Results > UniQ2


Prediction of the student performance with gradient-based matrix factorisation


Team Leader

Sharon Lee
University of Queensland
Australia

Overview

Supplementary online material

Provide a URL to a web page, technical memorandum, or a paper.

No response.

Background*

Provide a general summary with relevant background information: Where does the method come from? Is it novel? Name the prior art.

Using given training data, we computed the matrix of empirical probabilities for the students/opportunities. Where the confidence was not sufficient, we used the corresponding averages for students or opportunities. Then, we applied gradient-based matrix factorisation in order to extract latent factors (the range of the number of factors was between 20 and 100). The required predictions were based on the above matrices of the latent factors. The different sets of the KC-opportunities were considered separately, and the final solution was constructed using GBM function in R. We consider our approach as a novel.

Method

Summarize the algorithms you used in a way that those skilled in the art should understand what to do. Profile of your methods as follows:

Data exploration and understanding

Did you use data exploration techniques to

  • [not checked]  Identify selection biases
  • [checked]  Identify temporal effects (e.g. students getting better over time)
  • [checked]  Understand the variables
  • [checked]  Explore the usefulness of the KC models
  • [checked]  Understand the relationships between the different KC types

Please describe your data understanding efforts, and interesting observations:

the most interesting was the student progress in time.

Preprocessing

Feature generation

  • [not checked]  Features designed to capture the step type (e.g. enter given, or ... )
  • [not checked]  Features based on the textual step name
  • [checked]  Features designed to capture the KC type
  • [not checked]  Features based on the textual KC name
  • [checked]  Features derived from opportunity counts
  • [checked]  Features derived from the problem name
  • [checked]  Features based on student ID
  • [not checked]  Other features

Details on feature generation:

No response.

Feature selection

  • [not checked]  Feature ranking with correlation or other criterion (specify below)
  • [not checked]  Filter method (other than feature ranking)
  • [not checked]  Wrapper with forward or backward selection (nested subset method)
  • [not checked]  Wrapper with intensive search (subsets not nested)
  • [not checked]  Embedded method
  • [not checked]  Other method not listed above (specify below)

Details on feature selection:

No response.

Did you attempt to identify latent factors?

  • [checked]  Cluster students
  • [checked]  Cluster knowledge components
  • [not checked]  Cluster steps
  • [not checked]  Latent feature discovery was performed jointly with learning

Details on latent factor discovery (techniques used, useful student/step features, how were the factors used, etc.):

No response.

Other preprocessing

  • [not checked]  Filling missing values (for KC)
  • [not checked]  Principal component analysis

More details on preprocessing:

No response.

Classification

Base classifier

  • [not checked]  Decision tree, stub, or Random Forest
  • [checked]  Linear classifier (Fisher's discriminant, SVM, linear regression)
  • [not checked]  Non-linear kernel method (SVM, kernel ridge regression, kernel logistic regression)
  • [checked]  Naïve
  • [not checked]  Bayesian Network (other than Naïve Bayes)
  • [not checked]  Neural Network
  • [not checked]  Bayesian Neural Network
  • [checked]  Nearest neighbors
  • [checked]  Latent variable models (e.g. matrix factorization)
  • [not checked]  Neighborhood/correlation based collaborative filtering
  • [not checked]  Bayesian Knowledge Tracing
  • [not checked]  Additive Factor Model
  • [not checked]  Item Response Theory
  • [not checked]  Other classifier not listed above (specify below)

Loss Function

  • [not checked]  Hinge loss (like in SVM)
  • [checked]  Square loss (like in ridge regression)
  • [checked]  Logistic loss or cross-entropy (like in logistic regression)
  • [checked]  Exponential loss (like in boosting)
  • [not checked]  None
  • [not checked]  Don't know
  • [not checked]  Other loss (specify below)

Regularizer

  • [not checked]  One-norm (sum of weight magnitudes, like in Lasso)
  • [not checked]  Two-norm (||w||^2, like in ridge regression and regular SVM)
  • [not checked]  Structured regularizer (like in group lasso)
  • [not checked]  None
  • [not checked]  Don't know
  • [not checked]  Other (specify below)

Ensemble Method

  • [checked]  Boosting
  • [not checked]  Bagging (check this if you use Random Forest)
  • [checked]  Other ensemble method
  • [not checked]  None

Were you able to use information present only in the training set?

  • [not checked]  Corrects, incorrects, hints
  • [not checked]  Step start/end times

Did you use post-training calibration to obtain accurate probabilities?

