orthoMTL

Multi-task learning with orthogonality and disjoint-support constraints, for regression, classification and survival analysis

Overview

orthoMTL fits multi-task learning models in which several related tasks are learned jointly through a shared coefficient matrix. An orthogonality (or disjoint-support) penalty encourages different tasks to select different features, which gives sparse, interpretable models when the tasks are expected to depend on distinct sets of features.

Three kinds of tasks are supported by the same solver:

Regression: several continuous outcomes.
Classification: several binary outcomes.
Survival analysis: time-to-event data, recast as binary classification tasks at several time thresholds (censored entries are masked in the loss). This relaxes the constant-effect assumption of the Cox proportional hazards model and lets the effect of a feature vary over time.

The method is based on:

Vervier, K., Mahé, P., d'Aspremont, A., Veyrieras, J.-B., & Vert, J.-P. (2014). On Learning Matrices with Orthogonal Columns or Disjoint Supports. ECML-PKDD 2014. https://hal.science/hal-00985654

The survival extension is described in:

Juric, D. et al. (2026). Genomic Determinants of Response to Alpelisib Plus Fulvestrant in the SOLAR-1 Trial. Annals of Oncology. https://doi.org/10.1016/j.annonc.2026.04.003

Installation

From CRAN

install.packages("orthoMTL")

Development version from GitHub

# install.packages("pak")
# pak::pak("Novartis/orthoMTL")
install.packages("orthoMTL", repos = c('https://novartis.r-universe.dev', 'https://cloud.r-project.org'))

Or using remotes:

# install.packages("remotes")
# remotes::install_github("Novartis/orthoMTL")
install.packages("orthoMTL", repos = c('https://novartis.r-universe.dev', 'https://cloud.r-project.org'))

Quick start

The mode is selected on the solver with the logistic / survival flags (both FALSE for regression). Score with the matching metric and, for cross-validation, let cv_orthoMTL() pick the metric automatically.

Regression and classification

library(orthoMTL)

# --- Multi-task regression ---
sim <- simulate_mtl(n = 200, p = 20, n_signals = 5,
                    mode = "regression", seed = 42)
fit <- orthoMTL(sim$X, sim$Y, lambda = 1e-3)      # logistic = survival = FALSE
pred <- predict(fit, newdata = sim$X)             # type = "link"
rmse_mtl(sim$Y, pred)
r2_mtl(sim$Y, pred)

# --- Multi-task classification (labels in {-1, +1}) ---
sim <- simulate_mtl(n = 200, p = 20, n_signals = 5,
                    mode = "classification", seed = 42)
fit <- orthoMTL(sim$X, sim$Y, lambda = 1e-3, logistic = TRUE)
prob <- predict(fit, newdata = sim$X, type = "response")   # P(Y = +1)
cls  <- predict(fit, newdata = sim$X, type = "class")      # {-1, +1}
auc_mtl(sim$Y, predict(fit, newdata = sim$X))              # AUC on link scores
accuracy_mtl(sim$Y, predict(fit, newdata = sim$X))

# CV picks the metric by mode (cindex / auc / rmse) unless overridden
cv <- cv_orthoMTL(sim$X, sim$Y, logistic = TRUE, survival = FALSE,
                  lambdas = c(1e-3, 1e-2), n_cores = 1)
cv$best

Survival analysis

library(orthoMTL)

# Simulate data with known time-varying effects
sim <- simulate_mtl(n = 200, p = 20, n_signals = 5, seed = 42)

# Convert survival times to binary labels at each threshold
Y <- create_longitudinal_labels(sim$SurvTime, sim$Event, sim$thresholds)
W <- create_indicator_matrix(Y)   # censoring mask
K <- create_constraint_matrix(length(sim$thresholds))

# Fit the model
fit <- orthoMTL(sim$X, Y, lambda = 1e-3, K = K,
                survival = TRUE, censored.mat = W)
summary(fit)

# Visualise coefficients across time thresholds
plot_heatmap(fit)

For a full walkthrough — including cross-validation, bootstrap inference, and comparison with Cox — see the package vignette:

vignette("introduction", package = "orthoMTL")

Key functions

Function	Purpose
`orthoMTL()`	Core solver (regression / classification / survival)
`cv_orthoMTL()`	Parallel hyperparameter grid search
`bootstrap_orthoMTL()`	Bootstrap coefficient stability vs null
`simulate_mtl()`	Simulate data with time-varying ground truth
`create_longitudinal_labels()`	Survival → binary label matrix
`create_indicator_matrix()`	Censoring indicator matrix
`create_constraint_matrix()`	Diffusion constraint matrix for tasks
`predict()`, `coef()`	Predictions (`type = "link"/"response"/"class"`) and coefficients
`cindex_mtl()`	Survival concordance index
`rmse_mtl()`, `r2_mtl()`	Regression metrics
`accuracy_mtl()`, `auc_mtl()`	Classification metrics
`plot_heatmap()`, `plot_correlation()`, `plot_bootstrap()`	Visualisation

Citation

If you use orthoMTL in your work, please cite:

@inproceedings{vervier2014,
  author    = {Vervier, Kevin and Mah{\'e}, Pierre and d'Aspremont,
               Alexandre and Veyrieras, Jean-Baptiste and Vert, Jean-Philippe},
  title     = {On Learning Matrices with Orthogonal Columns or Disjoint Supports},
  booktitle = {Machine Learning and Knowledge Discovery in Databases (ECML-PKDD 2014)},
  year      = {2014},
  publisher = {Springer},
  url       = {https://hal.science/hal-00985654}
}

Getting help and reporting bugs

Questions, bug reports and feature requests are welcome on the issue tracker. For a bug, a minimal reproducible example (data simulated with simulate_mtl() is fine) and the output of sessionInfo() help a lot.

License

GPL-3.