  The information diffusion prediction on social networks aims to predict
future recipients of a message, with practical applications in marketing and
social media. While different prediction models all claim to perform well,
general frameworks for performance evaluation remain limited. Here, we aim to
identify a performance characteristic curve for a model, which captures its
performance on tasks of different complexity. We propose a metric based on
information entropy to quantify the randomness in diffusion data, then identify
a scaling pattern between the randomness and the prediction accuracy of the
model. Data points in the patterns by different sequence lengths, system sizes,
and randomness all collapse into a single curve, capturing a model's inherent
capability of making correct predictions against increased uncertainty. Given
that this curve has such important properties that it can be used to evaluate
the model, we define it as the performance characteristic curve of the model.
The validity of the curve is tested by three prediction models in the same
family, reaching conclusions in line with existing studies. Also, the curve is
successfully applied to evaluate two distinct models from the literature. Our
work reveals a pattern underlying the data randomness and prediction accuracy.
The performance characteristic curve provides a new way to systematically
evaluate models' performance, and sheds light on future studies on other
frameworks for model evaluation.
