Package 'PartialTL'

Partial Transfer Learning for Causal Estimation and Source Detection

Description

Implements partial transfer learning (PTL) and heterogeneous partial transfer learning (HPTL) for causal effect estimation using source and target data. Uses double machine learning for nuisance estimation and cross-fitting. Provides bootstrap-based source detection to identify which sources are transferable to the target. Includes data generating processes and nuisance functions for simulation.

Details

Main functions:

• fit_PTL: PTL causal estimate (single source).

• fit_HPTL: Heterogeneous PTL with multiple sources and covariate modules.

• boot_detection: Bootstrap-based source detection.

• run_bootstrap_E_hat: Bootstrap for nuisance function estimation.

• DGP: Data generating process for simulations.

• RMSE: Root mean squared error for evaluation.

• f_0, g_0, f_k, g_k: Nuisance functions for target and source models.

Run demo(package = "PartialTL") for demo scripts.

Author(s)

Author [email protected]

References

(Add references to the partial transfer learning and DML literature.)

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Bootstrap-Based Source Detection

Description

Identifies which sources are transferable to the target by comparing bootstrap estimates of the nuisance function on the target and each source. A source is detected as transferable if the difference is below a threshold proportional to the combined standard error.

Usage

boot_detection(D_t, X_t, Y_t, D_s_all, X_s_all, Y_s_all, source_sizes, B,
               ml_f, ml_g)

Arguments

D_t	Target treatment; $n_t \times 1$.
X_t	Target design matrix; $n_t \times p$.
Y_t	Target outcome; $n_t \times 1$.
D_s_all	Source treatments concatenated by row; rows split by source_sizes.
X_s_all	Source design matrices concatenated by row.
Y_s_all	Source outcomes concatenated by row.
source_sizes	Integer vector of length K: sample size of each source.
B	Number of bootstrap replications.
ml_f	Outcome learner for DoubleML.
ml_g	Treatment learner for DoubleML.

Value

A data frame with columns Source (label) and detected.source (list of logical vectors of length B per source).

See Also

run_bootstrap_E_hat, fit_PTL, fit_HPTL

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Data Generating Process

Description

Generates $(X, D, Y)$ for simulations: multivariate normal X with AR(1)-type covariance, treatment D from a linear confounding model plus noise, and outcome Y = rho*D + f(X) + error.

Usage

DGP(n, q, p, p.nonzero, rho, Beta, Gamma, mu = rep(10, p), sigma = 0.5,
    f_func = f_0, g_func = g_0, seed = NULL)

Arguments

n	Sample size.
q	Causal dimension (kept for interface; unused in current body).
p	Nuisance dimension (number of covariates).
p.nonzero	Number of non-zero coefficients for Beta and Gamma.
rho	Causal effect (scalar).
Beta	Nuisance coefficient vector for outcome; $p \times 1$.
Gamma	Nuisance coefficient vector for treatment; $p \times 1$.
mu	Mean vector of X; length p.
sigma	Base for AR(1)-type covariance: $\Sigma_{i,j} = \sigma^{|i-j|}$.
f_func	Function f(X, Beta) for outcome nuisance; default f_0.
g_func	Function g(X, Gamma) for treatment equation; default g_0.
seed	Optional random seed.

Value

A list with components D (treatment), X (design matrix), Y (outcome), and data (cbind(Y, D, X)).

See Also

f_0, g_0, f_k, g_k, fit_PTL, RMSE

Examples

set.seed(1)
  n <- 50
  p <- 10
  p.nz <- 3
  Beta <- matrix(c(rep(0.5, p.nz), rep(0, p - p.nz)))
  Gamma <- matrix(c(rep(0.3, p.nz), rep(0, p - p.nz)))
  dat <- DGP(n, q = 1, p, p.nz, rho = 0.5, Beta, Gamma, seed = 1)
  str(dat)

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Outcome Nuisance Function (Target Model)

Description

Linear outcome nuisance function for the target model: $f_0(X, \beta) = X \beta$.

Usage

f_0(X, Beta)

Arguments

X	Design matrix; $n \times p$.
Beta	Coefficient vector (column matrix); $p \times 1$.

Value

Numeric vector of outcome nuisance values; length n.

See Also

g_0, f_k, g_k, DGP

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Outcome Nuisance Function (Source Model)

Description

Linear outcome nuisance function for source models: $f_k(X, \beta) = X \beta$. Same form as f_0; used in DGP for source data.

Usage

f_k(X, Beta)

Arguments

X	Design matrix; $n \times p$.
Beta	Coefficient vector (column matrix); $p \times 1$.

Value

Numeric vector of outcome nuisance values; length n.

See Also

f_0, g_k, DGP

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HPTL (Heterogeneous Partial Transfer Learning) Fit

Description

Fits heterogeneous partial transfer learning with multiple sources and covariate modules. Each source has its own module of covariates; PTL is applied per source and results are combined for the target causal estimate.

