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Journal articles on the topic 'Higher Order Information'

Author: Grafiati

Published: 3 June 2025

Last updated: 22 June 2025

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1

Anh, V. V., N. N. Leonenko, and L. M. Sakhno. "Statistical inference using higher-order information." Journal of Multivariate Analysis 98, no. 4 (2007): 706–42. http://dx.doi.org/10.1016/j.jmva.2006.09.009.

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2

Carlet, Claude, Finley Freibert, Sylvain Guilley, Michael Kiermaier, Jon-Lark Kim, and Patrick Sole. "Higher-Order CIS Codes." IEEE Transactions on Information Theory 60, no. 9 (2014): 5283–95. http://dx.doi.org/10.1109/tit.2014.2332468.

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3

Zhou, Qianli, and Yong Deng. "Higher order information volume of mass function." Information Sciences 586 (March 2022): 501–13. http://dx.doi.org/10.1016/j.ins.2021.12.005.

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4

Edelsbrunner, Herbert, Katharina Ölsböck, and Hubert Wagner. "Understanding Higher-Order Interactions in Information Space." Entropy 26, no. 8 (2024): 637. http://dx.doi.org/10.3390/e26080637.

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Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics.

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5

Sibbald, Peter R., Satindranath Banerjee, and Jack Maze. "Calculating higher order DNA sequence information measures." Journal of Theoretical Biology 136, no. 4 (1989): 475–83. http://dx.doi.org/10.1016/s0022-5193(89)80159-6.

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6

Omar, Elmahdi, Sudipto Ghosh, and Darrell Whitley. "Subtle higher order mutants." Information and Software Technology 81 (January 2017): 3–18. http://dx.doi.org/10.1016/j.infsof.2016.01.016.

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7

Reing, Kyle, Greg Ver Steeg, and Aram Galstyan. "Discovering Higher-Order Interactions Through Neural Information Decomposition." Entropy 23, no. 1 (2021): 79. http://dx.doi.org/10.3390/e23010079.

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If regularity in data takes the form of higher-order functions among groups of variables, models which are biased towards lower-order functions may easily mistake the data for noise. To distinguish whether this is the case, one must be able to quantify the contribution of different orders of dependence to the total information. Recent work in information theory attempts to do this through measures of multivariate mutual information (MMI) and information decomposition (ID). Despite substantial theoretical progress, practical issues related to tractability and learnability of higher-order functions are still largely unaddressed. In this work, we introduce a new approach to information decomposition—termed Neural Information Decomposition (NID)—which is both theoretically grounded, and can be efficiently estimated in practice using neural networks. We show on synthetic data that NID can learn to distinguish higher-order functions from noise, while many unsupervised probability models cannot. Additionally, we demonstrate the usefulness of this framework as a tool for exploring biological and artificial neural networks.

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8

Reing, Kyle, Greg Ver Steeg, and Aram Galstyan. "Discovering Higher-Order Interactions Through Neural Information Decomposition." Entropy 23, no. 1 (2021): 79. http://dx.doi.org/10.3390/e23010079.

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If regularity in data takes the form of higher-order functions among groups of variables, models which are biased towards lower-order functions may easily mistake the data for noise. To distinguish whether this is the case, one must be able to quantify the contribution of different orders of dependence to the total information. Recent work in information theory attempts to do this through measures of multivariate mutual information (MMI) and information decomposition (ID). Despite substantial theoretical progress, practical issues related to tractability and learnability of higher-order functions are still largely unaddressed. In this work, we introduce a new approach to information decomposition—termed Neural Information Decomposition (NID)—which is both theoretically grounded, and can be efficiently estimated in practice using neural networks. We show on synthetic data that NID can learn to distinguish higher-order functions from noise, while many unsupervised probability models cannot. Additionally, we demonstrate the usefulness of this framework as a tool for exploring biological and artificial neural networks.

