Quick Start with CRAM

Introduction

The Cram package provides a unified framework for:

🧠 Cram Policy (cram_policy): Learn and evaluate individualized binary treatment rules using Cram. Supports flexible models, including causal forests and custom learners. Common examples include whether to treat a patient, send a discount offer, or provide financial aid based on estimated benefit.
📈 Cram ML (cram_ml): Learn and evaluate standard machine learning models using Cram. It estimates the expected loss at the population level, giving you a reliable measure of how well the final model is likely to generalize to new data. Supports flexible training via caret or custom learners, and allows evaluation with user-defined loss metrics. Ideal for classification, regression, and other predictive tasks.
🎰 Cram Bandit (cram_bandit): Perform on-policy evaluation of contextual bandit algorithms using Cram. Supports both real data and simulation environments with built-in policies.

This vignette walks through these three core modules.

Cram User file

For reproducible use cases, see the example script provided in the Cram GitHub repository:

View user_cram.R on GitHub

1. `cram_policy()` — Binary Policy Learning & Evaluation

Generate Simulated Data

generate_data <- function(n) {
  X <- data.table(
    binary = rbinom(n, 1, 0.5),
    discrete = sample(1:5, n, replace = TRUE),
    continuous = rnorm(n)
  )
  D <- rbinom(n, 1, 0.5)
  treatment_effect <- ifelse(X$binary == 1 & X$discrete <= 2, 1,
                       ifelse(X$binary == 0 & X$discrete >= 4, -1, 0.1))
  Y <- D * (treatment_effect + rnorm(n)) + (1 - D) * rnorm(n)
  list(X = X, D = D, Y = Y)
}

set.seed(123)
data <- generate_data(1000)
X <- data$X; D <- data$D; Y <- data$Y

Run `cram_policy()` with causal forest

res <- cram_policy(
  X, D, Y,
  batch = 20,
  model_type = "causal_forest",
  learner_type = NULL,
  baseline_policy = as.list(rep(0, nrow(X))),
  alpha = 0.05
)
print(res)
#> $raw_results
#>                        Metric   Value
#> 1              Delta Estimate 0.23208
#> 2        Delta Standard Error 0.05862
#> 3              Delta CI Lower 0.11718
#> 4              Delta CI Upper 0.34697
#> 5       Policy Value Estimate 0.21751
#> 6 Policy Value Standard Error 0.05237
#> 7       Policy Value CI Lower 0.11486
#> 8       Policy Value CI Upper 0.32016
#> 9          Proportion Treated 0.60500
#> 
#> $interactive_table
#> 
#> $final_policy_model
#> GRF forest object of type causal_forest 
#> Number of trees: 100 
#> Number of training samples: 1000 
#> Variable importance: 
#>     1     2     3 
#> 0.437 0.350 0.213

Case of categorical target Y

Use caret and choose a classification method outputting probabilities i.e. using the key word classProbs = TRUE in trainControl, see the following as an example with a Random Forest Classifier:

model_params <- list(formula = Y ~ ., caret_params = list(method = "rf", trControl = trainControl(method = "none", classProbs = TRUE)))

Also note that all data inputs needs to be of numeric types, hence for Y categorical, it should contain numeric values representing the class of each observation. No need to use the type factor for cram_policy().

Custom Models with `cram_policy()`

Set model_params to NULL and specify custom_fit and custom_predict.

custom_fit <- function(X, Y, D, n_folds = 5) {
  treated <- which(D == 1); control <- which(D == 0)
  m1 <- cv.glmnet(as.matrix(X[treated, ]), Y[treated], alpha = 0, nfolds = n_folds)
  m0 <- cv.glmnet(as.matrix(X[control, ]), Y[control], alpha = 0, nfolds = n_folds)
  tau1 <- predict(m1, as.matrix(X[control, ]), s = "lambda.min") - Y[control]
  tau0 <- Y[treated] - predict(m0, as.matrix(X[treated, ]), s = "lambda.min")
  tau <- c(tau0, tau1); X_all <- rbind(X[treated, ], X[control, ])
  final_model <- cv.glmnet(as.matrix(X_all), tau, alpha = 0)
  final_model
}

