CODEWITHSUNDEEP
machine-learningneural-network
shamwow
shamwow

Reputation: 335

Estimating both the category and the magnitude of output using neural networks

Let's say I want to calculate which courses a final year student will take and which grades they will receive from the said courses. We have data of previous students'courses and grades for each year (not just the final year) to train with. We also have data of the grades and courses of the previous years for students we want to estimate the results for. I want to use a recurrent neural network with long-short term memory to solve this problem. (I know this problem can be solved by regression, but I want the neural network specifically to see if this problem can be properly solved using one)

The way I want to set up the output (label) space is by having a feature for each of the possible courses a student can take, and having a result between 0 and 1 in each of those entries to describe whether if a student will attend the class (if not, the entry for that course would be 0) and if so, what would their mark be (ie if the student attends class A and gets 57%, then the label for class A will have 0.57 in it)

Am I setting the output space properly?

Upvotes: 1

Views: 72

Answers (2)

Imran
Imran

Reputation: 13468

There is more than one way to solve this problem. Andrey's answer gives a one good approach.

I would like to suggest simplifying the problem by bucketing grades into categories and adding an additional category for "did not take", for both input and output.

This turns the task into a classification problem only, and solves the issue of trying to differentiate between receiving a low grade and not taking the course in your output.

For example your training set might have m students, n possible classes, and six possible results: ['A', 'B', 'C', 'D', 'F', 'did_not_take'].

And you might choose the following architecture:

Input -> Dense Layer -> RELU -> Dense Layer -> RELU -> Dense Layer -> Softmax

Your input shape is (m, n, 6) and your output shape could be (m, n*6), where you apply softmax for every group of 6 outputs (corresponding to one class) and sum into a single loss value. This is an example of multiclass, multilabel classification.

I would start by trying 2n neurons in each hidden layer.

If you really want a continuous output for grades, however, then I recommend using separate classification and regression networks. This way you don't have to combine classification and regression loss into one number, which can get messy with scaling issues.

You can keep the grade buckets for input data only, so the two networks take the same input data, but for the grade regression network your last layer can be n sigmoid units with log loss. These will output numbers between 0 and 1, corresponding the predicted grade for each class.

If you want to go even further, consider using an architecture that considers the order in which students took previous classes. For example if a student took French I the previous year, it is more likely he/she will take French II this year than if he/she took French Freshman year and did not continue with French after that.

Upvotes: 0

Andrey Tyukin
Andrey Tyukin

Reputation: 44992

If I understood you correctly, you want that the network is given the history of a student, and then outputs one entry for each course. This entry is supposed to simultaneously signify whether the student will take the course (0 for not taking the course, 1 for taking the course), and also give the expected grade? Then the interpretation of the output for a single course would be like this:

0.0 -> won't take the course
0.1 -> will take the course and get 10% of points
0.5 -> will take the course and get half of points
1.0 -> will take the course and get full points

If this is indeed your plan, I would definitely advise to rethink it. Some obviously realistic cases do not fit into this pattern. For example, how would you represent an (A+)-student is "unlikely" to take a course? Should the network output 0.9999, because (s)he is very likely to get the maximum amount of points if (s)he takes the course, OR should the network output 0.0001, because the student is very unlikely to take the course?

Instead, you should output two values between [0,1] for each student and each course.

  • First value in [0, 1] gives the probability that the student will participate in the course
  • Second value in [0, 1] gives the expected relative number of points.

As loss, I'd propose something like binary cross-entropy on the first value, and simple square error on the second, and then combine all the losses using some L^p metric of your choice (e.g. simply add everything up for p=1, square and add for p=2).

Few examples:

(0.01, 1.0) : very unlikely to participate, would probably get 100%
(0.5, 0.8): 50%-50% whether participates or not, would get 80% of points
(0.999, 0.15): will participate, but probably pretty much fail

The quantity that you wanted to output seemed to be something like the product of these two, which is a bit difficult to interpret.

Upvotes: 1

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