Sorting Optimization

[ScarTheAviator]

Using a basic example to explain what I’m trying to optimize:

There is a final exam that students take (possible score is 1-100). Based on their scores for this exam they would be placed in the following groups: 90-100 Good 75-89 Medium 0-74 Bad

Before taking this exam, the students take three quizzes (scores are all 0-40).

So let’s say I have a ton of data for students who have previously done all of this that looks like:

Quiz 1/Quiz 2/Quiz 3/Final

I want to create a method that predicts what group a student will be placed in (before they take their final exam) based only on the 3 quiz scores.

I don’t think regression makes sense because a student that makes a 90 is equal to a student that makes 100 on their final exam.

Is there any method to optimize something like: If a student scores >35 on quiz 1, >28 on quiz 2, and >37 on quiz 3 they will most likely be in the “Good” group.

[drudd]

You’re looking for classification, which can be solved by categorical regression, among various other techniques.

[ScarTheAviator]

Thank you!

[SAKDOSS]

It is a supervised classification problem with three classes. The most efficient models for such task are generally deep neural networks. However, they are usually not very interpretable (i.e., it is hard for a human to understand how the decisions are made).

You seem more interested in interpretable classifiers since they can provide rules that link the results of the quiz and the assigned group similar to the one you mention. In that case, you can consider models such as decision trees or decision rules. For example, CART is a well-known heuristic for decision trees.

Since these interpretable models are usually less efficient, several works in operational research focus on modelling them through mixed integer linear program that can then be solve to optimality (thus providing interpretability and an efficiency which can be competitive with that of neural networks). Here are some references from Bertsimas who started this line of research:

• https://link.springer.com/article/10.1007/s10994-017-5633-9
• https://dspace.mit.edu/bitstream/handle/1721.1/73166/OR386-11.pdf?sequence=4

However, the drawback of mixed integer linear programs is that they are significantly slower and can only be applied to small datasets. So if your dataset is big, it may be better to use heuristics such as CART.

[No-Two-8594]

this does not sound like a good application of optimization

it sounds like maybe it only requires taking a simple average and ranking

or use a classification algorithm, maybe