custom_predict <- function(model, X, D) {
  as.numeric(predict(model, as.matrix(X), s = "lambda.min") > 0)
}

res <- cram_policy(
  X, D, Y,
  batch = 20,
  model_type = NULL,
  custom_fit = custom_fit,
  custom_predict = custom_predict
)
print(res)
#> $raw_results
#>                        Metric   Value
#> 1              Delta Estimate 0.22542
#> 2        Delta Standard Error 0.06004
#> 3              Delta CI Lower 0.10774
#> 4              Delta CI Upper 0.34310
#> 5       Policy Value Estimate 0.21085
#> 6 Policy Value Standard Error 0.04280
#> 7       Policy Value CI Lower 0.12696
#> 8       Policy Value CI Upper 0.29475
#> 9          Proportion Treated 0.54500
#> 
#> $interactive_table
#> 
#> $final_policy_model
#> 
#> Call:  cv.glmnet(x = as.matrix(X_all), y = tau, alpha = 0) 
#> 
#> Measure: Mean-Squared Error 
#> 
#>     Lambda Index Measure      SE Nonzero
#> min 0.0395   100  0.9194 0.02589       3
#> 1se 0.4872    73  0.9423 0.03002       3

2. `cram_ml()` — ML Learning & Evaluation

Regression with `cram_ml()`

Specify formula and caret_paramsconforming to the popular caret::train() and set an individual loss under loss_name.

set.seed(42)
data_df <- data.frame(
  x1 = rnorm(100), x2 = rnorm(100), x3 = rnorm(100), Y = rnorm(100)
)

caret_params <- list(
  method = "lm",
  trControl = trainControl(method = "none")
)

res <- cram_ml(
  data = data_df,
  formula = Y ~ .,
  batch = 5,
  loss_name = "se",
  caret_params = caret_params
)
print(res)
#> $raw_results
#>                         Metric    Value
#> 1       Expected Loss Estimate  0.86429
#> 2 Expected Loss Standard Error  0.73665
#> 3       Expected Loss CI Lower -0.57952
#> 4       Expected Loss CI Upper  2.30809
#> 
#> $interactive_table
#> 
#> $final_ml_model
#> Linear Regression 
#> 
#> 100 samples
#>   3 predictor
#> 
#> No pre-processing
#> Resampling: None

Classification with `cram_ml()`

All data inputs needs to be of numeric types, hence for Y categorical, it should contain numeric values representing the class of each observation. No need to use the type factor for cram_ml().

Case 1: Predicting Class labels

In this case, the model outputs hard predictions (labels, e.g. 0, 1, 2 etc.), and the metric used is classification accuracy—the proportion of correctly predicted labels.

Use loss_name = "accuracy"
Set classProbs = FALSE in trainControl
Set classify = TRUE in cram_ml()

set.seed(42)

# Generate binary classification dataset
X_data <- data.frame(x1 = rnorm(100), x2 = rnorm(100), x3 = rnorm(100))
Y_data <- rbinom(nrow(X_data), 1, 0.5)
data_df <- data.frame(X_data, Y = Y_data)

# Define caret parameters: predict labels (default behavior)
caret_params_rf <- list(
  method = "rf",
  trControl = trainControl(method = "none")
)

# Run CRAM ML with accuracy as loss
result <- cram_ml(
  data = data_df,
  formula = Y ~ .,
  batch = 5,
  loss_name = "accuracy",
  caret_params = caret_params_rf,
  classify = TRUE
)

print(result)
#> $raw_results
#>                         Metric    Value
#> 1       Expected Loss Estimate  0.48750
#> 2 Expected Loss Standard Error  0.43071
#> 3       Expected Loss CI Lower -0.35668
#> 4       Expected Loss CI Upper  1.33168
#> 
#> $interactive_table
#> 
#> $final_ml_model
#> Random Forest 
#> 
#> 100 samples
#>   3 predictor
#>   2 classes: 'class0', 'class1' 
#> 
#> No pre-processing
#> Resampling: None

Case 2: Predicting Class Probabilities

In this setup, the model outputs class probabilities, and the loss is evaluated using logarithmic loss (logloss)—a standard metric for probabilistic classification.

