rrpack_robust

See the paper: "Robust reduced rank regression under heavy-tailed noise and missing data via non-convex penalization".

rrpackrobust is an R package for robust multiple-response linear regression with low-rank structure, combining
Huber loss for robustness against heavy-tailed noise and outliers with spectral regularization to enforce reduced rank.

The package supports nonconvex penalties (SCAD, MCP) as well as the nuclear norm, and provides cross-validated tuning via an efficient proximal-gradient algorithm implemented in C++.

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Key Features

• Robust multivariate regression using Huber loss
• Reduced rank structure via spectral penalties
  • SCAD
  • MCP
  • Nuclear norm
• Efficient proximal-gradient solver implemented in C++
• K-fold cross-validation for tuning regularization parameters: for both lambda and tau (in Huber loss)
• Handles missing values in the response matrix
• Designed for high-dimensional and heavy-tailed data

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Installation From GitHub

# install.packages("devtools")
devtools::install_github("tienmt/rrpackrobust")

You will need a working C++ toolchain:

• Windows: Rtools
• macOS: Xcode Command Line Tools
• Linux: g++ / clang

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Main Functions

rr.robust()

Fits a robust reduced rank regression model for fixed tuning parameters.

rr.robust(
  X, Y,
  penalty = c("SCAD", "MCP", "nuclear"),
  tau = 1,
  lambda = 1,
  scad_a = 3.7,
  mcp_gamma = 3,
  max_iter = 2000,
  tol = 1e-5,
  svd_rank = NULL,
  verbose = TRUE
)

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cv.rr.robust()

Performs K-fold cross-validation to select tuning parameters and refits the final model.

cv.rr.robust(
  X, Y,
  penalty = c("SCAD", "MCP", "nuclear"),
  lambda_grid = NULL,
  tau_grid = NULL,
  nfolds = 5,
  seed = 1,
  scad_a = 3.7,
  mcp_gamma = 3,
  max_iter = 2000,
  tol = 1e-5,
  svd_rank = NULL,
  verbose = TRUE
)

Returns the optimal coefficient matrix, CV loss surface, and selected parameters.

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Example

 library(rrpackrobust)

set.seed(123)

n <- 200
p <- 12
q <- 7
r_true <- 2

## True low-rank coefficient matrix
U <- matrix(rnorm(p * r_true), p, r_true)
V <- matrix(rnorm(q * r_true), q, r_true)
Btrue <- U %*% t(V)

## Design matrix
X <- matrix(rnorm(n * p), n, p)

## Heavy-tailed noise
Y <- X %*% Btrue + matrix(rt(n * q, df = 3), n, q)

## Introduce missing values
missing_rate = 0.2
idx_na <- sample(seq_len(n * q), floor(missing_rate * n * q))
Y[idx_na] <- NA

## Cross-validated robust RRR
fit <- cv.rr.robust(
  X = X,
  Y = Y,
  penalty = "SCAD",
  verbose = FALSE
)

## Estimated coefficients
Bhat <- fit$B_best

## Estimation error
sum((Btrue - Bhat)^2)

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Supported Penalties

Penalty	Type	Description
SCAD	Nonconvex	Reduces bias for large singular values
MCP	Nonconvex	Nearly unbiased low-rank estimation
Nuclear	Convex	Standard trace-norm regularization

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Implementation Details

• Optimization via proximal gradient descent
• Singular value thresholding with nonconvex penalties
• Optional truncated SVD for computational efficiency
• Core solver implemented in C++ (Rcpp)

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References

• Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood. Journal of the American Statistical Association.

• Zhang, C.-H. (2010). Nearly unbiased variable selection under minimax concave penalty. Annals of Statistics.

• Bunea, F., She, Y., Wegkamp, M. (2011). Optimal selection of reduced rank estimators. Annals of Statistics.

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Status

• Actively developed
• Research-oriented
• Not yet submitted to CRAN

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License

GPL (>= 3)

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Contact

Author: The Tien Mai For questions, issues, or contributions, please use GitHub Issues.