Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-76c49bb84f-sz5hq Total loading time: 0 Render date: 2025-07-07T20:34:12.510Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  17 May 2025

Tomaso Aste
Tomaso Aste
Affiliation:
University College London
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'

Information

Type
Chapter
Information
Probabilistic Data-Driven Modeling , pp. 419 - 428
Publisher: Cambridge University Press
Print publication year: 2025

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Book purchase

Temporarily unavailable

References

Abdallah, S. A. and Plumbley, M. D.. A measure of statistical complexity based on predictive information with application to finite spin systems. Physics Letters A, 376(4):275–281, 2012.CrossRefGoogle Scholar
Adler, R., Feldman, R., and Taqqu, M.. A Practical Guide to Heavy Tails: Statistical Techniques and Applications. Springer Science & Business Media, 1998.Google Scholar
Aït-Sahalia, Y. and Jacod, J.. From tick data to semimartingales. The Annals of Applied Probability, 30(6):2740–2768, 2020.CrossRefGoogle Scholar
Anand, K. and Bianconi, G.. Entropy measures for networks: Toward an information theory of complex topologies. Physical Review E, 80(4):045102, 2009.CrossRefGoogle ScholarPubMed
Anand, K. and Bianconi, G.. Gibbs entropy of network ensembles by cavity methods. Physical Review E, 82(1):011116, 2010.CrossRefGoogle ScholarPubMed
Anderson, T. W. and Darling, D. A.. Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. The Annals of Mathematical Statistics, 23(2):193–212, 1952.CrossRefGoogle Scholar
Aste, T. Cryptocurrency market structure: connecting emotions and economics. Digital Finance, 1(1):5–21, 2019.CrossRefGoogle Scholar
Aste, T. Stress testing and systemic risk measures using elliptical conditional multivariate probabilities. Journal of Risk and Financial Management, 14(5):213, 2021.CrossRefGoogle Scholar
Aste, T. Topological regularization with information filtering networks. Information Sciences, 608:655–669, 2022.CrossRefGoogle Scholar
Aste, T. and Di Matteo, T.. Emergence of gamma distributions in granular materials and packing models. Physical Review E, 77(2):021309, 2008.CrossRefGoogle ScholarPubMed
Aste, T., Shaw, W., and Di Matteo, T.. Correlation structure and dynamics in volatile markets. New Journal of Physics, 12(8):085009, 2010.CrossRefGoogle Scholar
Aste, T., Massara, G., Briola, A., and Wang, R.. Software tools repository for the financial computing and analytics group UCL, 2024. https://github.com/FinancialComputingUCL. [Accessed 10 July 2024].Google Scholar
Bachelier, L. Théorie de la spéculation. In Annales scientifiques de l’École normale supérieure, volume 17, pages 21–86, 1900.CrossRefGoogle Scholar
Balatoni, J. and Rényi, A.. Remarks on entropy. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, 1:9–40, 1956.Google Scholar
Barabási, A.-L. Scale-free networks: a decade and beyond. Science, 325(5939):412–413, 2009.CrossRefGoogle Scholar
Barfuss, W., Massara, G. P., Di Matteo, T., and Aste, T.. Parsimonious modeling with information filtering networks. Physical Review E, 94(6):062306, 2016.CrossRefGoogle ScholarPubMed
Bartlett, P. L., Long, P. M., Lugosi, G., and Tsigler, A.. Benign overfitting in linear regression. Proceedings of the National Academy of Sciences, 117(48):30063–30070, 2020.CrossRefGoogle ScholarPubMed
Battiston, F., Amico, E., Barrat, A., Bianconi, G., Ferraz de Arruda, G., Franceschiello, B., Iacopini, I., Kéfi, S., Latora, V., Moreno, Y., Murray, M. M., Peixoto, T. P., Vaccarino, F., and Petri, G.. The physics of higher-order interactions in complex systems. Nature Physics, 17 (10):1093–1098, 2021.CrossRefGoogle Scholar
Bayes, T. An essay towards solving a problem in the doctrine of chances. by the late Rev. Mr. Bayes, frs communicated by Mr. Price, in a letter to John Canton, AMFR S. Philosophical transactions of the Royal Society of London, 53:370–418, 1763.Google Scholar
Belkin, M., Hsu, D., Ma, S., and Mandal, S.. Reconciling modern machine-learning practice and the classical bias–variance trade-off. Proceedings of the National Academy of Sciences, 116 (32):15849–15854, 2019.CrossRefGoogle ScholarPubMed
