# huge.inference: Graph inference In huge: High-Dimensional Undirected Graph Estimation

## Description

Implements the inference for high dimensional graphical models, including Gaussian and Nonparanormal graphical models We consider the problems of testing the presence of a single edge and the hypothesis is that the edge is absent.

## Usage

 `1` ```huge.inference(data, T, adj, alpha = 0.05, type = "Gaussian", method = "score") ```

## Arguments

 `data` The input `n` by `d` data matrix(`n` is the sample size and `d` is the dimension). `T` The estimated inverse of correlation matrix of the data. `adj` The adjacency matrix corresponding to the graph. `alpha` The significance level of hypothesis.The default value is `0.05`. `type` The type of input data. There are 2 options: `"Gaussian"` and `"Nonparanormal"`. The default value is `"Gaussian"`. `method` When using nonparanormal graphical model. Test method with 2 options: `"score"` and `"wald"`. The default value is `"score"`.

## Details

For Nonparanormal graphical model we provide Score test method and Wald Test. However it is really slow for inferencing on Nonparanormal model, especially for large data.

## Value

An object is returned:

 `data` The `n` by `d` data matrix from the input. `p` The `d` by `d` p-value matrix of hypothesis. `error` The type I error of hypothesis at alpha significance level.

## References

1.Q Gu, Y Cao, Y Ning, H Liu. Local and global inference for high dimensional nonparanormal graphical models.
2.J Jankova, S Van De Geer. Confidence intervals for high-dimensional inverse covariance estimation. Electronic Journal of Statistics, 2015.

`huge`, and `huge-package`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```#generate data L = huge.generator(n = 50, d = 12, graph = "hub", g = 4) #graph path estimation using glasso est = huge(L\$data, method = "glasso") #inference of Gaussian graphical model at 0.05 significance level T = tail(est\$icov, 1)[[1]] out1 = huge.inference(L\$data, T, L\$theta) #inference of Nonparanormal graphical model using score test at 0.05 significance level T = tail(est\$icov, 1)[[1]] out2 = huge.inference(L\$data, T, L\$theta, type = "Nonparanormal") #inference of Nonparanormal graphical model using wald test at 0.05 significance level T = tail(est\$icov, 1)[[1]] out3 = huge.inference(L\$data, T, L\$theta, type = "Nonparanormal", method = "wald") #inference of Nonparanormal graphical model using wald test at 0.1 significance level T = tail(est\$icov, 1)[[1]] out4 = huge.inference(L\$data, T, L\$theta, 0.1, type = "Nonparanormal", method = "wald") ```

### Example output

```Generating data from the multivariate normal distribution with the hub graph structure....done.

Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 9%
Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 19%
Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 30%
Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 40%
Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 50%
Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 60%
Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 70%
Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 80%
Conducting the graphical lasso (glasso) wtih lossless screening....in progress: 90%
Conducting the graphical lasso (glasso)....done.
```

huge documentation built on July 1, 2021, 1:06 a.m.