Family¶

In [ ]:

family   = c("reg_ld", "reg_hd", "reg_ml", "cls")

family = c("reg_ld", "reg_hd", "reg_ml", "cls")

Family	Description	Statistical Inference
reg_ld	Linear prediction model (low-dimensional)	✅
reg_hd	High-dimensional linear model	✅
reg_ml	Machine learning prediction model	❌
cls	Linear model for classification task	✅

Arguments¶

family = reg_ld¶

cgdro_()¶

intercept

Whether to include intercept in outcome models. Default is FALSE.

delta

Regularization parameter in weight optimization. Default is 0.

infer_cgdro_()¶

tau Variance inflation parameter. Default is 0.2.

alpha_thres

Threshold for small eigenvalues. Default is 0.01.

threshold

Threshold for eigenvalue truncation. Default is 0.

summary_cgdro_()¶

index

Index of the coefficients of interest.

family = reg_hd¶

cgdro_()¶

intercept

Whether to include intercept in outcome models. Default is FALSE.

intercept_loading

Whether to include intercept in loading matrix defined by index. Default is FALSE.

delta

Regularization parameter in weight optimization. Default is 0.

lambda

Regularization parameter in high-dimensional outcome models; if "CV.min" or "CV.1se", use cross-validation to select. Default is NULL.

infer_cgdro_()¶

tau Variance inflation parameter. Default is 0.2.

alpha_thres

Threshold for small eigenvalues. Default is 0.01.

threshold

Threshold for eigenvalue truncation. Default is 0.

family = reg_ml¶

cgdro_()¶

bias_correct

Whether to use bias-corrected estimator for Γ. Default is TRUE.

priors

Optional list with two elements: prior weight vector (length L) and radius (nonnegative scalar). Default is NULL (no prior).

ridge

Ridge regularization parameter (nonnegative scalar) for numerical stability. Default is 1e-8.

solver

Solver for the quadratic program. Options: "ECOS", "SCS". Default is "ECOS".

seed

Random seed for reproducibility in data splitting. Default is 123.

family = cls¶

cgdro_()¶

split

Whether to use sample-splitting in outcome/density estimation. Default is TRUE.

max_iter

Maximum number of iterations. Default is 1000.

tol

Tolerance for convergence. Default is 1e-6.

Check_dual

Whether to compute duality gap every 50 iterations. Default is FALSE.

seed

Random seed for reproducibility in data splitting. Default is 123.

infer_cgdro_()¶

parallel

Whether to use parallel computing. Default is FALSE.

n_workers

number of workers for parallel computing. Default is 4.

diag

whether to use diagonal approximation for covariance estimation. Default is TRUE.

summary_cgdro_()¶

index

Index of the coefficients of interest.

class_index

Index of the class of coefficients of interest.

Example¶

Example of Low-dimensional Linear Regression¶

In [ ]:

  # number of source groups = 3, with 1000 samples each
  # sigma: source group 1,3: 0.5; source group 2: 2
  # target sample size = 10000
  # dimension p = 5
  data <- simu_linear_reg_lowd(n_list = list(1000,1000,1000), N=10000, p = 5, seed = 123)
  Xlist = data$X_list
  Ylist = data$Y_list
  X0 = data$X0
  ## fit cgdro
  ## Note: only when loss_type='reward', infer() can be called to get confidence intervals
  ## For other loss_type, only point estimation and prediction can be done
  fit <- cgdro_(Xlist, Ylist, X0, loss_type = "reward",
               family = "reg_ld",  intercept = TRUE,
               delta = 0,  verbose = FALSE)
  inf <- infer_cgdro_(fit, M = 200, alpha = 0.05)
  ## summary
  summary_cgdro_(fit, infer=inf)
  ## predict
  pred <- predict_cgdro_(fit)  # N x 1 vector of predicted values
  head(pred)


  ## fit cgdro
  fit <- cgdro_(Xlist, Ylist, X0, loss_type = "squaredloss",
               family = "reg_ld",  intercept = TRUE,
               delta = 0,  verbose = FALSE)
  ## summary
  summary(fit)
  ## predict
  pred <- predict_cgdro_(fit)  # N x 1 vector of predicted values
  head(pred)


