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Half-Life Regression

Copyright (c) 2016 Duolingo, Inc. MIT License.

Half-life regression (HLR) is a model for spaced repetition practice, with particular applications to second language acquisition. The model marries psycholinguistic theory with modern machine learning techniques, indirectly estimating the "half-life" of words (and potentially any other item or fact) in a student's long-term memory.

This repository contains a public release of the data and code used for several experiments in the following paper (which introduces HLR):

B. Settles and B. Meeder. 2016. A Trainable Spaced Repetition Model for Language Learning. In Proceedings of the Association for Computational Linguistics (ACL), pages 1848-1858.

When using this data set and/or software, please cite this publication. A BibTeX record is:

    Author = {B. Settles and B. Meeder},
    Booktitle = {Proceedings of the Association for Computational Linguistics (ACL)},
    Pages = {1848--1858},
    Publisher = {ACL},
    Title = {A Trainable Spaced Repetition Model for Language Learning},
    Year = {2016}
    DOI = {10.18653/v1/P16-1174},
    URL = {}


The file contains a Python implementation of half-life regression, as well as several baseline spaced repetition algorithms used in Section 4.1 of the paper above. It is implemented in pure Python, and we recommend using pypy on large data sets for efficiency. The software creates the subfolder results/ for outputting model predictions on the test partition and induced model weights for inspection.

The file evaluation.r implements an R function, sr_evaluate(), which takes a prediction file from the script above and implements the three metrics we use for evaluation: mean absolute error (MAE), area under the ROC curve (AUC), and Spearman correlation for estimated half-life. Significance tests are also included.

Data Set and Format

The data set is available on Dataverse (361 MB). This is a gzipped CSV file containing the 13 million Duolingo student learning traces used in our experiments.

The columns are as follows:

  • p_recall - proportion of exercises from this lesson/practice where the word/lexeme was correctly recalled
  • timestamp - UNIX timestamp of the current lesson/practice
  • delta - time (in seconds) since the last lesson/practice that included this word/lexeme
  • user_id - student user ID who did the lesson/practice (anonymized)
  • learning_language - language being learned
  • ui_language - user interface language (presumably native to the student)
  • lexeme_id - system ID for the lexeme tag (i.e., word)
  • lexeme_string - lexeme tag (see below)
  • history_seen - total times user has seen the word/lexeme prior to this lesson/practice
  • history_correct - total times user has been correct for the word/lexeme prior to this lesson/practice
  • session_seen - times the user saw the word/lexeme during this lesson/practice
  • session_correct - times the user got the word/lexeme correct during this lesson/practice

The lexeme_string column contains a string representation of the "lexeme tag" used by Duolingo for each lesson/practice (data instance) in our experiments. It has been added for this release to facilitate future research and analysis. Only the lexeme_id column was used in our original experiments. The lexeme_string field uses the following format:


Where surface-form refers to the inflected form seen in (or intended for) the exercise, lemma is the uninflected root, pos is the high-level part of speech, and each of the modifers encodes a morphological component specific to the surface form (tense, gender, person, case, etc.). A few examples from Spanish:


Some tags contain wildcard components, written as <*...>. For example, <*sf> refers to a "generic" lexeme without any specific surface form (e.g., a lexeme tag that represents all conjugations of a verb: "run," "ran," "running," etc.). The <*numb> modifier subsumes both singular and plural forms of a noun (e.g., "teacher" and "teachers"). The file lexeme_reference.txt contains a reference of pos and modifier components used for lexeme tags.


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