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9

Samushia, Lado, Zachary Slepian, and Francisco Villaescusa-Navarro. "Information content of higher order galaxy correlation functions." Monthly Notices of the Royal Astronomical Society 505, no. 1 (2021): 628–41. http://dx.doi.org/10.1093/mnras/stab1199.

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ABSTRACT The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance–redshift relationship. The cosmological density fields traced by late-time galaxy formation are initially nearly Gaussian, and hence, all the cosmological information can be extracted from their two-point correlation function. Subsequent non-linear evolution under gravity, as well as halo and then galaxy formation, generates higher order correlation functions. Since the mapping of the initial to the final density field is, on large scales, invertible, it is often claimed that the information content of the initial field’s power spectrum is equal to that of all the higher order functions of the final, non-linear field. This claim implies that reconstruction of the initial density field from the non-linear field renders analysis of higher order correlation functions of the latter superfluous. We show that this claim is false when the N-point functions are used as standard rulers. Constraints available from joint analysis of the two and three-point correlation functions can, in some cases, exceed those offered by the initial power spectrum. We provide a mathematical justification for this claim and demonstrate it using a large suite of N-body simulations. In particular, we show that for the z = 0 real-space matter field in the limit of vanishing shot-noise, taking modes up to kmax = 0.2 h Mpc−1, using the bispectrum alone offers a factor of 2 reduction in the variance on the cosmic distance scale relative to that available from the linear power spectrum.

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10

Angeletos, George-Marios, and Jennifer La’O. "Incomplete information, higher-order beliefs and price inertia." Journal of Monetary Economics 56 (October 2009): S19—S37. http://dx.doi.org/10.1016/j.jmoneco.2009.07.001.

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11

Qiao, Ya-nan, Qi Yong, and Hou Di. "Tensor Field Model for higher-order information retrieval." Journal of Systems and Software 84, no. 12 (2011): 2303–13. http://dx.doi.org/10.1016/j.jss.2011.06.057.

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12

Hosoya, Yuzo. "Information amount and higher-order efficiency in estimation." Annals of the Institute of Statistical Mathematics 42, no. 1 (1990): 37–49. http://dx.doi.org/10.1007/bf00050777.

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13

Lei, Fangyuan, Xun Liu, Qingyun Dai, Bingo Wing-Kuen Ling, Huimin Zhao, and Yan Liu. "Hybrid Low-Order and Higher-Order Graph Convolutional Networks." Computational Intelligence and Neuroscience 2020 (June 23, 2020): 1–9. http://dx.doi.org/10.1155/2020/3283890.

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With the higher-order neighborhood information of a graph network, the accuracy of graph representation learning classification can be significantly improved. However, the current higher-order graph convolutional networks have a large number of parameters and high computational complexity. Therefore, we propose a hybrid lower-order and higher-order graph convolutional network (HLHG) learning model, which uses a weight sharing mechanism to reduce the number of network parameters. To reduce the computational complexity, we propose a novel information fusion pooling layer to combine the high-order and low-order neighborhood matrix information. We theoretically compare the computational complexity and the number of parameters of the proposed model with those of the other state-of-the-art models. Experimentally, we verify the proposed model on large-scale text network datasets using supervised learning and on citation network datasets using semisupervised learning. The experimental results show that the proposed model achieves higher classification accuracy with a small set of trainable weight parameters.

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14

Duggan, Dominic. "Higher-Order Substitutions." Information and Computation 164, no. 1 (2001): 1–53. http://dx.doi.org/10.1006/inco.2000.2887.

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15

Kumon, Masayuki. "Studies of information quantities and information geometry of higher order cumulant spaces." Statistical Methodology 7, no. 2 (2010): 152–72. http://dx.doi.org/10.1016/j.stamet.2009.12.003.

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16

Dwyer, Roger F. "Sequential classification of moving objects from higher‐order information." Journal of the Acoustical Society of America 98, no. 5 (1995): 2951. http://dx.doi.org/10.1121/1.414054.