Use loss_name = "logloss"
Set classProbs = TRUE in trainControl
Set classify = TRUE in cram_ml()

set.seed(42)

# Generate binary classification dataset
X_data <- data.frame(x1 = rnorm(100), x2 = rnorm(100), x3 = rnorm(100))
Y_data <- rbinom(nrow(X_data), 1, 0.5)
data_df <- data.frame(X_data, Y = Y_data)

# Define caret parameters for probability output
caret_params_rf_probs <- list(
  method = "rf",
  trControl = trainControl(method = "none", classProbs = TRUE)
)

# Run CRAM ML with logloss as the evaluation loss
result <- cram_ml(
  data = data_df,
  formula = Y ~ .,
  batch = 5,
  loss_name = "logloss",
  caret_params = caret_params_rf_probs,
  classify = TRUE
)

print(result)
#> $raw_results
#>                         Metric    Value
#> 1       Expected Loss Estimate  0.93225
#> 2 Expected Loss Standard Error  0.48118
#> 3       Expected Loss CI Lower -0.01085
#> 4       Expected Loss CI Upper  1.87534
#> 
#> $interactive_table
#> 
#> $final_ml_model
#> Random Forest 
#> 
#> 100 samples
#>   3 predictor
#>   2 classes: 'class0', 'class1' 
#> 
#> No pre-processing
#> Resampling: None

In addition to using built-in learners via caret, cram_ml() also supports fully custom model workflows. You can specify your own:

Model fitting function (custom_fit)
Prediction function (custom_predict)
Loss function (custom_loss)

See the vignette “Cram ML” for more details.

3. `cram_bandit()` — Contextual Bandits for On-policy Statistical Evaluation

Specify:

pi: An array of shape (T × B, T, K) or (T × B, T), where:
- \(T\) is the number of learning steps (or policy updates)
- \(B\) is the batch size
- \(K\) is the number of arms
- \(T \times B\) is the total number of contexts
- In the natural 3D version, pi[j, t, a] gives the probability that the policy \(\hat{\pi}_t\) assigns arm a to context \(X_j\). In the 2D version, we only keep the probabilities assigned to the chosen arm \(A_j\) for each context \(X_j\) in the historical data - and not the probabilities for all of the arms \(a\) under each context \(X_j\).
arm: A vector of length \(T \times B\) indicating which arm was selected in each context.
reward: A vector of observed rewards of length \(T \times B\).
batch: (optional) Integer batch size \(B\). Default is 1.
alpha: Significance level for confidence intervals.

set.seed(42)
T <- 100; K <- 4
pi <- array(runif(T * T * K, 0.1, 1), dim = c(T, T, K))
for (t in 1:T) for (j in 1:T) pi[j, t, ] <- pi[j, t, ] / sum(pi[j, t, ])
arm <- sample(1:K, T, replace = TRUE)
reward <- rnorm(T, 1, 0.5)

res <- cram_bandit(pi, arm, reward, batch=1, alpha=0.05)
print(res)
#> $raw_results
#>                        Metric   Value
#> 1       Policy Value Estimate 0.67621
#> 2 Policy Value Standard Error 0.04394
#> 3       Policy Value CI Lower 0.59008
#> 4       Policy Value CI Upper 0.76234
#> 
#> $interactive_table

Quick Start with CRAM

Introduction

Cram User file

1. cram_policy() — Binary Policy Learning & Evaluation

Generate Simulated Data

Run cram_policy() with causal forest

Case of categorical target Y

Custom Models with cram_policy()

2. cram_ml() — ML Learning & Evaluation

Regression with cram_ml()

Classification with cram_ml()