macks22/ersgen

educational recommender systems data generation and analysis

ersgen's Issues

Implement probabilistic version of MLR using PyMC3.

b_s ~ Normal(0, sigma_s * I)
b_c ~ Normal(0, sigma_c * I)
P[s] ~ Dirichlet(alpha)
W ~ Multivariate Normal(mu, sigma * I)

Feature selection for MLR method.

Perhaps consider a t-cutoff approach. That would require calculating the standard error of each regression coefficient in W, while accounting for the importance of each regression model via the student memberships P.

Generative process based on FM model.

Define a list of questions to answer for a qualitative analysis paper.

Given the relative scarcity of traditional university data as compared to other educational data sources, such as online courses, it would be useful to try to characterize the data thoroughly. Devising a list of questions to answer would help guide exploration to uncover useful observations that would be worth publishing.

In particular, we have data about students, courses, instructors (three main entities), and their interactions. We have both transfer and non-transfer students, and we have various classifications for each of the three main entities. What are interesting questions to ask about this data? What does it look like? Can we replicate it through a probabilistic process in order to generate synthetic data that realistically emulates a traditional university setting?

Devise MLR/FM hybrid model.

The goal is to determine whether or not it is useful to combine factorized 2-way interactions with mixed membership 1-way interactions. Intuitively, this should give increased personalization. Making the inference efficient may be challenging.

b_s[s] + b_c[c] + P[s].T.dot(W).dot(x[i]) + v[s].T.dot(v[c]) * x[i].dot(x[i])

... or something like that.

Implement early stopping for MLR.

Compute training RMSE each iteration and add a threshold. If the RMSE reduction is less than the threshold (or RMSE is increased), then terminate training.

Devise a proper generative process for traditional university data.

Based on my limited experience, one must choose a generative process to model the data. There are an infinite number of suitable generative processes that could produce reasonable data. The question is which one to choose, and why?

Initially, it would make sense to come up with a generative process using the MLR model. After that, it would probably be useful to come up with one using the FM model.

Generative process based directly on probabilistic MLR model.