---
OA_place: repository
OA_type: green
_id: '20081'
abstract:
- lang: eng
  text: 'Information measures can be constructed from Rényi divergences much like
    mutual information from Kullback-Leibler divergence. One such information measure
    is known as Sibson α-mutual information and has received renewed attention recently
    in several contexts: concentration of measure under dependence, statistical learning,
    hypothesis testing, and estimation theory. In this paper, we survey and extend
    the state of the art. In particular, we introduce variational representations
    for Sibson α-mutual information and employ them in each described context to derive
    novel results. Namely, we produce generalized Transportation-Cost inequalities
    and Fano-type inequalities. We also present an overview of known applications,
    spanning from learning theory and Bayesian risk to universal prediction.'
acknowledgement: "This work was supported by the Swiss National Science Foundation
  under\r\nGrant 200364. An earlier version of this paper was presented in part at\r\nthe
  2024 IEEE International Symposium on Information Theory, Athens,\r\nGreece [DOI:
  10.1109/ISIT57864.2024.10619378]. (Corresponding author:\r\nAmedeo Roberto Esposito.)"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Amedeo Roberto
  full_name: Esposito, Amedeo Roberto
  id: 9583e921-e1ad-11ec-9862-cef099626dc9
  last_name: Esposito
- first_name: Michael
  full_name: Gastpar, Michael
  last_name: Gastpar
- first_name: Ibrahim
  full_name: Issa, Ibrahim
  last_name: Issa
citation:
  ama: Esposito AR, Gastpar M, Issa I. Sibson α-mutual information and its variational
    representations. <i>IEEE Transactions on Information Theory</i>. 2026;72(7):4434-4467.
    doi:<a href="https://doi.org/10.1109/TIT.2025.3587340">10.1109/TIT.2025.3587340</a>
  apa: Esposito, A. R., Gastpar, M., &#38; Issa, I. (2026). Sibson α-mutual information
    and its variational representations. <i>IEEE Transactions on Information Theory</i>.
    IEEE. <a href="https://doi.org/10.1109/TIT.2025.3587340">https://doi.org/10.1109/TIT.2025.3587340</a>
  chicago: Esposito, Amedeo Roberto, Michael Gastpar, and Ibrahim Issa. “Sibson α-Mutual
    Information and Its Variational Representations.” <i>IEEE Transactions on Information
    Theory</i>. IEEE, 2026. <a href="https://doi.org/10.1109/TIT.2025.3587340">https://doi.org/10.1109/TIT.2025.3587340</a>.
  ieee: A. R. Esposito, M. Gastpar, and I. Issa, “Sibson α-mutual information and
    its variational representations,” <i>IEEE Transactions on Information Theory</i>,
    vol. 72, no. 7. IEEE, pp. 4434–4467, 2026.
  ista: Esposito AR, Gastpar M, Issa I. 2026. Sibson α-mutual information and its
    variational representations. IEEE Transactions on Information Theory. 72(7), 4434–4467.
  mla: Esposito, Amedeo Roberto, et al. “Sibson α-Mutual Information and Its Variational
    Representations.” <i>IEEE Transactions on Information Theory</i>, vol. 72, no.
    7, IEEE, 2026, pp. 4434–67, doi:<a href="https://doi.org/10.1109/TIT.2025.3587340">10.1109/TIT.2025.3587340</a>.
  short: A.R. Esposito, M. Gastpar, I. Issa, IEEE Transactions on Information Theory
    72 (2026) 4434–4467.
das_tickbox: '0'
date_created: 2025-07-27T22:01:26Z
date_published: 2026-07-01T00:00:00Z
date_updated: 2026-07-23T11:38:30Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TIT.2025.3587340
external_id:
  arxiv:
  - '2405.08352'
intvolume: '        72'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2405.08352
month: '07'
oa: 1
oa_version: Preprint
page: 4434-4467
publication: IEEE Transactions on Information Theory
publication_identifier:
  eissn:
  - 1557-9654
  issn:
  - 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Sibson α-mutual information and its variational representations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 72
year: '2026'
...
---
_id: '15172'
abstract:
- lang: eng
  text: 'We propose a novel approach to concentration for non-independent random variables.
    The main idea is to “pretend” that the random variables are independent and pay
    a multiplicative price measuring how far they are from actually being independent.