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17

Slapak, Alon, and Arie Yeredor. "Charrelation and Charm: Generic Statistics Incorporating Higher-Order Information." IEEE Transactions on Signal Processing 60, no. 10 (2012): 5089–106. http://dx.doi.org/10.1109/tsp.2012.2205572.

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18

Cureton, Geoffrey P. "Retrieval of Higher Order Ocean Spectral Information From Sunglint." IEEE Transactions on Geoscience and Remote Sensing 53, no. 1 (2015): 36–50. http://dx.doi.org/10.1109/tgrs.2014.2317477.

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19

Win, M. N., and C. D. Smolke. "Higher-Order Cellular Information Processing with Synthetic RNA Devices." Science 322, no. 5900 (2008): 456–60. http://dx.doi.org/10.1126/science.1160311.

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20

Chua, Kuang Chua, V. Chandran, U. Rajendra Acharya, and C. M. Lim. "Application of Higher Order Spectra to Identify Epileptic EEG." Journal of Medical Systems 35, no. 6 (2010): 1563–71. http://dx.doi.org/10.1007/s10916-010-9433-z.

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21

Morris, Joseph M., and Malcolm Tyrrell. "Modelling higher-order dual nondeterminacy." Acta Informatica 45, no. 6 (2008): 441–65. http://dx.doi.org/10.1007/s00236-008-0076-1.

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22

Nadathur, Gopalan, and Dale Miller. "Higher-order Horn clauses." Journal of the ACM 37, no. 4 (1990): 777–814. http://dx.doi.org/10.1145/96559.96570.

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23

Tikhonova, Elena, and Natalia Kudinova. "Sophisticated Thinking: Higher Order Thinking Skills." Journal of Language and Education 1, no. 3 (2015): 12–23. http://dx.doi.org/10.17323/2411-7390-2015-1-3-12-23.

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The information-based society determines that the key factor to achieve success is the development of sophisticated thinking. That said, the thinking process cannot be just a mere imitation of cognitive work, since the digital age requires the authentic skills of working with a flow of information that is being constantly updated. This paper deals with the last stage of the study devoted to the development of sophisticated thinking. It focuses on the enhancement of higher order thinking skills. We claim that the cognitive processes should be based on three phases: development of disposition towards both thinking process and processed information; development of lower order thinking skills which serves as an indispensable basis for developing higher order thinking skills; and development of higher order thinking skills. The omission or reordering of any of these phases may result in significant deterioration of the obtained results. The special emphasis is put on the idea that higher order thinking skills are more effectively developed when lower order thinking skills have already been interiorized. Furthermore, the development of disposition is regarded as the cornerstone of the development of sophisticated thinking in general. Also, due to its defining feature of polysemy, a literary text is considered to be the most appropriate basis for enhancing students’ thinking skills. For the purpose of verifying the theoretical ideas, a qualitative study has been conducted. The two groups of students, who participated in the first and second stages (three-month cycle each) of our project, continue to be involved in this one. They are second-year bachelor students of the Higher School of Economics who are studying English as a second language. On the basis of the ideas expressed by B. Bloom about the division between lower and higher order thinking skills and by J. Mezirow about transformative learning we designed tasks to enhance higher order thinking skills. These tasks were related to the short stories written by D. Barthelme and printed as a collection, Sixty Stories. To teach the students of both groups (control and experimental), the text-based approach with special techniques to measure the students’ level of understanding and the ability to apply the given information was used. The results of the experiment indicated that the students of both groups made headway in their application of thinking skills. However, the students of the experimental group demonstrated a more significant shift due to the fact that the development of their disposition towards cognitive processes and processed information had been specifically targeted over the course of the first and second stages of the project. Another important outcome of the study was that the participants’ frame of reference was extended which allows us to speculate that the development of sophisticated thinking may result in the change of a person’s interpretation of socio-cultural situation. Hence, a further in-depth study of the issue should be conducted.

