missoNet

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Multi-task regression and network estimation with missing responses — no imputation required!

missoNet jointly estimates regression coefficients and the response network (precision matrix) from multi-response data where some responses are missing (MCAR/MAR/MNAR). Estimation is based on unbiased estimating equations with separate L1 regularization for coefficients and the precision matrix, enabling robust multi-trait analysis under incomplete outcomes.

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Why missoNet?

• Native handling of missing responses without ad‑hoc imputation.
• Joint learning of effects (Beta) and conditional dependency structure (Theta).
• Two regularization paths with glmnet-like ergonomics.
• Reliable model selection via cross‑validation (with the 1‑SE rule) or information criteria (e.g., BIC).
• Built for scale: warm starts, parallel, and adaptive lambda grids.

If you only have a single response, classical lasso/elastic net (e.g., glmnet) is simpler and likely faster.

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Installation

CRAN (stable) r install.packages("missoNet")

GitHub (development) ```r

install.packages("devtools")

devtools::installgithub("yixiao-zeng/missoNet", buildvignettes = TRUE) ```

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Quick start

```r library(missoNet)

Example data with ~15% missing responses (MCAR)

sim <- generateData(n = 300, p = 50, q = 10, rho = 0.15, missing.type = "MCAR")

Fit along two lambda paths; choose via BIC (no CV)

fit <- missoNet(X = sim$X, Y = sim$Z, GoF = "BIC")

Extract estimates at the selected solution

Beta <- fit$est.min$Beta # p x q regression coefficients Theta <- fit$est.min$Theta # q x q precision (conditional network)

Visualize selection path

plot(fit, type = "scatter") ```

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Cross‑validation & prediction

```r

5-fold CV over (lambda.beta, lambda.theta)

cvfit <- cv.missoNet(X = sim$X, Y = sim$Z, kfold = 5)

Inspect CV heatmap and selected models (min and 1-SE variants)

plot(cvfit, type = "heatmap")

Predict responses on new data

Y_hat <- predict(cvfit, newx = sim$X, s = "lambda.min") ```

Tip: Try s = "lambda.1se.beta" or "lambda.1se.theta" for more conservative sparsity when available.

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Parallel processing

```r library(parallel)

cl <- makeCluster(max(1, detectCores() - 1)) cvfit <- cv.missoNet(X = sim$X, Y = sim$Z, kfold = 5, parallel = TRUE, cl = cl) stopCluster(cl) ```

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Advanced usage

Custom penalty factors

```r

Lessen the penalty for prior-important predictors

p <- ncol(sim$X); q <- ncol(sim$Z) beta.pen.factor <- matrix(1, p, q) beta.pen.factor[c(1, 2), ] <- 0.1

fit <- missoNet(X = sim$X, Y = sim$Z, beta.pen.factor = beta.pen.factor) ```

Adaptive search (faster large runs)

r fit <- missoNet(X = sim$X, Y = sim$Z, adaptive.search = TRUE, n.lambda.beta = 50, n.lambda.theta = 50)

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Documentation

r vignette("missoNet-introduction") vignette("missoNet-cross-validation") vignette("missoNet-case-study")

If vignettes are not available from CRAN binaries on your platform, install from source using the GitHub command above with build_vignettes = TRUE.

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Performance notes

• Handles substantial missingness in responses, without imputation.
• Warm starts and adaptive grids often yield 5–10× speedups in large problems.
• Scales to p > 1,000 predictors and q > 100 responses with reasonable settings.

Actual performance will depend on sparsity, signal-to-noise, and missingness mechanisms.

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When to use (and not)

Great for

• Multi-trait genomic studies (eQTL, meQTL, pQTL)
• High-dimensional omics with partially observed outcomes
• Longitudinal studies with dropout
• Network inference under incomplete responses

Not ideal for - Single-response regression (use glmnet or similar) - Extremely sparse information (e.g., >50% missing responses across most traits)

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Citation

If you use missoNet in your research, please cite:

bibtex @article{zeng2025missonet, title = {Multivariate regression with missing response data for modelling regional DNA methylation QTLs}, author = {Zeng, Yixiao and Alam, Shomoita and Bernatsky, Sasha and Hudson, Marie and Colmegna, In{\'e}s and Stephens, David A and Greenwood, Celia MT and Yang, Archer Y}, journal = {arXiv preprint arXiv:2507.05990}, year = {2025}, url = {https://arxiv.org/abs/2507.05990} }

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Contributing

Contributions and issues are welcome! Please open a discussion or pull request on the GitHub repository.

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License

GPL-2. See the LICENSE file.