    This price is encapsulated in the Hellinger integral between the joint and the
    product of the marginals, which is then upper bounded leveraging tensorisation
    properties. Our bounds represent a natural generalisation of concentration inequalities
    in the presence of dependence: we recover exactly the classical bounds (McDiarmid’s
    inequality) when the random variables are independent. Furthermore, in a “large
    deviations” regime, we obtain the same decay in the probability as for the independent
    case, even when the random variables display non-trivial dependencies. To show
    this, we consider a number of applications of interest. First, we provide a bound
    for Markov chains with finite state space. Then, we consider the Simple Symmetric
    Random Walk, which is a non-contracting Markov chain, and a non-Markovian setting
    in which the stochastic process depends on its entire past. To conclude, we propose
    an application to Markov Chain Monte Carlo methods, where our approach leads to
    an improved lower bound on the minimum burn-in period required to reach a certain
    accuracy. In all of these settings, we provide a regime of parameters in which
    our bound fares better than what the state of the art can provide.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Amedeo Roberto
  full_name: Esposito, Amedeo Roberto
  id: 9583e921-e1ad-11ec-9862-cef099626dc9
  last_name: Esposito
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
citation:
  ama: Esposito AR, Mondelli M. Concentration without independence via information
    measures. <i>IEEE Transactions on Information Theory</i>. 2024;70(6):3823-3839.
    doi:<a href="https://doi.org/10.1109/TIT.2024.3367767">10.1109/TIT.2024.3367767</a>
  apa: Esposito, A. R., &#38; Mondelli, M. (2024). Concentration without independence
    via information measures. <i>IEEE Transactions on Information Theory</i>. IEEE.
    <a href="https://doi.org/10.1109/TIT.2024.3367767">https://doi.org/10.1109/TIT.2024.3367767</a>
  chicago: Esposito, Amedeo Roberto, and Marco Mondelli. “Concentration without Independence
    via Information Measures.” <i>IEEE Transactions on Information Theory</i>. IEEE,
    2024. <a href="https://doi.org/10.1109/TIT.2024.3367767">https://doi.org/10.1109/TIT.2024.3367767</a>.
  ieee: A. R. Esposito and M. Mondelli, “Concentration without independence via information
    measures,” <i>IEEE Transactions on Information Theory</i>, vol. 70, no. 6. IEEE,
    pp. 3823–3839, 2024.
  ista: Esposito AR, Mondelli M. 2024. Concentration without independence via information
    measures. IEEE Transactions on Information Theory. 70(6), 3823–3839.
  mla: Esposito, Amedeo Roberto, and Marco Mondelli. “Concentration without Independence
    via Information Measures.” <i>IEEE Transactions on Information Theory</i>, vol.
    70, no. 6, IEEE, 2024, pp. 3823–39, doi:<a href="https://doi.org/10.1109/TIT.2024.3367767">10.1109/TIT.2024.3367767</a>.
  short: A.R. Esposito, M. Mondelli, IEEE Transactions on Information Theory 70 (2024)
    3823–3839.
corr_author: '1'
date_created: 2024-03-24T23:01:00Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2025-09-04T13:06:53Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/TIT.2024.3367767
external_id:
  arxiv:
  - '2303.07245'
  isi:
  - '001230181100001'
intvolume: '        70'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2303.07245
month: '06'
oa: 1
oa_version: Preprint
page: 3823-3839
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: IEEE Transactions on Information Theory
publication_identifier:
  eissn:
  - 1557-9654
  issn:
  - 0018-9448
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
  record:
  - id: '14922'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: Concentration without independence via information measures
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 70
year: '2024'
...
---
_id: '17893'
abstract:
- lang: eng
  text: Strong data processing inequalities (SDPI) are an important object of study
    in Information Theory and have been well studied for f -divergences. Universal
    upper and lower bounds have been provided along with several applications, connecting
    them to impossibility (converse) results, concentration of measure, hypercontractivity,
    and so on. In this paper, we study Renyi divergence and the corresponding SDPI
    constant whose behavior seems to deviate from that of ordinary <1>-divergences.