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24

XIA, Zhiming, and Zongben XU. "Information compression based on principal component analysis: from one-order to higher-order." SCIENTIA SINICA Informationis 48, no. 12 (2018): 1622–33. http://dx.doi.org/10.1360/n112017-00238.

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25

Astesiano, Egidio, and Maura Cerioli. "Partial Higher-Order Specifications1." Fundamenta Informaticae 16, no. 2 (1992): 101–26. http://dx.doi.org/10.3233/fi-1992-16203.

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In this paper the classes of extensional models of higher-order partial conditional specifications are studied, with the emphasis on the closure properties of these classes. Further it is shown that any equationally complete inference system for partial conditional specifications may be extended to an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models. Then, applying some previous results, a deduction system is proposed, equationally complete for the class of extensional models of a partial conditional specification. Finally, turning the attention to the special important case of termextensional models, it is first shown a sound and equationally complete inference system and then necessary and sufficient conditions are given for the existence of free models, which are also free in the class of term-generated extensional models.

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26

Saebi, Mandana, Giovanni Luca Ciampaglia, Lance M. Kaplan, and Nitesh V. Chawla. "HONEM: Learning Embedding for Higher Order Networks." Big Data 8, no. 4 (2020): 255–69. http://dx.doi.org/10.1089/big.2019.0169.

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27

Neirynck, Anne, Prakash Panangaden, and Alan J. Demers. "Effect analysis in higher-order languages." International Journal of Parallel Programming 18, no. 1 (1989): 1–36. http://dx.doi.org/10.1007/bf01409744.

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28

Ma, Hui, Klaus-Dieter Schewe, and Qing Wang. "Distribution design for higher-order data models." Data & Knowledge Engineering 60, no. 2 (2007): 400–434. http://dx.doi.org/10.1016/j.datak.2006.03.006.

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29

Kingstone, Alan, and Michael S. Gazzaniga. "Subcortical transfer of higher order information: More illusory than real?" Neuropsychology 9, no. 3 (1995): 321–28. http://dx.doi.org/10.1037/0894-4105.9.3.321.

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30

Carbone, Mathieu, Yannick Teglia, Gilles R. Ducharme, and Philippe Maurine. "Mutual information analysis: higher-order statistical moments, efficiency and efficacy." Journal of Cryptographic Engineering 7, no. 1 (2016): 1–17. http://dx.doi.org/10.1007/s13389-016-0123-8.

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31

Neske, Garrett T., and Jessica A. Cardin. "Higher-order thalamic input to cortex selectively conveys state information." Cell Reports 44, no. 2 (2025): 115292. https://doi.org/10.1016/j.celrep.2025.115292.

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32

Pedrycz, Witold, Rami Al-Hmouz, Abdullah Saeed Balamash, and Ali Morfeq. "Hierarchical Granular Clustering: An Emergence of Information Granules of Higher Type and Higher Order." IEEE Transactions on Fuzzy Systems 23, no. 6 (2015): 2270–83. http://dx.doi.org/10.1109/tfuzz.2015.2417896.

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33

Havlíček, J., J. Hron, and I. Tichá. "Knowledge based higher education." Agricultural Economics (Zemědělská ekonomika) 52, No. 3 (2012): 107–16. http://dx.doi.org/10.17221/5002-agricecon.

