Covariance Selection

The covariance selection problem is formulated as this:

$$\max_{X} \log(\det X) - Tr(\Sigma X)-\rho Card(X)$$

in the variable of $X$ in $S^n$, where $\Sigma \in S^n$ is the sample covariance matrix, $Card(X)$ the cardinality of $X$, i.e., the number of non-zero coefficients in $X$. $\rho > 0$ is a parameter controlling the tradeoff between the likelihood and structure.

References

1. “O. Banerjee, L. E. Ghaoui and A. d’Aspremont, “Model Selection Through Sparse Maximum Likelihood Estimation for multivariate Gaussian or Binary Data,” Journal of Machine Learning Research, 9, pp. 485-516, March 2008.”
2. “A. d’Aspremont, “Identifying Small Mean Reverting Portfolios”, 2008.”