Joint Covariance Estimation with Mutual Linear Structure

Ami Wiesel; Ilya Soloveychik

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Joint Covariance Estimation with Mutual Linear Structure

Ilya Soloveychik, Ami Wiesel

Statistics Theory · Submitted 1 Jul 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Numerical simulations are presented to illustrate the performance benefits of the proposed method.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.20 · human participants 0.04 · controlled comparison 0.17 · randomized assignment 0.02 · states quantitative result 0.51 · compares with prior results 0.78 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered populations with different covariances, our aim is to determine the mutual structure of these covariance matrices and estimate them. Supposing that the covariances span a low dimensional affine subspace in the space of symmetric matrices, we develop a new efficient algorithm discovering the structure and using it to improve the estimation. Our technique is based on the application of principal component analysis in the matrix space. We also derive an upper performance bound of the proposed algorithm in the Gaussian scenario and compare it with the Cramer-Rao lower bound. Numerical simulations are presented to illustrate the performance benefits of the proposed method.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider the problem of joint estimation of structured covariance matrices.	background 0.93	0.42	0.04	asserted 0.70
s1	Assuming the structure is unknown, estimation is achieved using heterogeneous training sets.	method 0.84	0.64	0.05	asserted 1.00
s2	Namely, given groups of measurements coming from centered populations with different covariances, our aim is to determine the mutual structure of these covariance matrices and estimate them.	background 0.64	0.28	0.08	asserted 0.92
s3	Supposing that the covariances span a low dimensional affine subspace in the space of symmetric matrices, we develop a new efficient algorithm discovering the structure and using it to improve the estimation.	contribution 0.54	0.94	0.25	asserted 0.99
s4	Our technique is based on the application of principal component analysis in the matrix space.	method 0.99	0.85	0.04	asserted 1.00
s5	We also derive an upper performance bound of the proposed algorithm in the Gaussian scenario and compare it with the Cramer-Rao lower bound.	contribution 0.54	0.96	0.11	asserted 1.00
s6	Numerical simulations are presented to illustrate the performance benefits of the proposed method.	result 0.53	0.93	0.12	asserted 0.95

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.85.

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Original abstract

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered populations with different covariances, our aim is to determine the mutual structure of these covariance matrices and estimate them. Supposing that the covariances span a low dimensional affine subspace in the space of symmetric matrices, we develop a new efficient algorithm discovering the structure and using it to improve the estimation. Our technique is based on the application of principal component analysis in the matrix space. We also derive an upper performance bound of the proposed algorithm in the Gaussian scenario and compare it with the Cramer-Rao lower bound. Numerical simulations are presented to illustrate the performance benefits of the proposed method.

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1 arXiv paper cite this in 9 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Uses its method or tool 1 paper

The truncation threshold for the SVD was chosen according to the rule described in [ref] in such a way, that the truncated signal would convey $90%$ of the original power.

Joint Inverse Covariances Estimation with Mutual Linear Structure · Circulant Model · 0.97

Compares with it 1 paper

Denote [equation] to get the bound [equation] As expected, the dependence on the model parameters is similar to that obtained in [ref] for the joint structured covariance estimation and in [ref] for the problem of low-rank matrix reconstruction.

Joint Inverse Covariances Estimation with Mutual Linear Structure · Lower Performance Bounds · 0.96

What it cites · 2 sentences without a confident label

Uses the method or tool of 1 paper

Here the function $ω(β)$ is defined in [ref] together with the numerical algorithm of its evaluation, and $σ_m()$ is the median of the singular values of $$.

The Optimal Hard Threshold for Singular Values is 4/sqrt(3) · TSVD Performance in Toeplitz Model · 0.91

Compares with 1 paper

Donoho in [ref] and the so-called “elbow method”.

The Optimal Hard Threshold for Singular Values is 4/sqrt(3) · TSVD Performance in Toeplitz Model · 0.88

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