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While data and/or information based education was built on pedagogic, psychology, philosophy of science and didactic disciplines, the new dimension of knowledge based education will involve new disciplines such as Knowledge Management, Epistemology, Systems Theory, Artificial Knowledge Management Systems, Value Theory and Theory of Measurement. It is often assumed that data, information and knowledge are depicted as a pyramid. The data, the most plentiful type, are at the bottom, information, produced from data, is above it and knowledge, produced from information through the hard work of refining or mining, above it. This schema satisfies specific needs of an organisation of warehouse data systems but it does not explain the role of these objects in the educational process. In education, the distinctions among data, information and knowledge need to be distinguished from the complex pedagogical point of view. Knowledge is the engine asking for more information and more data. Knowledge life cycle produces more information, more information asks for more data &ndash; that is: there is &ldquo;just information&rdquo;. Data, information and knowledge can be considered as object oriented measures assigned to real objects (entities). The following measures can be assigned to the objects: Measure of the zero order &ndash; name. Measure of the first order &ndash; data. Measure of the second order &ndash; information. Metrics of the third order &ndash; knowledge. Knowledge based curriculum involves knowledge into study plans and it considers knowledge as a distinctive part of study. Knowledge becomes the engine starting cycle of new information acquisition, reproduction and integration. The following problems have to be solved in building of knowledge based curriculum: Methodology and organisation of educational process. Technical support for knowledge based education. Evaluation and assessment of the process.

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34

LAGDALI, Salwa, and Mohammed RZIZA. "Noisy texture analysis based on higher order spectra." International Journal of Engineering & Technology 7, no. 3 (2018): 1622. http://dx.doi.org/10.14419/ijet.v7i3.14066.

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Texture is described in several approaches by 1st and 2nd order statistics which cannot preserve phase information carried by the Fourier spectrum. Besides, these statistics are very sensitive to noise. In this paper, we study features derived from higher order spectra, especially the third order spectrum, namely the bispectrum, known to offer a high noise immunity and to recover Fourier phase information. In this paper, we exploit phase preservation property by using bispectrum phase. We propose wrapped Cauchy distribution to model phase. Wrapped Cauchy parameters are estimated by maximizing the log-likelihood function. Experiments show that the wrapped Cauchy distribution fits our phase information well. Hence, their parameters are used to feed our feature vector in order to classify textures corrupted by Gaussian noise. Classification results using the proposed approach show a good noise immunity compared to a statistical model based on Gabor phase.

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35

Kobayashi, Naoki. "Model Checking Higher-Order Programs." Journal of the ACM 60, no. 3 (2013): 1–62. http://dx.doi.org/10.1145/2487241.2487246.

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36

Afşer, H., and H. Deliç. "Polar Codes with Higher-Order Memory." Problems of Information Transmission 54, no. 4 (2018): 301–28. http://dx.doi.org/10.1134/s0032946018040014.

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37

Xu, Xian. "Distinguishing and relating higher-order and first-order processes by expressiveness." Acta Informatica 49, no. 7-8 (2012): 445–84. http://dx.doi.org/10.1007/s00236-012-0168-9.

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38

Nakajima, Toshi, Hajime Mushiake, Toshio Inui, and Jun Tanji. "Decoding higher-order motor information from primate non-primary motor cortices." Technology and Health Care 15, no. 2 (2007): 103–10. http://dx.doi.org/10.3233/thc-2007-15204.

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39

Gajowniczek, Krzysztof, Jialin Wu, Soumyajit Gupta, and Chandrajit Bajaj. "HOFS: Higher order mutual information approximation for feature selection in R." SoftwareX 19 (July 2022): 101148. http://dx.doi.org/10.1016/j.softx.2022.101148.

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40

Kamigaito, Hidetaka, Katsuhiko Hayashi, Tsutomu Hirao, Masaaki Nagata, and Manabu Okumura. "Effectiveness of Syntactic Dependency Information for Higher-Order Syntactic Attention Network." Journal of Natural Language Processing 28, no. 2 (2021): 321–49. http://dx.doi.org/10.5715/jnlp.28.321.

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41

Wang, Dan, Peng Nie, Xiubin Zhu, Witold Pedrycz, and Zhiwu Li. "Designing of higher order information granules through clustering heterogeneous granular data." Applied Soft Computing 112 (November 2021): 107820. http://dx.doi.org/10.1016/j.asoc.2021.107820.

