think about data (preferences) input

[floswald]

• what would be a good way to get student's preferences into your app?
• for example, assume we were given a csv file like

id	course1	course2	course3	...
1	100	20	30	....
2	89	95	13	....

how could we get that into our model? related to #2

[Gegas2231]

We could have a matrix for each student. Rows and columns represent courses, the values in the diagonal will represent individual utility for each course. Elements outside diagonal represent substitutes (-200) and complements (+200)

[Gegas2231]

I think the best way is using the matrix form that I mentioned. The diagonal elements will represent the individual utility, outside the diagonal substitutes and complements. Think on the following matrix for 3 courses.

[80 10 -50; 10 90 0; -50 0 60]

So each course will report 80, 90 and 60 utility units respectively. courses 1 and 2 together will report 20 points of additional utility (I write 10 but it'll make sense later). On the contrary, course 1 and 3 are substitutes, so together that will mean minus 100 points of utility. Course 2 and 3 together report no additional utility for the sake of the example. We can easily tune the additional values of utility to achieve the +200 and -200 from the paper.

With this matrix form, the computation of the utility becomes as follows:

X is a row vector of 0s or 1s. Say the utility Matrix is U.

The final utility will be X'UX. This matrix form is the reason why outside the diagonal we report the bonus utility divided by 2.

I checked with a simple example that this method works, can someone else check if what I'm writting above is true.

A problem with this approach is that our objective becomes nonlinear

[floswald]

• this could work
• maybe too complicated for the user
• how to scale "i really like/dislike a couple"