Abstract:
We consider the problem of joint estimation of inverse covariance matrices lying in an unknown subspace of the linear space of symmetric matrices. We perform the estimati...Show MoreMetadata
Abstract:
We consider the problem of joint estimation of inverse covariance matrices lying in an unknown subspace of the linear space of symmetric matrices. We perform the estimation using groups of measurements with different covariances. Assuming the inverse covariances span a low-dimensional subspace, our aim is to determine this subspace and to exploit this knowledge in order to improve the estimation. We develop a novel optimization algorithm discovering and exploiting the underlying low-dimensional subspace. We provide a computationally efficient algorithm and derive a tight upper performance bound. Numerical simulations on synthetic and real world data are presented to illustrate the performance benefits of the algorithm.
Published in: IEEE Transactions on Signal Processing ( Volume: 65, Issue: 9, 01 May 2017)
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- IEEE Keywords
- Index Terms
- Covariance Matrix ,
- Estimated Covariance Matrix ,
- Inverse Covariance Matrix ,
- Inverse Covariance ,
- Numerical Simulations ,
- Real-world Data ,
- Symmetric Matrix ,
- Estimation Problem ,
- Measures In Group ,
- Low-dimensional Subspace ,
- Sample Groups ,
- Real Applications ,
- Singular Value ,
- Conditional Independence ,
- Regularization Parameter ,
- Data Streams ,
- Positive Definite Matrix ,
- Definite Matrix ,
- Covariance Estimation ,
- Data Window ,
- Precision Matrix ,
- True Covariance ,
- Nuclear Norm ,
- Gaussian Graphical Models ,
- Gaussian Random Vector ,
- Circulant Matrix ,
- Positive Definite ,
- Linear Subspace ,
- Sample Covariance Matrix ,
- Singular Values Of Matrix
- Author Keywords
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Covariance Matrix ,
- Estimated Covariance Matrix ,
- Inverse Covariance Matrix ,
- Inverse Covariance ,
- Numerical Simulations ,
- Real-world Data ,
- Symmetric Matrix ,
- Estimation Problem ,
- Measures In Group ,
- Low-dimensional Subspace ,
- Sample Groups ,
- Real Applications ,
- Singular Value ,
- Conditional Independence ,
- Regularization Parameter ,
- Data Streams ,
- Positive Definite Matrix ,
- Definite Matrix ,
- Covariance Estimation ,
- Data Window ,
- Precision Matrix ,
- True Covariance ,
- Nuclear Norm ,
- Gaussian Graphical Models ,
- Gaussian Random Vector ,
- Circulant Matrix ,
- Positive Definite ,
- Linear Subspace ,
- Sample Covariance Matrix ,
- Singular Values Of Matrix
- Author Keywords