Pub Date : 2022-10-01DOI: 10.1109/MBITS.2022.3205288
Haizi Yu, L. Varshney, Heinrich Taube, James A. Evans
Information lattice learning (ILL) is a novel framework for knowledge discovery based on group-theoretic and information-theoretic foundations, which can rediscover the rules of music as known in the canon of music theory and also discover new rules that have remained unexamined. Such probabilistic rules are further demonstrated to be human-interpretable. ILL itself is a rediscovery and generalization of Shannon’s lattice theory of information, where probability measures are not given but are learned from training data. This article explains the basics of the ILL framework, including both how to construct a lattice-structured abstraction universe that specifies the structural possibilities of rules, and how to find the most informative rules by performing statistical learning through an iterative student–teacher algorithmic architecture that optimizes information functionals. The ILL framework is finally shown to support both pedagogy and novel patterns of music co-creativity.
{"title":"(Re)discovering Laws of Music Theory Using Information Lattice Learning","authors":"Haizi Yu, L. Varshney, Heinrich Taube, James A. Evans","doi":"10.1109/MBITS.2022.3205288","DOIUrl":"https://doi.org/10.1109/MBITS.2022.3205288","url":null,"abstract":"Information lattice learning (ILL) is a novel framework for knowledge discovery based on group-theoretic and information-theoretic foundations, which can rediscover the rules of music as known in the canon of music theory and also discover new rules that have remained unexamined. Such probabilistic rules are further demonstrated to be human-interpretable. ILL itself is a rediscovery and generalization of Shannon’s lattice theory of information, where probability measures are not given but are learned from training data. This article explains the basics of the ILL framework, including both how to construct a lattice-structured abstraction universe that specifies the structural possibilities of rules, and how to find the most informative rules by performing statistical learning through an iterative student–teacher algorithmic architecture that optimizes information functionals. The ILL framework is finally shown to support both pedagogy and novel patterns of music co-creativity.","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116411540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1109/mbits.2022.3217879
{"title":"IEEE BITS Editorial Board","authors":"","doi":"10.1109/mbits.2022.3217879","DOIUrl":"https://doi.org/10.1109/mbits.2022.3217879","url":null,"abstract":"","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132351817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-06DOI: 10.1109/MBITS.2022.3205143
J. Calder, Reed Coil, J. A. Melton, P. Olver, G. Tostevin, K. Yezzi-Woodley
Machine learning (ML), being now widely accessible to the research community at large, has fostered a proliferation of new and striking applications of these emergent mathematical techniques across a wide range of disciplines. In this article, we will focus on a particular case study: the field of paleoanthropology, which seeks to understand the evolution of the human species based on biological (e.g., bones, genetics) and cultural (e.g., stone tools) evidence. As we will show, the easy availability of ML algorithms and lack of expertise on their proper use among the anthropological research community has led to the foundational misapplications that have appeared throughout the literature. The resulting unreliable results not only undermine efforts to legitimately incorporate ML into anthropological research, but produce potentially faulty understandings about our human evolutionary and behavioral past. The aim of this article is to provide a brief introduction to some of the ways in which ML has been applied within paleoanthropology; we also include a survey of some basic ML algorithms for those who are not fully conversant with the field, which remains under active development. We discuss a series of missteps, errors, and violations of correct protocols of ML methods that appear disconcertingly often within the accumulating body of anthropological literature. These mistakes include the use of outdated algorithms and practices; inappropriate testing/training splits, sample composition, and textual explanations; as well as an absence of transparency due to the lack of data/code sharing, and the subsequent limitations imposed on independent replication. We assert that expanding samples, sharing data and code, re-evaluating approaches to peer review, and, most importantly, developing interdisciplinary teams that include experts in ML are all necessary for the progress in future research incorporating ML within anthropology and beyond.
