---
_id: '14117'
abstract:
- lang: eng
  text: 'The two fields of machine learning and graphical causality arose and are
    developed separately. However, there is, now, cross-pollination and increasing
    interest in both fields to benefit from the advances of the other. In this article,
    we review fundamental concepts of causal inference and relate them to crucial
    open problems of machine learning, including transfer and generalization, thereby
    assaying how causality can contribute to modern machine learning research. This
    also applies in the opposite direction: we note that most work in causality starts
    from the premise that the causal variables are given. A central problem for AI
    and causality is, thus, causal representation learning, that is, the discovery
    of high-level causal variables from low-level observations. Finally, we delineate
    some implications of causality for machine learning and propose key research areas
    at the intersection of both communities.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Bernhard
  full_name: Scholkopf, Bernhard
  last_name: Scholkopf
- first_name: Francesco
  full_name: Locatello, Francesco
  id: 26cfd52f-2483-11ee-8040-88983bcc06d4
  last_name: Locatello
  orcid: 0000-0002-4850-0683
- first_name: Stefan
  full_name: Bauer, Stefan
  last_name: Bauer
- first_name: Nan Rosemary
  full_name: Ke, Nan Rosemary
  last_name: Ke
- first_name: Nal
  full_name: Kalchbrenner, Nal
  last_name: Kalchbrenner
- first_name: Anirudh
  full_name: Goyal, Anirudh
  last_name: Goyal
- first_name: Yoshua
  full_name: Bengio, Yoshua
  last_name: Bengio
citation:
  ama: Scholkopf B, Locatello F, Bauer S, et al. Toward causal representation learning.
    <i>Proceedings of the IEEE</i>. 2021;109(5):612-634. doi:<a href="https://doi.org/10.1109/jproc.2021.3058954">10.1109/jproc.2021.3058954</a>
  apa: Scholkopf, B., Locatello, F., Bauer, S., Ke, N. R., Kalchbrenner, N., Goyal,
    A., &#38; Bengio, Y. (2021). Toward causal representation learning. <i>Proceedings
    of the IEEE</i>. Institute of Electrical and Electronics Engineers. <a href="https://doi.org/10.1109/jproc.2021.3058954">https://doi.org/10.1109/jproc.2021.3058954</a>
  chicago: Scholkopf, Bernhard, Francesco Locatello, Stefan Bauer, Nan Rosemary Ke,
    Nal Kalchbrenner, Anirudh Goyal, and Yoshua Bengio. “Toward Causal Representation
    Learning.” <i>Proceedings of the IEEE</i>. Institute of Electrical and Electronics
    Engineers, 2021. <a href="https://doi.org/10.1109/jproc.2021.3058954">https://doi.org/10.1109/jproc.2021.3058954</a>.
  ieee: B. Scholkopf <i>et al.</i>, “Toward causal representation learning,” <i>Proceedings
    of the IEEE</i>, vol. 109, no. 5. Institute of Electrical and Electronics Engineers,
    pp. 612–634, 2021.
  ista: Scholkopf B, Locatello F, Bauer S, Ke NR, Kalchbrenner N, Goyal A, Bengio
    Y. 2021. Toward causal representation learning. Proceedings of the IEEE. 109(5),
    612–634.
  mla: Scholkopf, Bernhard, et al. “Toward Causal Representation Learning.” <i>Proceedings
    of the IEEE</i>, vol. 109, no. 5, Institute of Electrical and Electronics Engineers,
    2021, pp. 612–34, doi:<a href="https://doi.org/10.1109/jproc.2021.3058954">10.1109/jproc.2021.3058954</a>.
  short: B. Scholkopf, F. Locatello, S. Bauer, N.R. Ke, N. Kalchbrenner, A. Goyal,
    Y. Bengio, Proceedings of the IEEE 109 (2021) 612–634.
date_created: 2023-08-21T12:19:30Z
date_published: 2021-05-01T00:00:00Z
date_updated: 2023-09-11T11:43:35Z
day: '01'
department:
- _id: FrLo
doi: 10.1109/jproc.2021.3058954
extern: '1'
external_id:
  arxiv:
  - '2102.11107'
intvolume: '       109'
issue: '5'
keyword:
- Electrical and Electronic Engineering
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1109/JPROC.2021.3058954
month: '05'
oa: 1
oa_version: Published Version
page: 612-634
publication: Proceedings of the IEEE
publication_identifier:
  eissn:
  - 1558-2256
  issn:
  - 0018-9219
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Toward causal representation learning
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 109
year: '2021'
...