    In particular, one can find examples showing that the universal upper bound relating
    its SDPI constant to the one of Total Variation does not hold in general. In this
    work, we prove, however, that the universal lower bound involving the SDPI constant
    of the Chi-square divergence does indeed hold. Furthermore, we also provide a
    characterization of the distribution that achieves the supremum when is equal
    to 2 and consequently compute the SDPI constant for Renyi divergence of the general
    binary channel.
acknowledgement: "The work in this paper was supported in part by the Swiss National
  Science Foundation under Grant 200364.\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Lifu
  full_name: Jin, Lifu
  last_name: Jin
- first_name: Amedeo Roberto
  full_name: Esposito, Amedeo Roberto
  id: 9583e921-e1ad-11ec-9862-cef099626dc9
  last_name: Esposito
- first_name: Michael
  full_name: Gastpar, Michael
  last_name: Gastpar
citation:
  ama: 'Jin L, Esposito AR, Gastpar M. Properties of the strong data processing constant
    for Rényi divergence. In: <i>Proceedings of the 2024 IEEE International Symposium
    on Information Theory</i>. IEEE; 2024:3178-3183. doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619367">10.1109/ISIT57864.2024.10619367</a>'
  apa: 'Jin, L., Esposito, A. R., &#38; Gastpar, M. (2024). Properties of the strong
    data processing constant for Rényi divergence. In <i>Proceedings of the 2024 IEEE
    International Symposium on Information Theory</i> (pp. 3178–3183). Athens, Greece:
    IEEE. <a href="https://doi.org/10.1109/ISIT57864.2024.10619367">https://doi.org/10.1109/ISIT57864.2024.10619367</a>'
  chicago: Jin, Lifu, Amedeo Roberto Esposito, and Michael Gastpar. “Properties of
    the Strong Data Processing Constant for Rényi Divergence.” In <i>Proceedings of
    the 2024 IEEE International Symposium on Information Theory</i>, 3178–83. IEEE,
    2024. <a href="https://doi.org/10.1109/ISIT57864.2024.10619367">https://doi.org/10.1109/ISIT57864.2024.10619367</a>.
  ieee: L. Jin, A. R. Esposito, and M. Gastpar, “Properties of the strong data processing
    constant for Rényi divergence,” in <i>Proceedings of the 2024 IEEE International
    Symposium on Information Theory</i>, Athens, Greece, 2024, pp. 3178–3183.
  ista: 'Jin L, Esposito AR, Gastpar M. 2024. Properties of the strong data processing
    constant for Rényi divergence. Proceedings of the 2024 IEEE International Symposium
    on Information Theory. ISIT: International Symposium on Information Theory, 3178–3183.'
  mla: Jin, Lifu, et al. “Properties of the Strong Data Processing Constant for Rényi
    Divergence.” <i>Proceedings of the 2024 IEEE International Symposium on Information
    Theory</i>, IEEE, 2024, pp. 3178–83, doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619367">10.1109/ISIT57864.2024.10619367</a>.
  short: L. Jin, A.R. Esposito, M. Gastpar, in:, Proceedings of the 2024 IEEE International
    Symposium on Information Theory, IEEE, 2024, pp. 3178–3183.
conference:
  end_date: 2024-07-12
  location: Athens, Greece
  name: 'ISIT: International Symposium on Information Theory'
  start_date: 2024-07-07
corr_author: '1'
date_created: 2024-09-08T22:01:12Z
date_published: 2024-08-19T00:00:00Z
date_updated: 2026-08-12T06:38:02Z
day: '19'
department:
- _id: MaMo
doi: 10.1109/ISIT57864.2024.10619367
external_id:
  arxiv:
  - '2403.10656'
  isi:
  - '001304426903055'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: 'https://doi.org/10.48550/arXiv.2403.10656 '
month: '08'
oa: 1
oa_version: Preprint
page: 3178-3183
publication: Proceedings of the 2024 IEEE International Symposium on Information Theory
publication_identifier:
  isbn:
  - '9798350382846'
  issn:
  - 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Properties of the strong data processing constant for Rényi divergence
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '17894'
abstract:
- lang: eng
  text: 'Sibson''s α -mutual information has received renewed attention recently in
    several contexts: concentration of measure under dependence, statistical learning,
    hypothesis testing, and estimation theory. In this work, we introduce several
    variational representations of Sibson''s α -mutual information: 1) as a supremum
    over joint distributions of (a combination of) KL divergences; and 2) as a supremum
    over functions of opportune expected values. Leveraging them, we produce a variety
    of novel and known results, including a generalization of transportation-cost
    inequalities and Fano''s inequality.'