  • [not selected]  Yes
  • [not selected]  No

Did you make use of the development data sets for training?

  • [not selected]  Yes
  • [not selected]  No

Details on classification:

No response.

Model selection/hyperparameter selection

  • [checked]  We used the online feedback of the leaderboard.
  • [checked]  K-fold or leave-one-out cross-validation (using training data)
  • [not checked]  Virtual leave-one-out (closed for estimations of LOO with a single classifier training)
  • [not checked]  Out-of-bag estimation (for bagging methods)
  • [not checked]  Bootstrap estimation (other than out-of-bag)
  • [not checked]  Other cross-validation method
  • [not checked]  Bayesian model selection
  • [not checked]  Penalty-based method (non-Bayesian)
  • [not checked]  Bi-level optimization
  • [not checked]  Other method not listed above (specify below)

Details on model selection:

No response.

Results

Final Team Submission

Scores shown in the table below are Cup scores, not leaderboard scores. The difference between the two is described on the Evaluation page.

A reader should also know from reading the fact sheet what the strength of the method is.

Please comment about the following:

Quantitative advantages (e.g., compact feature subset, simplicity, computational advantages).

based on our experience the gradient-based matrix factorisation (GMF) is a very reliable and fast method. It may be very easily programmed in Matlab or C. We do not need any standard software packages for the GMF.

Qualitative advantages (e.g. compute posterior probabilities, theoretically motivated, has some elements of novelty).

the method is interesting and novel.

Other methods. List other methods you tried.

No response.

How helpful did you find the included KC models?

  • [selected]  Crucial in getting good predictions
  • [not selected]  Somewhat helpful in getting good predictions
  • [not selected]  Neutral
  • [not selected]  Not particularly helpful
  • [not selected]  Irrelevant

If you learned latent factors, how helpful were they?

  • [selected]  Crucial in getting good predictions
  • [not selected]  Somewhat helpful in getting good predictions
  • [not selected]  Neutral
  • [not selected]  Not particularly helpful
  • [not selected]  Irrelevant

Details on the relevance of the KC models and latent factors:

No response.

Software Implementation

Availability

  • [checked]  Proprietary in-house software
  • [not checked]  Commercially available in-house software
  • [not checked]  Freeware or shareware in-house software
  • [not checked]  Off-the-shelf third party commercial software
  • [checked]  Off-the-shelf third party freeware or shareware

Language

  • [checked]  C/C++
  • [not checked]  Java
  • [checked]  Matlab
  • [not checked]  Python/NumPy/SciPy
  • [checked]  Other (specify below)

Details on software implementation:

R and Perl

Hardware implementation

Platform

  • [not checked]  Windows
  • [checked]  Linux or other Unix
  • [not checked]  Mac OS
  • [not checked]  Other (specify below)

Memory

  • [not selected]  <= 2 GB
  • [not selected]  <= 8 GB
  • [selected]  >= 8 GB
  • [not selected]  >= 32 GB

Parallelism

  • [checked]  Multi-processor machine
  • [not checked]  Run in parallel different algorithms on different machines
  • [not checked]  Other (specify below)

Details on hardware implementation. Specify whether you provide a self contained-application or libraries.

No response.

Code URL

Provide a URL for the code (if available):

No response.

Competition Setup

From a performance point of view, the training set was

  • [selected]  Too big (could have achieved the same performance with significantly less data)
  • [not selected]  Too small (more data would have led to better performance)

From a computational point of view, the training set was

  • [not selected]  Too big (imposed serious computational challenges, limited the types of methods that can be applied)
  • [not selected]  Adequate (the computational load was easy to handle)

Was the time constraint imposed by the challenge a difficulty or did you feel enough time to understand the data, prepare it, and train models?

  • [selected]  Not enough time
  • [not selected]  Enough time
  • [not selected]  It was enough time to do something decent, but there was a lot left to explore. With more time performance could have been significantly improved.

How likely are you to keep working on this problem?

  • [not selected]  It is my main research area.
  • [selected]  It was a very interesting problem. I'll keep working on it.
  • [not selected]  This data is a good fit for the data mining methods I am using/developing. I will use it in the future for empirical evaluation.
  • [not selected]  Maybe I'll try some ideas , but it is not high priority.
  • [not selected]  Not likely to keep working on it.

Comments on the problem (What aspects of the problem you found most interesting? Did it inspire you to develop new techniques?)

we had experienced some problems with the pre-processing of the data

References

List references below.

No response.