bic.netEst.undir: Bayesian information criterion to select the tuning...
In drjingma/netgsa: Network-Based Gene Set Analysis

Description Usage Arguments Details Value Author(s) References See Also

This function uses the Bayesian information criterion to select the optimal tuning parameters needed in netEst.undir.

1 2	bic.netEst.undir(x, zero = NULL, one = NULL, lambda, rho = NULL, weight = NULL, eta = 0, verbose = FALSE, eps = 1e-08)

`x`	The p x n data matrix as in `netEst.undir`.
`zero`	(Optional) indices of entries of the matrix to be constrained to be zero. The input should be a matrix of p x p, with 1 at entries to be constrained to be zero and 0 elsewhere. The matrix must be symmetric.
`one`	(Optional) indices of entries of the matrix to be kept regardless of the regularization parameter for lasso. The input is similar to that of `zero` and needs to be symmetric.
`lambda`	(Non-negative) user-supplied lambda sequence.
`rho`	(Non-negative) numeric scalar representing the regularization parameter for estimating the weights in the inverse covariance matrix. This is the same as `rho` in the graphical lasso algorithm `glassoFast`.
`weight`	(Optional) whether to add penalty to known edges. If NULL (default), then the known edges are assumed to be true. If nonzero, then a penalty equal to `lambda * weight` is added to penalize the known edges to account for possible uncertainty. Only non-negative values are accepted for the weight parameter.
`eta`	(Non-negative) a small constant added to the diagonal of the empirical covariance matrix of `X` to ensure it is well conditioned. By default, `eta` is set to 0.
`verbose`	Whether to print out information as estimation proceeds. Default=`FALSE`.
`eps`	Numeric scalar >=0, indicating the tolerance level for differentiating zero and non-zero edges: entries < `eps` will be set to 0.

Let \hatΣ represent the empirical covariance matrix of data x. For a given λ, denote the estimated inverse covariance matrix by \hatΩ_{λ}. the Bayesian information criterion (BIC) is defined as

trace(\hatΣ \hatΩ_{λ}) - \log \det (\hatΩ_{λ}) + \frac{\log n}{n} \cdot df,

where df represents the degrees of freedom in the selected model and can be estimated via the number of edges in \hatΩ_{λ}. The optimal tuning parameter is selected as the one that minimizes the BIC over the range of lambda.

Note when the penalty parameter lambda is too large, the estimated adjacency matrix may be zero. The function will thus return a warning message.

`lambda`	The values of `lambda` used.
`weight`	The values of `weight` used.
`BIC`	If `weight=NULL`, then a numeric vector of the same length as `lambda` with the corresponding BIC. If `weight` is a vector, then a matrix of size `length(lambda)` by `length(weight)` with the corresponding BIC.
`df`	The degrees of freedom corresponding to each BIC.

Jing Ma

Ma, J., Shojaie, A. & Michailidis, G. (2016) Network-based pathway enrichment analysis with incomplete network information. Bioinformatics 32(20):165–3174. https://doi.org/10.1093/bioinformatics/btw410

netEst.undir

drjingma/netgsa documentation built on Feb. 22, 2022, 5:18 p.m.