Bell, A. J. The co-information lattice. In Proceedings of the Fifth International Workshop on Independent Component Analysis and Blind Signal Separation: ICA, volume 10. Citeseer, 2003.Google Scholar
Bellman, R. On the theory of dynamic programming. Proceedings of the National Academy of Sciences of the United States of America, 38(8):716–719, 1952.CrossRefGoogle ScholarPubMed
Bellman, R. The theory of dynamic programming. Bulletin of the American Mathematical Society, 60(6):503–515, 1954.CrossRefGoogle Scholar
Berkane, M. and Bentler, P.. Moments of elliptically distributed random variates. Statistics & Probability Letters, 4(6):333–335, 1986.CrossRefGoogle Scholar
Berry, A. C. The accuracy of the Gaussian approximation to the sum of independent variates. Transactions of the American Mathematical Society, 49(1):122–136, 1941.CrossRefGoogle Scholar
Bertsekas, D. P. Constrained optimization and Lagrange multiplier methods. Academic Press, 1982.Google Scholar
Bettencourt, L. M., Gintautas, V., and Ham, M. I.. Identification of functional information subgraphs in complex networks. Physical Review Letters, 100(23):238701, 2008.CrossRefGoogle ScholarPubMed
Bianconi, G. Higher order networks: an introduction to simplicial complexes. Cambridge University Press, 2021.CrossRefGoogle Scholar
Bianconi, G. and Barabási, A.-L.. Bose-Einstein condensation in complex networks. Physical Review Letters, 86(24):5632, 2001a.CrossRefGoogle ScholarPubMed
Bianconi, G. and Barabási, A.-L.. Competition and multiscaling in evolving networks. Europhysics Letters, 54(4):436, 2001b.CrossRefGoogle Scholar
Bianconi, G. and Barabási, A.-L.. Competition and multiscaling in evolving networks. Princeton University Press, 2011.CrossRefGoogle Scholar
Bianconi, G. and Rahmede, C.. Network geometry with flavor: from complexity to quantum geometry. Physical Review E, 93(3):032315, 2016.CrossRefGoogle ScholarPubMed
Bianconi, G. and Rahmede, C.. Emergent hyperbolic network geometry. Scientific reports, 7(1): 41974, 2017.Google Scholar
Biggs, N. Algebraic graph theory, volume 67. Cambridge University Press, 1993.Google Scholar
Billings, J. C. W., Hu, M., Lerda, G., Medvedev, A. N., Mottes, F., Onicas, A., Santoro, A., and Petri, G.. Simplex2Vec embeddings for community detection in simplicial complexes. arXiv preprint arXiv:1906.09068, 2019.Google Scholar
Birnbaum, A. On the foundations of statistical inference. Journal of the American Statistical Association, 57(298):269–306, 1962.CrossRefGoogle Scholar
Boccara, N. Modeling complex systems. Springer Science & Business Media, 2010.CrossRefGoogle Scholar
Boltzmann, L. Studien uber das gleichgewicht der lebenden kraft. Wissenschafiliche Abhandlungen, 1:49–96, 1868.Google Scholar
Bonanno, G., Caldarelli, G., Lillo, F., Micciche, S., Vandewalle, N., and Mantegna, R. N.. Networks of equities in financial markets. The European Physical Journal B, 38(2):363–371, 2004.CrossRefGoogle Scholar
Bonferroni, C. Teoria statistica delle classi e calcolo delle probabilità. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commericiali di Firenze, 8:3–62, 1936.Google Scholar
Boruvka, O. Ojistém problému minimálním. Acta Societatis Scientiarum Naturalium Moravicae, 3(3):1–22, 1926.Google Scholar
Boughorbel, S., Jarray, F., and El-Anbari, M.. Optimal classifier for imbalanced data using Matthews correlation coefficient metric. PLoS ONE, 12(6):e0177678, 2017.CrossRefGoogle ScholarPubMed
Brillinger, D. R. A note on the rate of convergence of a mean. Biometrika, 49(3/4):574–576, 1962.CrossRefGoogle Scholar
Caldarelli, G., Capocci, A., De Los Rios, P., and Munoz, M. A.. Scale-free networks from varying vertex intrinsic fitness. Physical Review Letters, 89(25):258702, 2002.CrossRefGoogle ScholarPubMed
Cantelli, F. P. Sulla determinazione empirica delle leggi di probabilita. Giornale Istituto Italiano degli Attuari, 4:421–424, 1933.Google Scholar
Casella, G. and Berger, R. L.. Statistical inference. Cengage Learning, 2021.Google Scholar
Chaudhary, S., Down, J., D’Souza, N., Gu, Y., and Yan, H.. Parameter-wise double descent: A unified model or not? UCL–COMP0031 student project, March 2023.Google ScholarPubMed
