Description Usage Arguments Details Value References Examples

The `HGMND`

is the main function to estimate the conditional dependence matrices of variables from different datasets.

1 2 3 4 5 6 7 8 9 10 11 |

`x` |
a list of data matrices sharing the same variables in their columns. |

`setting` |
a string that indicates the data distribution, must be chosen from |

`h` |
the function |

`centered` |
logical, if |

`mat.adj` |
the adjacency matrix of the network among the multiple datasets, containing only 0s and 1s. Only the upper-triangle of |

`lambda1` |
the non-negative tuning parameter which controls the sparsity level of the estimation. |

`lambda2` |
the non-negative tuning parameter which controls the homogeneity level of the estimation. |

`gamma` |
the step size parameter in ADMM. Default to |

`maxit` |
maximum number of iterations. Default to |

`tol` |
tolerance in the convergence criterion. Default to |

`silent` |
logical, if |

`h`

can be generated by function `get_h_hp`

in package `genscore`

. See more details in Yu S., Lin, L. & Gilks, W. (2020). genscore: Generalized Score Matching Estimators. R package version 1.0.2. https://CRAN.R-project.org/package=genscore and Yu, S., Drton, M., & Shojaie, A. (2019). Generalized Score Matching for Non-Negative Data. J. Mach. Learn. Res., 20, 76-1.

Suppose we have *M* datasets, and we demand the network among them to be connected and have *M - 1* edges, hence acyclic. This is sufficient for computational feasibility, which however does not prevent our method from being applicable to diverse network structures.

The `HGMND`

method returns the estimated conditional dependence matrix of each dataset.

`Theta` |
the 3-dimensional array containing the estimation of the multiple conditional dependence matrices. The 3rd dimension represents different datasets. |

`M` |
an integer, the number of datasets. |

`P` |
an integer, dimension of the random vector of interest. |

Yu, S., Drton, M., & Shojaie, A. (2019). Generalized Score Matching for Non-Negative Data. J. Mach. Learn. Res., 20, 76-1.

Yu S., Lin, L. & Gilks, W. (2020). genscore: Generalized Score Matching Estimators. R package version 1.0.2. https://CRAN.R-project.org/package=genscore.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# This is an example of HGMND with simulated data
data(HGMND_SimuData)
h <- genscore::get_h_hp("mcp", 1, 5)
HGMND_SimuData <- lapply(HGMND_SimuData, function(x) scale(x, center = FALSE))
mat.chain <- diag(length(HGMND_SimuData))
diag(mat.chain[-nrow(mat.chain), -1]) <- 1
result <- HGMND(x = HGMND_SimuData,
setting = "gaussian",
h = h,
centered = FALSE,
mat.adj = mat.chain,
lambda1 = 0.086,
lambda2 = 3.6,
gamma = 1,
tol = 1e-3,
silent = TRUE)
Theta <- result[["Theta"]]
``` |

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