2020, unknown): “Marčenko and Pastur (1967) showed that as n, p → ∞ and p/n = γ ∈ (0 , ∞ ) , the empirical spectral density µ W p ( dλ ) converges to a limiting density µ MP ( γ ) ( λ ) almost surely: We say µ MP ( γ ) is the density of the Marčenko–Pastur distribution this implies that the smallest non-zero…”
- Determining the Number of Factors from Empirical Distribution of Eigenvalues (2010, background): “When the data are i.i.d. and thus have no signals, the empirical distribution of eigenvalues of the sample covariance matrix converges to a known nonrandom distribution as the dimensionality of the data and the number of observations rise (see Marčenko & Pastur, 1967).”
- Spiked separable covariance matrices and principal components (2019, unknown): “In the null case with r A “ Ip, it is wellknown that the empirical spectral distribution (ESD) of r Q1 converges to the celebrated Marchenko-Pastur (MP) law [37], whose rightmost edge λr gives the asymptotic location of the largest eigenvalue.”
- Universality of local eigenvalue statistics for some sample covariance matrices (2005, background): “Then, it is the first fundamental result due to [26] (see also [32]) that, as N grows to infinity,μN converges to the Marchenko-Pastur law with density ρσ , depending only on the varianceσ 2 given by (1.”
- Tensor Programs III: Neural Matrix Laws (2020, methodology): “H Proving the Marchenko-Pastur Law by Tensor Programs Marchenko-Pastur law [27] is another cornerstone random matrix result on the level of semicircle law.”