Which method visually compares the change in a model's performance against the number of data examples used?

The learning curve is specifically designed to visualize how a model's performance varies with changes in the number of training data examples. It typically plots the model's accuracy or error rate on the y-axis against the number of training samples on the x-axis. This allows practitioners to see how increasing the amount of training data can improve the model's performance, indicating whether the model benefits from additional data or if it has reached a point of diminishing returns.

In practice, a learning curve can also indicate potential problems such as underfitting or overfitting. For instance, if the learning curve shows high training performance and low validation performance as more data is added, it may suggest that the model is overfitting. Conversely, if both training and validation performances are low with an increasing dataset, it may indicate underfitting.

Other methods such as the ROC curve and precision-recall curve focus on evaluating model performance concerning different thresholds or classes but do not specifically illustrate how model performance changes with data size. Custom graph analysis might encompass various types of visualizations but lacks the specific focus on the relationship between training data size and model performance that the learning curve provides. Thus, the learning curve stands out as the appropriate method for this particular comparison.