acknowledgement: The work in this paper was supported in part by the Swiss National
  Science Foundation under Grant 200364.
article_processing_charge: No
author:
- first_name: Amedeo Roberto
  full_name: Esposito, Amedeo Roberto
  id: 9583e921-e1ad-11ec-9862-cef099626dc9
  last_name: Esposito
- first_name: Michael
  full_name: Gastpar, Michael
  last_name: Gastpar
- first_name: Ibrahim
  full_name: Issa, Ibrahim
  last_name: Issa
citation:
  ama: 'Esposito AR, Gastpar M, Issa I. Variational characterizations of Sibson’s
    α-mutual information. In: <i>Proceedings of the 2024 IEEE International Symposium
    on Information Theory </i>. IEEE; 2024:2110-2115. doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619378">10.1109/ISIT57864.2024.10619378</a>'
  apa: 'Esposito, A. R., Gastpar, M., &#38; Issa, I. (2024). Variational characterizations
    of Sibson’s α-mutual information. In <i>Proceedings of the 2024 IEEE International
    Symposium on Information Theory </i> (pp. 2110–2115). Athens, Greece: IEEE. <a
    href="https://doi.org/10.1109/ISIT57864.2024.10619378">https://doi.org/10.1109/ISIT57864.2024.10619378</a>'
  chicago: Esposito, Amedeo Roberto, Michael Gastpar, and Ibrahim Issa. “Variational
    Characterizations of Sibson’s α-Mutual Information.” In <i>Proceedings of the
    2024 IEEE International Symposium on Information Theory </i>, 2110–15. IEEE, 2024.
    <a href="https://doi.org/10.1109/ISIT57864.2024.10619378">https://doi.org/10.1109/ISIT57864.2024.10619378</a>.
  ieee: A. R. Esposito, M. Gastpar, and I. Issa, “Variational characterizations of
    Sibson’s α-mutual information,” in <i>Proceedings of the 2024 IEEE International
    Symposium on Information Theory </i>, Athens, Greece, 2024, pp. 2110–2115.
  ista: 'Esposito AR, Gastpar M, Issa I. 2024. Variational characterizations of Sibson’s
    α-mutual information. Proceedings of the 2024 IEEE International Symposium on
    Information Theory . ISIT: International Symposium on Information Theory, 2110–2115.'
  mla: Esposito, Amedeo Roberto, et al. “Variational Characterizations of Sibson’s
    α-Mutual Information.” <i>Proceedings of the 2024 IEEE International Symposium
    on Information Theory </i>, IEEE, 2024, pp. 2110–15, doi:<a href="https://doi.org/10.1109/ISIT57864.2024.10619378">10.1109/ISIT57864.2024.10619378</a>.
  short: A.R. Esposito, M. Gastpar, I. Issa, in:, Proceedings of the 2024 IEEE International
    Symposium on Information Theory , IEEE, 2024, pp. 2110–2115.
conference:
  end_date: 2024-07-12
  location: Athens, Greece
  name: 'ISIT: International Symposium on Information Theory'
  start_date: 2024-07-07
corr_author: '1'
date_created: 2024-09-08T22:01:12Z
date_published: 2024-08-19T00:00:00Z
date_updated: 2026-08-12T06:38:18Z
day: '19'
department:
- _id: MaMo
doi: 10.1109/ISIT57864.2024.10619378
external_id:
  isi:
  - '001304426902023'
isi: 1
language:
- iso: eng
month: '08'
oa_version: None
page: 2110-2115
publication: 'Proceedings of the 2024 IEEE International Symposium on Information
  Theory '
publication_identifier:
  isbn:
  - '9798350382846'
  issn:
  - 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Variational characterizations of Sibson's α-mutual information
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '14922'
abstract:
- lang: eng
  text: 'We propose a novel approach to concentration for non-independent random variables.
    The main idea is to ``pretend'''' that the random variables are independent and
    pay a multiplicative price measuring how far they are from actually being independent.
    This price is encapsulated in the Hellinger integral between the joint and the
    product of the marginals, which is then upper bounded leveraging tensorisation
    properties. Our bounds represent a natural generalisation of concentration inequalities
    in the presence of dependence: we recover exactly the classical bounds (McDiarmid''s
    inequality) when the random variables are independent. Furthermore, in a ``large
    deviations'''' regime, we obtain the same decay in the probability as for the
    independent case, even when the random variables display non-trivial dependencies.
