Last updated: 2020-05-18
Checks: 6 1
Knit directory: causal-TWAS/
This reproducible R Markdown analysis was created with workflowr (version 1.6.0). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.
The R Markdown file has unstaged changes. To know which version of the R Markdown file created these results, you’ll want to first commit it to the Git repo. If you’re still working on the analysis, you can ignore this warning. When you’re finished, you can run wflow_publish to commit the R Markdown file and build the HTML.
Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.
The command set.seed(20191103) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.
Great job! Recording the operating system, R version, and package versions is critical for reproducibility.
Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.
Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.
Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility. The version displayed above was the version of the Git repository at the time these results were generated.
Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:
Ignored files:
Ignored: .Rhistory
Ignored: .Rproj.user/
Ignored: .ipynb_checkpoints/
Ignored: code/.ipynb_checkpoints/
Ignored: data/
Untracked files:
Untracked: analysis/fusion_expr.Rmd
Untracked: analysis/mrash_model.Rmd
Untracked: code/temp.R
Unstaged changes:
Modified: analysis/VEB-boost-fitting.Rmd
Modified: analysis/index.Rmd
Modified: analysis/sparse_model.Rmd
Modified: code/run_test_veb-boost.R
Modified: code/simulate_phenotype.R
Modified: code/workflow-ashtest.ipynb
Modified: code/workflow-data.ipynb
Staged changes:
Deleted: analysis/mr.ash.Rmd
Deleted: analysis/plot_expression.R
Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.
These are the previous versions of the R Markdown and HTML files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view them.
| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 9bcc184 | simingz | 2020-03-31 | sparse model descriptoin |
| html | 9bcc184 | simingz | 2020-03-31 | sparse model descriptoin |
| Rmd | 83288ad | simingz | 2020-03-31 | sparse model description |
| html | 83288ad | simingz | 2020-03-31 | sparse model description |
You want to add up 2 linear regressions, which we might call “learners”. A learner is, roughly, a fucntion, that learns a relationshipo between Y and some predictors X (here the Xs are different for your 2 different learners) Let’s write this \(Y=L1(X1) + L2(X2) + E\).
The idea is that you can fit this model iteratively, by first applying \(L1\), and then applying \(L2\), each time applying it to the appropriate residuals.So you apply \(L1\) to learn a relationship between \(R=Y-L2\) (residuals) and \(X1\), and then \(L2\) to learn a relationship between \(R=Y-L1\) and \(X2\) and you just iterate….
Model:
\[Y = \mu_1 + \mu_2 + \epsilon\] \[ \mu_1= X_{N \times J}\beta_{J\times1}\] \[ \mu_2 = G_{N\times M}\theta_{M\times1}\] \[ \epsilon \sim MVN(0,\sigma^2I_N) \] Priors:
ASH prior for scaled \(\beta_j\) and \(\theta_m\) \[\beta_j | g_1, \sigma \sim g^1_\sigma(\cdot)\] ASH prior for \(\theta_m\): \[\theta_m | g_2, \sigma \sim g^2_\sigma(\cdot)\]
take \(\mu1\) as the example, \(\mu2\) works similarly.
\[E_q(\mu_1) = X\bar{\beta}\] \(\bar{\beta}\) is posterior mean of \(\beta\) given by mr.ash function.
\[E_q(\mu_{1}^2) = \sum_{j=1}^J{x^2_j E_q(\beta^2)} + [E_q(\mu_1)]^2 =\sum_{j=1}^J\sum_{k=1}^K{x^2_j\phi_k \frac{\sigma^2 d_j^2 \sigma_k^2}{1+ d_j^2 \sigma_k^2}} + [E_q(\mu_1)]^2\] where \[d_j=x^T_jx_j= \left\lVert x_j\right\rVert^2\].
\(d_j, \phi, \sigma, \sigma_k\) are estimates given by mr.ash function.
Shall we just use ELBO from mr.ash?
sessionInfo()R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)
Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
loaded via a namespace (and not attached):
[1] workflowr_1.6.0 Rcpp_1.0.4.6 digest_0.6.18 later_0.7.5
[5] rprojroot_1.3-2 R6_2.3.0 backports_1.1.2 git2r_0.26.1
[9] magrittr_1.5 evaluate_0.12 stringi_1.3.1 fs_1.3.1
[13] promises_1.0.1 whisker_0.3-2 rmarkdown_1.10 tools_3.5.1
[17] stringr_1.4.0 glue_1.3.0 httpuv_1.4.5 yaml_2.2.0
[21] compiler_3.5.1 htmltools_0.3.6 knitr_1.20