Usage

fit_HPTL(D_t, X_t, Y_t, D_s_all, X_s_all, Y_s_all, source_sizes, module_sizes,
         ml_f, ml_g, fold = 5)

Arguments

D_t	Target treatment; $n_t \times q$ matrix.
X_t	Target design matrix; $n_t \times p$ (same covariates as sources).
Y_t	Target outcome; $n_t \times 1$.
D_s_all	Source treatments concatenated by row; dimension is (sum of source_sizes) by $q$.
X_s_all	Source design matrices concatenated by row; rows split by source_sizes.
Y_s_all	Source outcomes concatenated by row; rows split by source_sizes.
source_sizes	Integer vector of length K: sample size of each source. Must sum to nrow(Y_s_all).
module_sizes	Integer vector of length K: covariate module sizes. The k-th source uses columns (cumsum(module_sizes)[k-1]+1):cumsum(module_sizes)[k] of X.
ml_f	Outcome learner for DoubleML.
ml_g	Treatment learner for DoubleML.
fold	Number of folds for cross-fitting (default 5).

Value

A list with component hat_rho_HPTL: HPTL causal estimate on target.

See Also

fit_PTL, boot_detection

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PTL (Partial Transfer Learning) Fit

Description

Fits partial transfer learning with cross-fitting and outcome reconstruction. Uses double machine learning on the source and SCAD on the outcome nuisance, then transfers to the target via the partial transfer formula.

Usage

fit_PTL(D_t, X_t, Y_t, D_s, X_s, Y_s, ml_f, ml_g, fold = 5L)

Arguments

D_t	Target treatment; $n_t \times 1$ matrix.
X_t	Target design matrix; $n_t \times p$.
Y_t	Target outcome; $n_t \times 1$.
D_s	Source treatment; $n_s \times 1$.
X_s	Source design matrix; $n_s \times p$.
Y_s	Source outcome; $n_s \times 1$.
ml_f	Outcome learner for DoubleML (e.g. lrn("regr.cv_glmnet")).
ml_g	Treatment learner for DoubleML (same type).
fold	Number of folds for cross-fitting (default 5).

Value

A list with components:

hat_rho_s	Source causal estimate.
beta_hat_s	Source nuisance coefficient estimate.
E_s	Estimated $E[Y - \rho D]$ on source (NA when q != 1).
hat_rho_PTL	PTL causal estimate on target.

See Also

fit_HPTL, DGP, RMSE

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Treatment Nuisance Function (Target Model)

Description

Linear treatment/confounding function for the target model: $g_0(X, \gamma) = X \gamma$.

Usage

g_0(X, Gamma)

Arguments

X	Design matrix; $n \times p$.
Gamma	Coefficient vector (column matrix); $p \times 1$.

Value

Numeric vector of treatment equation values; length n.

See Also

f_0, f_k, g_k, DGP

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Treatment Nuisance Function (Source Model)

Description

Linear treatment/confounding function for source models: $g_k(X, \gamma) = X \gamma$. Same form as g_0; used in DGP for source data.

Usage

g_k(X, Gamma)

Arguments

X	Design matrix; $n \times p$.
Gamma	Coefficient vector (column matrix); $p \times 1$.

Value

Numeric vector of treatment equation values; length n.

See Also

g_0, f_k, DGP

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Root Mean Squared Error

Description

Computes the root mean squared error of parameter estimates across simulations: for each component, $\sqrt{\mathrm{mean}((\hat{\theta} - \theta)^2)}$.

Usage

RMSE(Theta, Theta.hat)

Arguments

Theta	True parameter vector; $p \times 1$.
Theta.hat	Matrix of estimates; $p \times n_{sim}$.

Value

Numeric vector of length p: RMSE per parameter component.

See Also

DGP, fit_PTL, fit_HPTL

Examples

th <- c(1, 2)
  th_hat <- matrix(c(1.1, 2.2, 0.9, 1.8), nrow = 2)
  RMSE(th, th_hat)

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Bootstrap for Nuisance Function Estimation

Description

Runs bootstrap replications to estimate the nuisance quantity $E[Y - D \theta]$ using double machine learning, and returns the bootstrap distribution (mean and variance) of the estimate.

Usage

run_bootstrap_E_hat(D, X, Y, B, ml_f, ml_g)

Arguments

D	Treatment variable(s); matrix.
X	Design matrix.
Y	Outcome variable.
B	Number of bootstrap replications.
ml_f	Outcome learner for DoubleML.
ml_g	Treatment learner for DoubleML.

Value

A list with components:

E_hat	Numeric vector of length B: bootstrap estimates.
E_hat_mean	Mean of E_hat.
E_hat_var	Variance of E_hat.

See Also

boot_detection

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