{"title":"Use and Misuse of Machine Learning in Anthropology","authors":"J. Calder, Reed Coil, J. A. Melton, P. Olver, G. Tostevin, K. Yezzi-Woodley","doi":"10.1109/MBITS.2022.3205143","DOIUrl":"https://doi.org/10.1109/MBITS.2022.3205143","url":null,"abstract":"Machine learning (ML), being now widely accessible to the research community at large, has fostered a proliferation of new and striking applications of these emergent mathematical techniques across a wide range of disciplines. In this article, we will focus on a particular case study: the field of paleoanthropology, which seeks to understand the evolution of the human species based on biological (e.g., bones, genetics) and cultural (e.g., stone tools) evidence. As we will show, the easy availability of ML algorithms and lack of expertise on their proper use among the anthropological research community has led to the foundational misapplications that have appeared throughout the literature. The resulting unreliable results not only undermine efforts to legitimately incorporate ML into anthropological research, but produce potentially faulty understandings about our human evolutionary and behavioral past. The aim of this article is to provide a brief introduction to some of the ways in which ML has been applied within paleoanthropology; we also include a survey of some basic ML algorithms for those who are not fully conversant with the field, which remains under active development. We discuss a series of missteps, errors, and violations of correct protocols of ML methods that appear disconcertingly often within the accumulating body of anthropological literature. These mistakes include the use of outdated algorithms and practices; inappropriate testing/training splits, sample composition, and textual explanations; as well as an absence of transparency due to the lack of data/code sharing, and the subsequent limitations imposed on independent replication. We assert that expanding samples, sharing data and code, re-evaluating approaches to peer review, and, most importantly, developing interdisciplinary teams that include experts in ML are all necessary for the progress in future research incorporating ML within anthropology and beyond.","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"229 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131832253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-25DOI: 10.1109/MBITS.2023.3262219
E. Dallas, Faidon Andreadakis, Daniel A. Lidar
It is well-known that nondegenerate quantum error correcting codes (QECCs) are constrained by a quantum version of the Hamming bound. Whether degenerate codes also obey such a bound, however, remains a long-standing question with practical implications for the efficacy of QECCs. We employ a combination of previously derived bounds on QECCs to demonstrate that a subset of all codes must obey the quantum Hamming bound. Specifically, we combine an analytical bound due to Rains with a numerical bound due to Li and Xing to show that no $((n,K,d))$((n,K,d)) code with $d< 127$d<127 can violate the quantum Hamming bound.
{"title":"No $((n,K,d< 127))$ Code Can Violate the Quantum Hamming Bound","authors":"E. Dallas, Faidon Andreadakis, Daniel A. Lidar","doi":"10.1109/MBITS.2023.3262219","DOIUrl":"https://doi.org/10.1109/MBITS.2023.3262219","url":null,"abstract":"It is well-known that nondegenerate quantum error correcting codes (QECCs) are constrained by a quantum version of the Hamming bound. Whether degenerate codes also obey such a bound, however, remains a long-standing question with practical implications for the efficacy of QECCs. We employ a combination of previously derived bounds on QECCs to demonstrate that a subset of all codes must obey the quantum Hamming bound. Specifically, we combine an analytical bound due to Rains with a numerical bound due to Li and Xing to show that no $((n,K,d))$((n,K,d)) code with $d< 127$d<127 can violate the quantum Hamming bound.","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121933733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-13DOI: 10.1109/MBITS.2023.3246025
Benjamin J. Brown
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the leading efforts to demonstrate scalable quantum computing. Central to our discussion is the minimum-weight perfect-matching decoder. The decoder works by exploiting underlying structure that arises due to materialized symmetries among surface-code stabilizer elements. By concentrating on these symmetries, we begin to address the question of how a minimum-weight perfect-matching decoder might be generalized for other families of codes. We approach this question first by investigating examples of matching decoders for other codes. These include decoding algorithms that have been specialized to correct for noise models that demonstrate a particular structure or bias with respect to certain codes. In addition to this, we propose a systematic way of constructing a minimum-weight perfect-matching decoder for codes with certain characteristic properties. The properties we make use of are common among topological codes. We discuss the broader applicability of the proposal, and we suggest some questions we can address that may show us how to design a generalized matching decoder for arbitrary stabilizer codes.