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42

Shang, Ronghua, Weitong Zhang, Jingwen Zhang, Jie Feng, and Licheng Jiao. "Local community detection based on higher-order structure and edge information." Physica A: Statistical Mechanics and its Applications 587 (February 2022): 126513. http://dx.doi.org/10.1016/j.physa.2021.126513.

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43

Anastopoulos, Charis, and Ntina Savvidou. "Multi-time measurements in Hawking radiation: information at higher-order correlations." Classical and Quantum Gravity 37, no. 2 (2019): 025015. http://dx.doi.org/10.1088/1361-6382/ab5eb2.

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44

Matsuda, Hiroyuki. "Physical nature of higher-order mutual information: Intrinsic correlations and frustration." Physical Review E 62, no. 3 (2000): 3096–102. http://dx.doi.org/10.1103/physreve.62.3096.

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45

Petropulu, A. P., and C. L. Nikias. "Blind convolution using signal reconstruction from partial higher order cepstral information." IEEE Transactions on Signal Processing 41, no. 6 (1993): 2088–95. http://dx.doi.org/10.1109/78.218138.

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46

Guo, Xuan, Jie Li, Pengfei Jiao, Wang Zhang, Tianpeng Li, and Wenjun Wang. "Counterfactual learning for higher-order relation prediction in heterogeneous information networks." Neural Networks 183 (March 2025): 107024. https://doi.org/10.1016/j.neunet.2024.107024.

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47

He, Hairong, Meiyu Peng, Guangtao Cao, Yanbei Li, Hui Liu, and Hui Yang. "Higher-order Poincaré sphere multiplexed metasurface holography for optical information encryption." Optics & Laser Technology 180 (January 2025): 111555. http://dx.doi.org/10.1016/j.optlastec.2024.111555.

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48

Cornand, Camille, and Frank Heinemann. "Limited higher order beliefs and the welfare effects of public information." Journal of Economic Studies 42, no. 6 (2015): 1005–28. http://dx.doi.org/10.1108/jes-08-2015-0142.

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Purpose – In games with strategic complementarities, public information about the state of the world has a larger impact on equilibrium actions than private information of the same precision, because the former is more informative about the likely behavior of others. This may lead to welfare-reducing “overreactions” to public signals as shown by Morris and Shin (2002). Recent experiments on games with strategic complementarities show that subjects attach a lower weight to public signals than theoretically predicted. The purpose of this paper is to reconsider the welfare effects of public signals accounting for the weights observed in experiments. Design/methodology/approach – Aggregate behavior observed in experiments on games with strategic complementarities can be explained by a cognitive hierarchy model where subjects employ limited levels of reasoning. They respond in a rational way to the non-strategic part of a game and they account for other players responding rationally, but they neglect that other players also account for others’ rationality. This paper analyzes the welfare effects of public information under such limited levels of reasoning. Findings – In the model by Morris and Shin (2002) public information is always welfare improving if strategies are derived from such low reasoning levels. The optimal degree of publicity is decreasing in the levels of reasoning. For the observed average level of reasoning, full transparency is optimal, if public information is more precise than private information. If the policy maker has instruments that are perfect substitutes to private actions, the government should secretly respond to its information without disclosing or signaling it to the private sector independent of the degree of private agents’ rationality. Originality/value – This paper takes experimental evidence back to theory and shows that the main result obtained by the theory under rational behavior breaks down if theory accounts for the bounded rationality observed in experiments.

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49

Medikonda, Jeevan, and Hanmandlu Madasu. "Higher order information set based features for text-independent speaker identification." International Journal of Speech Technology 21, no. 3 (2017): 451–61. http://dx.doi.org/10.1007/s10772-017-9472-7.

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50

Maddison, James R., Daniel N. Goldberg, and Benjamin D. Goddard. "Automated Calculation of Higher Order Partial Differential Equation Constrained Derivative Information." SIAM Journal on Scientific Computing 41, no. 5 (2019): C417—C445. http://dx.doi.org/10.1137/18m1209465.

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