  ## fit cgdro
  fit <- cgdro_(Xlist, Ylist, X0, loss_type = "regret",
               family = "reg_ld",  intercept = TRUE,
               delta = 0,  verbose = FALSE)
  ## summary
  summary(fit)
  ## predict
  pred <- predict_cgdro_(fit)  # N x 1 vector of predicted values
  head(pred)

# number of source groups = 3, with 1000 samples each # sigma: source group 1,3: 0.5; source group 2: 2 # target sample size = 10000 # dimension p = 5 data <- simu_linear_reg_lowd(n_list = list(1000,1000,1000), N=10000, p = 5, seed = 123) Xlist = data$X_list Ylist = data$Y_list X0 = data$X0 ## fit cgdro ## Note: only when loss_type='reward', infer() can be called to get confidence intervals ## For other loss_type, only point estimation and prediction can be done fit <- cgdro_(Xlist, Ylist, X0, loss_type = "reward", family = "reg_ld", intercept = TRUE, delta = 0, verbose = FALSE) inf <- infer_cgdro_(fit, M = 200, alpha = 0.05) ## summary summary_cgdro_(fit, infer=inf) ## predict pred <- predict_cgdro_(fit) # N x 1 vector of predicted values head(pred) ## fit cgdro fit <- cgdro_(Xlist, Ylist, X0, loss_type = "squaredloss", family = "reg_ld", intercept = TRUE, delta = 0, verbose = FALSE) ## summary summary(fit) ## predict pred <- predict_cgdro_(fit) # N x 1 vector of predicted values head(pred) ## fit cgdro fit <- cgdro_(Xlist, Ylist, X0, loss_type = "regret", family = "reg_ld", intercept = TRUE, delta = 0, verbose = FALSE) ## summary summary(fit) ## predict pred <- predict_cgdro_(fit) # N x 1 vector of predicted values head(pred)

Example of High-dimensional Linear Regression¶

In [ ]:

  # two source groups, each with 100 samples, and 100 target samples
  data <- simu_linear_reg_highd(n_list = c(100, 100), N = 100, p = 100, seed = 123)
  Xlist = data$X_list
  Ylist = data$Y_list
  X0 = data$X0

  ## fit cgdro
  fit <- cgdro_(Xlist, Ylist, X0 = X0,
               family = "reg_hd",
               index = c(1,10,45,99), intercept = FALSE,
               delta = 0, lambda = "CV.min", verbose = FALSE)
  inf <- infer_cgdro_(fit, M = 200, alpha = 0.05)

  ## summary
  summary_cgdro_(fit, infer=inf)

  ## predict
  pred <- predict_cgdro_(fit)  # N x 1 vector of predicted values
  head(pred)

# two source groups, each with 100 samples, and 100 target samples data <- simu_linear_reg_highd(n_list = c(100, 100), N = 100, p = 100, seed = 123) Xlist = data$X_list Ylist = data$Y_list X0 = data$X0 ## fit cgdro fit <- cgdro_(Xlist, Ylist, X0 = X0, family = "reg_hd", index = c(1,10,45,99), intercept = FALSE, delta = 0, lambda = "CV.min", verbose = FALSE) inf <- infer_cgdro_(fit, M = 200, alpha = 0.05) ## summary summary_cgdro_(fit, infer=inf) ## predict pred <- predict_cgdro_(fit) # N x 1 vector of predicted values head(pred)

Example of Machine Learning Regression¶

In [ ]:

  # number of source groups = 3, each with 1000 samples, and 10000 target samples
  # dimension p = 5
  data <- simu_reg_ml(n_vec = c(1000,1000,1000), n0=10000, N_label=20, p=5, seed = 123)
  Xlist = data$X_list
  Ylist = data$Y_list
  X0 = data$X0

  ## fit cgdro
  fit <- cgdro_(Xlist, Ylist, X0, loss_type = "reward",
               family = "reg_ml", f_learner = "xgb", w_learner = "logistic",
               bias_correct = TRUE,
               priors = NULL,
               ridge = 1e-8,
               seed = 123,
               verbose = FALSE)
  fit$weight_