    To show this, we consider a number of applications of interest. First, we provide
    a bound for Markov chains with finite state space. Then, we consider the Simple
    Symmetric Random Walk, which is a non-contracting Markov chain, and a non-Markovian
    setting in which the stochastic process depends on its entire past. To conclude,
    we propose an application to Markov Chain Monte Carlo methods, where our approach
    leads to an improved lower bound on the minimum burn-in period required to reach
    a certain accuracy. In all of these settings, we provide a regime of parameters
    in which our bound fares better than what the state of the art can provide.'
acknowledgement: The authors are partially supported by the 2019 Lopez-Loreta Prize.
  They would also like to thank Professor Jan Maas for providing valuable suggestions
  and comments on an early version of the work.
article_processing_charge: No
arxiv: 1
author:
- first_name: Amedeo Roberto
  full_name: Esposito, Amedeo Roberto
  id: 9583e921-e1ad-11ec-9862-cef099626dc9
  last_name: Esposito
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
citation:
  ama: 'Esposito AR, Mondelli M. Concentration without independence via information
    measures. In: <i>Proceedings of 2023 IEEE International Symposium on Information
    Theory</i>. IEEE; 2023:400-405. doi:<a href="https://doi.org/10.1109/isit54713.2023.10206899">10.1109/isit54713.2023.10206899</a>'
  apa: 'Esposito, A. R., &#38; Mondelli, M. (2023). Concentration without independence
    via information measures. In <i>Proceedings of 2023 IEEE International Symposium
    on Information Theory</i> (pp. 400–405). Taipei, Taiwan: IEEE. <a href="https://doi.org/10.1109/isit54713.2023.10206899">https://doi.org/10.1109/isit54713.2023.10206899</a>'
  chicago: Esposito, Amedeo Roberto, and Marco Mondelli. “Concentration without Independence
    via Information Measures.” In <i>Proceedings of 2023 IEEE International Symposium
    on Information Theory</i>, 400–405. IEEE, 2023. <a href="https://doi.org/10.1109/isit54713.2023.10206899">https://doi.org/10.1109/isit54713.2023.10206899</a>.
  ieee: A. R. Esposito and M. Mondelli, “Concentration without independence via information
    measures,” in <i>Proceedings of 2023 IEEE International Symposium on Information
    Theory</i>, Taipei, Taiwan, 2023, pp. 400–405.
  ista: 'Esposito AR, Mondelli M. 2023. Concentration without independence via information
    measures. Proceedings of 2023 IEEE International Symposium on Information Theory.
    ISIT: International Symposium on Information Theory, 400–405.'
  mla: Esposito, Amedeo Roberto, and Marco Mondelli. “Concentration without Independence
    via Information Measures.” <i>Proceedings of 2023 IEEE International Symposium
    on Information Theory</i>, IEEE, 2023, pp. 400–05, doi:<a href="https://doi.org/10.1109/isit54713.2023.10206899">10.1109/isit54713.2023.10206899</a>.
  short: A.R. Esposito, M. Mondelli, in:, Proceedings of 2023 IEEE International Symposium
    on Information Theory, IEEE, 2023, pp. 400–405.
conference:
  end_date: 2023-06-30
  location: Taipei, Taiwan
  name: 'ISIT: International Symposium on Information Theory'
  start_date: 2023-06-25
corr_author: '1'
date_created: 2024-02-02T11:18:40Z
date_published: 2023-06-30T00:00:00Z
date_updated: 2025-09-04T13:06:52Z
day: '30'
department:
- _id: MaMo
doi: 10.1109/isit54713.2023.10206899
external_id:
  arxiv:
  - '2303.07245'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2303.07245
month: '06'
oa: 1
oa_version: Preprint
page: 400-405
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Proceedings of 2023 IEEE International Symposium on Information Theory
publication_identifier:
  eisbn:
  - '9781665475549'
  eissn:
  - 2157-8117
publication_status: published
publisher: IEEE
quality_controlled: '1'
related_material:
  record:
  - id: '15172'
    relation: later_version
    status: public
scopus_import: '1'
status: public
title: Concentration without independence via information measures
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...