a python implementation of mixture learning curve model

Mixture Learning Curve (MLC) model is proposed by Matthew Streeter(2015). The original paper is light on the derivation, which I supplemented in the document folder.

The canonical Bayesian Knowledge Tracing (BKT) can be viewed as a special case of the MLC. It imposes that the learning curve of each component is a step function with same upper and lower limit while the mixture density is govern by learning rate the prior.

The vanilla version of MLC imposes no structure on the learning curve. Therefore it also loses the ability to generate user specific learning curve parameter.

It is likely that student's response is right truncated. For example, if the max practice opportunity is 5, student's spell can practice 2 or 3 times. The last few obs is thus missing.

If the missing data is not correlated with the learning curve (missing at random), the estimator is consistent.

The mixed learning curve is not uniquely identified. The alogrithm fit 5 curves and chosen the curvature with largest l2 norm. The intuition is that we want to distinguish user with different learning speed.