Chawla, N. V., Bowyer, K. W., Hall, L. O., and Kegelmeyer, W. P.. SMOTE: synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 16:321–357, 2002.CrossRefGoogle Scholar
Chazelle, B. A minimum spanning tree algorithm with inverse-Ackermann type complexity. Journal of the ACM, 47(6):1028–1047, 2000.CrossRefGoogle Scholar
Chen, T., He, T., Benesty, M., Khotilovich, V., Tang, Y., Cho, H., Chen, K., Mitchell, R., Cano, I., Zhou, T., et al. Xgboost: extreme gradient boosting. R package version 0.4-2, 1(4):1–4, 2015.Google Scholar
Chicco, D. and Jurman, G.. The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation. BMC genomics, 21(1):1–13, 2020.CrossRefGoogle ScholarPubMed
Chow, C. and Liu, C.. Approximating discrete probability distributions with dependence trees. IEEE Transactions on Information Theory, 14(3):462–467, 1968.CrossRefGoogle Scholar
Clauset, A., Shalizi, C. R., and Newman, M. E.. Power-law distributions in empirical data. SIAM Review, 51(4):661–703, 2009.CrossRefGoogle Scholar
Clausius, R. The mechanical theory of heat. Macmillan, 1879.Google Scholar
Coniglio, A. Multifractal structure of clusters and growing aggregates. Physica A: Statistical Mechanics and its Applications, 140(1–2):51–61, 1986.CrossRefGoogle Scholar
Coniglio, A. and Marinaro, M.. A natural way of introducing asymmetry through a generalization of the scaling law. Physica, 54(2):261–270, 1971.CrossRefGoogle Scholar
Coniglio, A., Ciamarra, M. P., and Aste, T.. Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres. Soft Matter, 13(46):8766–8771, 2017.CrossRefGoogle ScholarPubMed
d’Ascoli, S., Refinetti, M., Biroli, G., and Krzakala, F.. Double trouble in double descent: bias and variance(s) in the lazy regime. In International Conference on Machine Learning, pages 2280–2290. PMLR, 2020.Google Scholar
de Arcangelis, L., Redner, S., and Coniglio, A.. Anomalous voltage distribution of random resistor networks and a new model for the backbone at the percolation threshold. Physical Review B, 31(7):4725, 1985.Google Scholar
Di Matteo, T., Aste, T., and Dacorogna, M. M.. Long-term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development. Journal of Banking & Finance, 29(4):827–851, 2005.CrossRefGoogle Scholar
Dijkstra, E. W. A note on two problems in connexion with graphs. Numerische Mathematik, 1 (1):269–271, 1959.CrossRefGoogle Scholar
Doob, J. L. Stochastic processes. Wiley, 1953.Google Scholar
Duke, R. A. The genus, regional number, and betti number of a graph. Canadian Journal of Mathematics, 18:817–822, 1966.CrossRefGoogle Scholar
Durrett, R. Probability: theory and examples, volume 49. Cambridge University Press, 2019.CrossRefGoogle Scholar
Dvoretzky, A., Kiefer, J., and Wolfowitz, J.. Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. The Annals of Mathematical Statistics, 27(3):642–669, 1956.CrossRefGoogle Scholar
Dyson, F. A meeting with Enrico Fermi. Nature, 427(6972):297–297, 2004.CrossRefGoogle Scholar
Edelman, A. Eigenvalues and condition numbers of random matrices. SIAM Journal on Matrix Analysis and Applications, 9(4):543–560, 1988.CrossRefGoogle Scholar
Edelsbrunner, H. and Harer, J.. Persistent homology – a survey. Contemporary Mathematics, 453:257–282, 2008.CrossRefGoogle Scholar
Einstein, A. Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen. Annalen der Physik, 4(17):549–560, 1905.CrossRefGoogle Scholar
Embrechts, P. Selfsimilar processes. Princeton University Press, 2009.Google Scholar
Erdös, P. and Rényi, A.. On random graphs I. Publicationes Mathematicae, 6(290–297):18, 1959.Google Scholar
Ernst, M. D. Permutation methods: a basis for exact inference. Statistical Science, 19:676–685, 2004.CrossRefGoogle Scholar
Fang, K. W. Symmetric multivariate and related distributions. CRC Press, 2018.CrossRefGoogle Scholar
Feller, W. An introduction to probability theory and its applications. Wailey & Sons, 1957.Google Scholar
Feyerabend, P. Against method: outline of an anarchistic theory of knowledge. New Left Books, 1975.Google Scholar
Fiedor, P. Networks in financial markets based on the mutual information rate. Physical Review E, 89(5):052801, 2014.CrossRefGoogle ScholarPubMed