  ## predict
  pred <- predict_cgdro_(fit)  # N x 1 vector of predicted values
  head(pred)

  ## fit cgdro
  fit <- cgdro_(Xlist, Ylist, X0, loss_type = "squaredloss",
               family = "reg_ml", f_learner = "xgb", w_learner = "logistic",
               bias_correct = TRUE,
               priors = NULL,
               ridge = 1e-8,
               seed = 123)
  fit$weight_

  ## predict
  pred <- predict_cgdro_(fit)  # N x 1 vector of predicted values
  head(pred)

  ## fit cgdro
  fit <- cgdro_(Xlist, Ylist, X0, loss_type = "regret",
               family = "reg_ml", f_learner = "xgb", w_learner = "logistic",
               bias_correct = TRUE,
               priors = NULL,
               ridge = 1e-8,
               seed = 123)
  fit$weight_

  ## predict
  pred <- predict_cgdro_(fit)  # N x 1 vector of predicted values
  head(pred)

# number of source groups = 3, each with 1000 samples, and 10000 target samples # dimension p = 5 data <- simu_reg_ml(n_vec = c(1000,1000,1000), n0=10000, N_label=20, p=5, seed = 123) Xlist = data$X_list Ylist = data$Y_list X0 = data$X0 ## fit cgdro fit <- cgdro_(Xlist, Ylist, X0, loss_type = "reward", family = "reg_ml", f_learner = "xgb", w_learner = "logistic", bias_correct = TRUE, priors = NULL, ridge = 1e-8, seed = 123, verbose = FALSE) fit$weight_ ## predict pred <- predict_cgdro_(fit) # N x 1 vector of predicted values head(pred) ## fit cgdro fit <- cgdro_(Xlist, Ylist, X0, loss_type = "squaredloss", family = "reg_ml", f_learner = "xgb", w_learner = "logistic", bias_correct = TRUE, priors = NULL, ridge = 1e-8, seed = 123) fit$weight_ ## predict pred <- predict_cgdro_(fit) # N x 1 vector of predicted values head(pred) ## fit cgdro fit <- cgdro_(Xlist, Ylist, X0, loss_type = "regret", family = "reg_ml", f_learner = "xgb", w_learner = "logistic", bias_correct = TRUE, priors = NULL, ridge = 1e-8, seed = 123) fit$weight_ ## predict pred <- predict_cgdro_(fit) # N x 1 vector of predicted values head(pred)

Example of Classification¶

In [ ]:

  # two source groups, each with 100 samples, and 1000 target samples
  n = 100; p = 5; L = 2; N = 1000; K = 2
  data <- simu_cls(n, N, p, L, K, seed=123)
  Xlist = data$X_list
  Ylist = data$Y_list
  X0 = data$X0

  ## fit cgdro
  fit <- cgdro_(Xlist, Ylist, X0,
               family = "cls", f_learner = "linear", w_learner = "logistic")
  inf <- infer_cgdro_(fit, M = 200, alpha = 0.05, parallel = FALSE, diag = TRUE)

  ## summary
  summary_cgdro_(fit, infer = inf)

  summary_cgdro_(fit, infer = inf, index = c(1,3), class_index = c(2))

  ## prediction
  pred <- predict_cgdro_(fit)  # N x C matrix of predicted probabilities
  head(pred$pred_proba)
  head(pred$pred)

# two source groups, each with 100 samples, and 1000 target samples n = 100; p = 5; L = 2; N = 1000; K = 2 data <- simu_cls(n, N, p, L, K, seed=123) Xlist = data$X_list Ylist = data$Y_list X0 = data$X0 ## fit cgdro fit <- cgdro_(Xlist, Ylist, X0, family = "cls", f_learner = "linear", w_learner = "logistic") inf <- infer_cgdro_(fit, M = 200, alpha = 0.05, parallel = FALSE, diag = TRUE) ## summary summary_cgdro_(fit, infer = inf) summary_cgdro_(fit, infer = inf, index = c(1,3), class_index = c(2)) ## prediction pred <- predict_cgdro_(fit) # N x C matrix of predicted probabilities head(pred$pred_proba) head(pred$pred)