Description Usage Arguments Details Value Examples

Estimates a sparse continuous time Lyapunov parametrization of a covariance matrix using a lasso (L1) penalty.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 |

`Sigma` |
covariance matrix |

`B` |
initial B matrix |

`C` |
diagonal of initial C matrix |

`C0` |
diagonal of penalization matrix |

`loss` |
one of "loglik" (default) or "frobenius" |

`eps` |
convergence threshold |

`alpha` |
parameter line search |

`maxIter` |
maximum number of iterations |

`lambda` |
penalization coefficient for B |

`lambdac` |
penalization coefficient for C |

`job` |
integer 0,1,10 or 11 |

`lambdas` |
sequence of lambda |

`...` |
additional arguments passed to |

`gclm`

performs proximal gradient descent for the optimization problem

*argmin L(Σ(B,C)) + λ ρ(B) + λ_C ||C - C0||_F^2*

subject to *B* stable and *C* diagonal, where *ρ(B)* is the l1 norm
of the off-diagonal element of *B*.

`gclm.path`

simply calls iteratively `gclm`

with different `lambda`

values. Warm start is used, that
is in the i-th call to `gclm`

the `B`

and `C`

matrices are initialized as the one obtained in the (i-1)th
call.

for `gclm`

: a list with the result of the optimization

for `gclm.path`

: a list of the same length of
`lambdas`

with the results of the optimization for
the different `lambda`

values

1 2 3 4 5 6 7 8 9 10 11 | ```
x <- matrix(rnorm(50*20),ncol=20)
S <- cov(x)
## l1 penalized log-likelihood
res <- gclm(S, eps = 0, lambda = 0.1, lambdac = 0.01)
## l1 penalized log-likelihood with fixed C
res <- gclm(S, eps = 0, lambda = 0.1, lambdac = -1)
## l1 penalized frobenius loss
res <- gclm(S, eps = 0, lambda = 0.1, loss = "frobenius")
``` |

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