Fourier, J. B. J. Théorie analytique de la chaleur. Firmin Didot, 1822.Google Scholar
Friedman, J., Hastie, T., and Tibshirani, R.. Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3):432–441, 2008.CrossRefGoogle ScholarPubMed
Friedman, J. H. Greedy function approximation: a gradient boosting machine. The Annals of Statistics, 29(5):1189–1232, 2001.CrossRefGoogle Scholar
Friedman, J. H. Stochastic gradient boosting. Computational Statistics & Data Analysis, 38(4): 367–378, 2002.CrossRefGoogle Scholar
Frisch, U. and Parisi, G.. Fully developed turbulence and intermittency. Annals of the New York Academy of Sciences, 357(1):359–367, 1980.CrossRefGoogle Scholar
Friz, P. K. and Hairer, M.. A course on rough paths. Springer, 2020.CrossRefGoogle Scholar
Garibaldi, U. and Scalas, E.. Finitary probabilistic methods in econophysics. Cambridge University Press, 2010.CrossRefGoogle Scholar
Germano, G. Lecture notes on probability theory and stochastic processes. University College London, 2023.Google Scholar
Gibbs, J. W. Elementary Principles in Statistical Mechanics: Developed with Especial Reference to The Rational Foundations of Thermodynamics. C. Scribner’s sons, 1902.Google Scholar
Gill, P. E., Murray, W., and Wright, M. H.. Practical optimization. Society for Industrial and Applied Mathematics, 2019.CrossRefGoogle Scholar
Glivenko, V. Sulla determinazione empirica delle leggi di probabilità. Giornale Istituto Italiano degli Attuari, 4:92–99, 1933.Google Scholar
Gnedenko, B. and Kolmogorov, A.. Limit distributions for sums of independent random variables. Addison-Wesley Mathematical Series, 1954.Google Scholar
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y.. Generative adversarial nets. Advances in Neural Information Processing Systems, 27:1–9, 2014.Google Scholar
Goodfellow, I., Bengio, Y., and Courville, A.. Deep learning. MIT Press, 2016.Google Scholar
Goodman, S. A dirty dozen: twelve p-value misconceptions. In Seminars in hematology, volume 45, pages 135–140. Elsevier, 2008.CrossRefGoogle ScholarPubMed
Gower, B. Scientific method: An historical and philosophical introduction. Psychology Press, 1997.Google Scholar
Grahovac, D. Multifractal processes: definition, properties and new examples. Chaos, Solitons & Fractals, 134:109735, 2020.CrossRefGoogle Scholar
Granger, C. W. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3):424–438, 1969.CrossRefGoogle Scholar
Grimmett, G. and Stirzaker, D.. Probability and random processes. Oxford University Press, 2020.Google Scholar
Hafner, J. Ab-initio simulations of materials using VASP: Density-functional theory and beyond. Journal of Computational Chemistry, 29(13):2044–2078, 2008.CrossRefGoogle ScholarPubMed
Hallac, D., Vare, S., Boyd, S., and Leskovec, J.. Toeplitz inverse covariance-based clustering of multivariate time series data. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 215–223, 2017.Google ScholarPubMed
Halmos, P. R. Measure theory, volume 18. Springer Science, 1950.CrossRefGoogle Scholar
Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., and Shraiman, B. I.. Fractal measures and their singularities: the characterization of strange sets. Physical Review A, 33(2):1141, 1986.CrossRefGoogle ScholarPubMed
Hammer, B. and Gersmann, K.. A note on the universal approximation capability of support vector machines. Neural Processing Letters, 17(1):43–53, 2003.CrossRefGoogle Scholar
Hastie, T., Tibshirani, R., and Friedman, J.. The elements of statistical learning. Springer Series in Statistics, 2001.CrossRefGoogle Scholar
Hastie, T., Montanari, A., Rosset, S., and Tibshirani, R. J.. Surprises in high-dimensional ridgeless least squares interpolation. The Annals of Statistics, 50(2):949–986, 2022.CrossRefGoogle ScholarPubMed
He, H., Bai, Y., Garcia, E. A., and Li, S.. ADASYN: adaptive synthetic sampling approach for imbalanced learning. In 2008 IEEE international joint conference on neural networks (IEEE world congress on computational intelligence), pages 1322–1328. IEEE, 2008.Google Scholar
Heermann, D. W. Computer-simulation methods. In Computer simulation methods in theoretical physics, pages 8–12. Springer, 1990.CrossRefGoogle Scholar