---
_id: '4598'
abstract:
- lang: eng
  text: A hybrid system is a dynamical system with both discrete and continuous state
    changes. For analysis purposes, it is often useful to abstract a system in a way
    that preserves the properties being analyzed while hiding the details that are
    of no interest. We show that interesting classes of hybrid systems can be abstracted
    to purely discrete systems while preserving all properties that are definable
    in temporal logic. The classes that permit discrete abstractions fall into two
    categories. Either the continuous dynamics must be restricted, as is the case
    for timed and rectangular hybrid systems, or the discrete dynamics must be restricted,
    as is the case for o-minimal hybrid systems. In this paper, we survey and unify
    results from both areas.
acknowledgement: The authors would like to thank the reviewers for their detailed
  comments.
article_processing_charge: No
article_type: original
author:
- first_name: Rajeev
  full_name: Alur, Rajeev
  last_name: Alur
- first_name: Thomas A
  full_name: Henzinger, Thomas A
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000−0002−2985−7724
- first_name: Gerardo
  full_name: Lafferriere, Gerardo
  last_name: Lafferriere
- first_name: George
  full_name: Pappas, George
  last_name: Pappas
citation:
  ama: Alur R, Henzinger TA, Lafferriere G, Pappas G. Discrete abstractions of hybrid
    systems. <i>Proceedings of the IEEE</i>. 2000;88(7):971-984. doi:<a href="https://doi.org/10.1109/5.871304
    ">10.1109/5.871304 </a>
  apa: Alur, R., Henzinger, T. A., Lafferriere, G., &#38; Pappas, G. (2000). Discrete
    abstractions of hybrid systems. <i>Proceedings of the IEEE</i>. IEEE. <a href="https://doi.org/10.1109/5.871304
    ">https://doi.org/10.1109/5.871304 </a>
  chicago: Alur, Rajeev, Thomas A Henzinger, Gerardo Lafferriere, and George Pappas.
    “Discrete Abstractions of Hybrid Systems.” <i>Proceedings of the IEEE</i>. IEEE,
    2000. <a href="https://doi.org/10.1109/5.871304 ">https://doi.org/10.1109/5.871304
    </a>.
  ieee: R. Alur, T. A. Henzinger, G. Lafferriere, and G. Pappas, “Discrete abstractions
    of hybrid systems,” <i>Proceedings of the IEEE</i>, vol. 88, no. 7. IEEE, pp.
    971–984, 2000.
  ista: Alur R, Henzinger TA, Lafferriere G, Pappas G. 2000. Discrete abstractions
    of hybrid systems. Proceedings of the IEEE. 88(7), 971–984.
  mla: Alur, Rajeev, et al. “Discrete Abstractions of Hybrid Systems.” <i>Proceedings
    of the IEEE</i>, vol. 88, no. 7, IEEE, 2000, pp. 971–84, doi:<a href="https://doi.org/10.1109/5.871304
    ">10.1109/5.871304 </a>.
  short: R. Alur, T.A. Henzinger, G. Lafferriere, G. Pappas, Proceedings of the IEEE
    88 (2000) 971–984.
date_created: 2018-12-11T12:09:41Z
date_published: 2000-07-01T00:00:00Z
date_updated: 2023-04-13T13:32:11Z
day: '01'
doi: '10.1109/5.871304 '
extern: '1'
intvolume: '        88'
issue: '7'
language:
- iso: eng
month: '07'
oa_version: None
page: 971 - 984
publication: Proceedings of the IEEE
publication_identifier:
  issn:
  - 0018-9219
publication_status: published
publisher: IEEE
publist_id: '107'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete abstractions of hybrid systems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 88
year: '2000'
...