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Knowledge Tracing Machines

  • Presented at the AAAI 2019 conference in Honolulu, Hawaii on January 27, 2019.
  • Applied in the Best Paper Award of the EDM 2019 conference in Montreal, Canada on July 2, 2019.

See our article: Knowledge Tracing Machines: Factorization Machines for Knowledge Tracing [pdf] [slides].
Comments are always welcome!

  Author = {{Vie}, Jill-J{\^e}nn and {Kashima}, Hisashi},
  Booktitle = {Proceedings of the 33th {AAAI} Conference on Artificial Intelligence},
  Title = {{Knowledge Tracing Machines: Factorization Machines for Knowledge Tracing}},
  Pages = {750--757},
  Url = {},
  Year = 2019}

Authors: Jill-Jênn Vie, Hisashi Kashima

Follow our tutorial

Presented at the Optimizing Human Learning workshop in Kingston, Jamaica on June 4, 2019.

Slides from the tutorial are available here. A notebook on Colab will be available "soon".

The tutorial makes you play with the models to assess weak generalization. To assess strong generalization and reproduce the experiments of the paper, you want to look at how folds are created in


python3 -m venv venv
. venv/bin/activate
pip install -r requirements.txt  # Will install numpy, scipy, pandas, scikit-learn, pywFM

If you also want to get the factorization machines running (KTM for d > 0), you should also do:

make libfm

Prepare data

Select a dataset and the features you want to include.

Case 1: There is only one skill per item.

data/<dataset>/data.csv should contain the following columns:

user, item, skill, correct, wins, fails

where wins and fails are the number of successful and unsuccessful attempts at the corresponding skill.

Case 2: There may be several skills associated to an item.

data/<dataset>/needed.csv needs to contain:

user_id, item_id, correct

(Note the difference.)

And data/<dataset>/q_mat.npz should be a q-matrix under scipy.sparse format.

If you want to compute wins and fails like in PFA or DAS3H, you should run instead of this file, with the --pfa option for PFA or --tw for DAS3H.


Available datasets

> install.packages('CDM')
> library('CDM')
> dim(
[1] 536  20
> dim(data.ecpe$data)
[1] 2922   29
> dim($data)
[1] 757  25

Encoding data into sparse features (quick start)

python --users --items  # To get the encodings (npz)
python data/dummy/X-ui.npz  # To get results (txt)

You can also download the Assistments 2009 dataset into data/assistments09 and change the dataset:

python --dataset assistments09 --skills --wins --fails  # Will encode PFA sparse features into X-swf.npz

If you are lazy, you can also just do make and try to understand what is going on in the Makefile.

Encoding time windows

Choffin et al. proposed the DAS3H model, and we implemented it using queues. This code is faster than the original KTM encoding.

To prepare a dataset like Assistments, see examples in the data folder.
Skill information should be available either as skill_id, or skill_ids separated with ~~, or in a q-matrix q_mat.npz.

python --dataset dummy_tw --tw  # Will encode DAS3H sparse features into X.npz

Then you can run or, see below.

Running a ML model

If you want to encode PFA features:

python --skills --wins --fails  # Will create X-swf.npz

For logistic regression:

python data/dummy/X-swf.npz
# Will save weights in coef0.npy

For factorization machines of size d = 5:

python --d 5 data/dummy/X-swf.npz
# Will save weights in w.npy and V.npy

The following code does not work if you don't have user_id as column in CSV file.

NEW! For an online MIRT model:

python --d 0 data/assist09/needed.csv  # Will load LR: coef0.npy
python --d 5 data/assist09/needed.csv  # Will load FM: w.npy and V.npy

# Will train a IRT model on Fraction dataset with learning rate 0.01
python --d 0 data/fraction/needed.csv --lr 0.01 --lr2 0.

NEW! For an IRT or deeper model with Keras, for batching and early stopping:

python data/assist09/needed.csv

It will also create a model.png file with the architecture (here just IRT with L2 regularization):


Weak generalization

Those numbers may change according to your random state seed.

On the Assistments 2009 dataset:

AUC time users + items skills + wins + fails items + skills + wins + fails
LR 0.734 (IRT) 2s 0.651 (PFA) 9s 0.737 23s
FM d = 20 0.730 2min9s 0.652 43s 0.739 2min30s

Computation times are given for a i7 with 2.6 GHz, with 200 epochs of FM training.

Strong generalization

On the Assistments 2009 dataset:

Model Dimension AUC Improvement
KTM: items, skills, wins, fails, extra 5 0.819
KTM: items, skills, wins, fails, extra 5 0.815 +0.05
KTM: items, skills, wins, fails 10 0.767
KTM: items, skills, wins, fails 0 0.759 +0.02
(DKT (Wilson et al., 2016)) 100 0.743 +0.05
IRT: users, items 0 0.691
PFA: skills, wins, fails 0 0.685 +0.07
AFM: skills, attempts 0 0.616

On the Duolingo French dataset:

Model Dimension AUC Improvement
KTM 20 0.822 +0.01
DeepFM 20 0.814 +0.04
Logistic regression + L2 reg 0 0.771

We also showed that Knowledge Tracing Machines (Bayesian FMs) got better results than Deep Factorization Machines on the Duolingo dataset. See our article: Deep Factorization Machines for Knowledge Tracing and poster at the BEA workshop at New Orleans, LA on June 5, 2018.

  Author = {{Vie}, Jill-J{\^e}nn},
  Booktitle = {{Proceedings of the Thirteenth Workshop on Innovative Use of NLP for Building Educational Applications}},
  Pages = {370--373},
  Title = {{Deep Factorization Machines for Knowledge Tracing}},
  Url = {},
  Year = 2018}


Knowledge Tracing Machines: Factorization Machines for Knowledge Tracing








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