cram_expected_loss

This function computes the Cram ML expected loss estimator
based on the given loss matrix and batch indices.

Performs the Cram method, a general and efficient approach to simultaneous learning and evaluation using a generic machine learning algorithm. In a single pass of batched data, the proposed method repeatedly trains a machine learning algorithm and tests its empirical performance. Because it utilizes the entire sample for both learning and evaluation, cramming is significantly more data-efficient than sample-splitting. Unlike cross-validation, Cram evaluates the final learned model directly, providing sharper inference aligned with real-world deployment. The method naturally applies to both policy learning and contextual bandits, where decisions are based on individual features to maximize outcomes. The package includes cram_policy() for learning and evaluating individualized binary treatment rules, cram_ml() to train and assess the population-level performance of machine learning models, and cram_bandit() for on-policy evaluation of contextual bandit algorithms. For all three functions, the package provides estimates of the average outcome that would result if the model were deployed, along with standard errors and confidence intervals for these estimates. Details of the method are described in Jia, Imai, and Li (2024) <https://www.hbs.edu/ris/Publication%20Files/2403.07031v1_a83462e0-145b-4675-99d5-9754aa65d786.pdf> and Jia et al. (2025) <doi:10.48550/arXiv.2403.07031>.

Yanis Vandecasteele

cramR

Cram Method for Efficient Simultaneous Learning and Evaluation

cram_expected_loss function

<dl><dt>loss</dt>
<dd>A matrix of loss values with N rows (data points) and K+1 columns (batches).
We assume that the first column of the loss matrix contains only zeros.
The following nb_batch columns contain the losses of each trained model for each individual.</dd>
<dt>batch_indices</dt>
<dd>A list where each element is a vector of indices corresponding to a batch.</dd></dl>

Arguments

Cram ML Expected Loss Estimate — cram_expected_loss

<dl>

<dt>loss</dt>
<dd>A matrix of loss values with N rows (data points) and K+1 columns (batches).
We assume that the first column of the loss matrix contains only zeros.
The following nb_batch columns contain the losses of each trained model for each individual.</dd>


<dt>batch_indices</dt>
<dd>A list where each element is a vector of indices corresponding to a batch.</dd>

</dl>

cram_expected_loss: Cram ML Expected Loss Estimate

Description

Usage

Value

Arguments