{"title":"Conservation Laws and Quantum Error Correction: Toward a Generalized Matching Decoder","authors":"Benjamin J. Brown","doi":"10.1109/MBITS.2023.3246025","DOIUrl":"https://doi.org/10.1109/MBITS.2023.3246025","url":null,"abstract":"Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the leading efforts to demonstrate scalable quantum computing. Central to our discussion is the minimum-weight perfect-matching decoder. The decoder works by exploiting underlying structure that arises due to materialized symmetries among surface-code stabilizer elements. By concentrating on these symmetries, we begin to address the question of how a minimum-weight perfect-matching decoder might be generalized for other families of codes. We approach this question first by investigating examples of matching decoders for other codes. These include decoding algorithms that have been specialized to correct for noise models that demonstrate a particular structure or bias with respect to certain codes. In addition to this, we propose a systematic way of constructing a minimum-weight perfect-matching decoder for codes with certain characteristic properties. The properties we make use of are common among topological codes. We discuss the broader applicability of the proposal, and we suggest some questions we can address that may show us how to design a generalized matching decoder for arbitrary stabilizer codes.","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125107323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-01DOI: 10.1109/mbits.2021.3134881
R. Calderbank
{"title":"Welcome to the First Issue of IEEE BITS","authors":"R. Calderbank","doi":"10.1109/mbits.2021.3134881","DOIUrl":"https://doi.org/10.1109/mbits.2021.3134881","url":null,"abstract":"","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125832123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-01DOI: 10.1109/mbits.2021.3132470
M. Medard
{"title":"Friends in Comment—A Conversation With Regina Barzilay","authors":"M. Medard","doi":"10.1109/mbits.2021.3132470","DOIUrl":"https://doi.org/10.1109/mbits.2021.3132470","url":null,"abstract":"","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130534365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-01DOI: 10.1109/mbits.2021.3129565
Martina Cardon
{"title":"The Virtual Year: Perspectives of JKW Best Paper Awardees","authors":"Martina Cardon","doi":"10.1109/mbits.2021.3129565","DOIUrl":"https://doi.org/10.1109/mbits.2021.3129565","url":null,"abstract":"","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127394282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-01DOI: 10.1109/mbits.2021.3134450
P. Regalia
{"title":"Information Theory at the U.S. National Science Foundation","authors":"P. Regalia","doi":"10.1109/mbits.2021.3134450","DOIUrl":"https://doi.org/10.1109/mbits.2021.3134450","url":null,"abstract":"","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"160 9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129024850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-01DOI: 10.1109/mbits.2021.3097878
R. Gallager
One of Claude Shannon’s best remembered “toys” was his maze-solving machine, created by partitions on a rectangular grid. A mechanical mouse was started at one point in the maze with the task of finding cheese at another point. Relays under the board guided successive moves, each of which were taken in the first open counterclockwise direction from the previous move. In belated honor of Shannon’s centenary and of amnesia in the mouse at age 70, we compare this deterministic search strategy with a random search requiring no memory. For simplicity, the rectangular grid with partitions is replaced by a finite connected graph. A maze is then a graph with some given destination node. The worst case required number of steps to find the cheese for deterministic searches and the expected number for random searches are remarkably similar, each being, for example, $|mathcal {E}^2|$|E2| taken over all graphs of $|mathcal {E}|$|E| edges. Finally, we demonstrate a simple improvement to the above algorithms that generates an Eulerian cycle on the directed edges of $G$G, i.e., a walk on $G$G of $2|mathcal {E}|$2|E| steps that traverses each edge in $G$G exactly once in each direction before returning to the starting point.
{"title":"Shannon, Euler, and Mazes","authors":"R. Gallager","doi":"10.1109/mbits.2021.3097878","DOIUrl":"https://doi.org/10.1109/mbits.2021.3097878","url":null,"abstract":"One of Claude Shannon’s best remembered “toys” was his maze-solving machine, created by partitions on a rectangular grid. A mechanical mouse was started at one point in the maze with the task of finding cheese at another point. Relays under the board guided successive moves, each of which were taken in the first open counterclockwise direction from the previous move. In belated honor of Shannon’s centenary and of amnesia in the mouse at age 70, we compare this deterministic search strategy with a random search requiring no memory. For simplicity, the rectangular grid with partitions is replaced by a finite connected graph. A maze is then a graph with some given destination node. The worst case required number of steps to find the cheese for deterministic searches and the expected number for random searches are remarkably similar, each being, for example, $|mathcal {E}^2|$|E2| taken over all graphs of $|mathcal {E}|$|E| edges. Finally, we demonstrate a simple improvement to the above algorithms that generates an Eulerian cycle on the directed edges of $G$G, i.e., a walk on $G$G of $2|mathcal {E}|$2|E| steps that traverses each edge in $G$G exactly once in each direction before returning to the starting point.","PeriodicalId":448036,"journal":{"name":"IEEE BITS the Information Theory Magazine","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128784340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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