elasticNetSEMpoint function

The Elastic Net penalty for SEM

For user provided one alpha in range (0,1) and one lambda_factor in range (0,1), the function perform selection path from lambda_max to lambda to determine the optimal network topology.

In the case of the grid search in elasticNetSEMcv() function may not be granular enough and user would like to explore/twist (alpha, lambda) a little bit, this function provides the solution.

elasticNetSEMpoint(Y, X, Missing, B, alpha_factor, lambda_factor, verbose)

Arguments

• Y: The observed node response data with dimension of M (nodes) by N (samples). Y is normalized inside the function.

• X: The network node attribute matrix with dimension of M by N. Theoretically, X can be L by N matrix, with L being the total node attributes. In current implementation, each node only allows one and only one attribute.

  If you have more than one attributes for some nodes, please consider selecting the top one by either correlation or principal component methods.

  If for some nodes there is no attribute available, fill in the rows with all zeros. See the yeast data yeast.rda for example.

  X is normalized inside the function.

• Missing: Optional M by N matrix corresponding to elements of Y. 0 denotes not missing, and 1 denotes missing. If a node i in sample j has the label missing (Missing[i,j] = 1), then Y[i,j] is set to 0.

• B: Optional input. For a network with M nodes, B is the M by M adjacency matrix. If data is simulated/with known true network topology (i.e., known adjacency matrix), the Power of detection (PD) and False Discovery Rate (FDR) is computed in the output parameter 'statistics'.

  If the true network topology is unknown, B is optional, and the PD/FDR in output parameter 'statistics' should be ignored.

• alpha_factor: alpha_factor: in range of (0, 1); must be scalar

• lambda_factor: penalty lambda_factor: in range of (0, 1); must be scalar

• verbose: describe the information output from -1 - 10, larger number means more output

Details

the function perform selection path from lambda_max to lambda, calculate power and FDR

Returns

• Bout: the computed weights for the network topology. B[i,j] = 0 means there is no edge between node i and j; B[i,j]!=0 denotes an (undirected) edge between note i and j.

• fout: f is 1 by M array keeping the weight for X (in SEM: Y = BY + FX + e). Theoretically, F can be M by L matrix, with M being the number of nodes, and L being the total node attributes. However, in current implementation, each node only allows one and only one attribute. If you have more than one attributes for some nodes, please consider selecting the top one by either correlation or principal component methods.

• stat: statistics is 1x6 array keeping record of:

  1. correct positive

  2. total positive

  3. false positive

  4. positive detected

  5. Power of detection (PD) = correct positive/total positive

  6. False Discovery Rate (FDR) = false positive/positive detected

• simTime: computational time

• call: the call that produced this object

References

1. Cai, X., Bazerque, J.A., and Giannakis, G.B. (2013). Inference of Gene Regulatory Networks with Sparse Structural Equation Models Exploiting Genetic Perturbations. PLoS Comput Biol 9, e1003068.

2. Huang, A. (2014). "Sparse model learning for inferring genotype and phenotype associations." Ph.D Dissertation. University of Miami(1186).

Author(s)

Anhui Huang; Dept of Electrical and Computer Engineering, Univ of Miami, Coral Gables, FL

Note

Difference in three functions:

1. elasticNetSEM: Default alpha = 0.95: -0.05: 0.05; default 20 lambdas

2. elasticNetSEMcv: user supplied alphas (one or more), lambdas; compute the optimal parameters and network parameters

3. elasticNetSEMpoint: user supplied one alpha and one lambda, compute the network parameters

Examples

library(sparseSEM)
        data(B);
        data(Y);
        data(X);
        data(Missing);
## Not run:
       OUT <- elasticNetSEMpoint(Y, X, Missing, B,
                alpha_factor = 0.5, lambda_factor = 0.1, verbose = 1);
## End(Not run)