Estimation of a covariance matrix with zeros

By Sanjay Chaudhuri, Mathias Drton, Thomas S. Richardson. 2005

141 citations recorded by the source corpus.

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm has guaranteed convergence properties. Dropping the assumption of multivariate normality, we show how to estimate the covariance matrix in an empirical likelihood approach. These approaches are then compared via simulation and on an example of gene expression. Copyright 2007, Oxford University Press.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/156fd61a56a6980b1dc2cb0ff2e6c0773fba25f6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Nanny Wermuth
2. Mathias Drton
3. Kayvan Sadeghi
4. Thomas S. Richardson
5. Mohsen Pourahmadi
6. Caroline Uhler
7. A. C. Davison
8. Miguel de Carvalho

In Statistics and Probability

1. Mathias Drton
2. Nanny Wermuth
3. Kayvan Sadeghi
4. Mohsen Pourahmadi
5. Thomas S. Richardson
6. A. C. Davison
7. Miguel de Carvalho
8. Caroline Uhler

Citations in the corpus

• Binary models for marginal independence (2007, methodology): “In the Gaussian case, Chaudhuri et al. (2007) described how to run the ICF algorithm with multivariate updates.”
• Sequences of regressions and their independences (2011, background): “To obtain the overall complexity of Algorithm 1, we denote by n the number of nodes in the graph and by e the number of edges in the graph.”
• Covariance Estimation: The GLM and Regularization Perspectives (2011, methodology): “An iterative conditional fitting procedure for solving the first problem is proposed by Chaudhuri et al. (2007). Friedman et al.”
• Identification and Likelihood Inference for Recursive Linear Models with Correlated Errors (2006, unknown): “the edge i ↔ j is not in G. In general, the solution of the likelihood equations of this covariance model requires another iterative method, such as the iterative conditional fitting of Chaudhuri et al. [ 10 ].”
• Adjusted Empirical Likelihood and its Properties (2008, methodology): “Chaudhuri et al. (2007) discussed the problem of estimating a covariance matrix of a random vector with many known zero entries.”
• Spectral Density Ratio Models for Multivariate Extremes (2014, methodology): “A similar two-step estimation strategy is used by Chaudhuri, Drton, and Richardson (2007), and a more general discussion on twostep nearly optimal estimators that behave asymptotically like M-estimators can be found in van der Vaart (1998, p. 71).”
• Maximum likelihood estimation for linear Gaussian covariance models (2014, background): “…likelihood estimation of correlation matrices for Gaussian populations [RM94, SWY00, SO91] or covariance matrices with prescribed zeros [DR04, CDR07], applications of stationary stochastic processes from repeated time series data [And70, And73], Brownian motion tree models for phylogenetic…”