Helbing, D. Agent-based modeling. In Social self-organization, pages 25–70. Springer, 2012.CrossRefGoogle Scholar
Hill, B. M. A simple general approach to inference about the tail of a distribution. The Annals of Statistics, pages 1163–1174, 1975.Google Scholar
Ho, T. K. Random decision forests. In Proceedings of the 3rd International Conference on Document Analysis and Recognition, volume 1, pages 278–282. IEEE, 1995.Google Scholar
Hoeffding, W. Masstabinvariante korrelationstheorie. Schriften des Mathematischen Instituts und Instituts fur Angewandte Mathematik der Universitat Berlin, 5:181–233, 1940.Google Scholar
Hornik, K., Stinchcombe, M., and White, H.. Multilayer feedforward networks are universal approximators. Neural Networks, 2(5):359–366, 1989.CrossRefGoogle Scholar
Hotelling, H. Analysis of a complex of statistical variables with principal components. Journal of Educational Psychology, 24:498–520, 1933.CrossRefGoogle Scholar
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.-C., Tung, C. C., and Liu, H. H.. The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A, 454(1971):903–995, 1998.CrossRefGoogle Scholar
Hulswit, M. From cause to causation: a Peircean perspective. Springer Science & Business Media. Philosophical Studies Series, volume 90, 2002.CrossRefGoogle Scholar
Hurvich, C. M. and Tsai, C.-L.. Regression and time series model selection in small samples. Biometrika, 76(2):297–307, 1989.CrossRefGoogle Scholar
James, G., Witten, D., Hastie, T., and Tibshirani, R.. An introduction to statistical learning, volume 112. Springer, 2013.CrossRefGoogle Scholar
James, R. G., Barnett, N., and Crutchfield, J. P.. Information flows? A critique of transfer entropies. Physical Review Letters, 116(23):238701, 2016.CrossRefGoogle ScholarPubMed
Jaynes, E. T. Probability theory: the logic of science. Cambridge University Press, 2003.CrossRefGoogle Scholar
Jolliffe, I. T. Principal component analysis for special types of data. Springer, 2002.Google Scholar
Khinchin, A. Y. Mathematical foundations of information theory. Courier Corporation, 2013.Google Scholar
Kingsford, C. and Salzberg, S. L.. What are decision trees? Nature Biotechnology, 26(9):1011–1013, 2008.CrossRefGoogle ScholarPubMed
Kirchgässner, G., Wolters, J., and Hassler, U.. Introduction to modern time series analysis. Springer Science & Business Media, 2012.Google Scholar
Kolmogorov, A. Grundbegriffe der wahrscheinlichkeitsrechnung. Springer, 1933.CrossRefGoogle Scholar
Kruskal, J. B. On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical society, 7(1):48–50, 1956.CrossRefGoogle Scholar
Kuratowski, C. Sur le probleme des courbes gauches en topologie. Fundamenta Mathematicae, 15(1):271–283, 1930.CrossRefGoogle Scholar
Lauritzen, S. L. Graphical models. Oxford University Press, 1996.CrossRefGoogle Scholar
Ledoit, O. and Wolf, M.. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5):603–621, 2003.CrossRefGoogle Scholar
Ledoit, O. and Wolf, M.. Honey, I shrunk the sample covariance matrix. The Journal of Portfolio Management, 30(4):110–119, 2004.CrossRefGoogle Scholar
Little, R. J. Statistical analysis of masked data. Journal of Official Statistics, 9(2):407, 1993.Google Scholar
Livan, G., Alfarano, S., and Scalas, E.. Fine structure of spectral properties for random correlation matrices: an application to financial markets. Physical Review E, 84(1):016113, 2011.CrossRefGoogle ScholarPubMed
Livan, G., Novaes, M., and Vivo, P.. Introduction to random matrices: theory and practice, volume 26. Springer, 2018.CrossRefGoogle Scholar
Mahalanobis, P. C. On the generalized distance in statistics. Prooceedings of the National Institute of Science of India, 2:49–55, 1936.Google Scholar
Mandelbrot, B. B. Possible refinement of the lognormal hypothesis concerning the distribution of energy dissipation in intermittent turbulence. In Statistical models and turbulence, pages 333–351. Springer, 1972.CrossRefGoogle Scholar
Mandelbrot, B. B. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. Journal of Fluid Mechanics, 62(2):331–358, 1974.CrossRefGoogle Scholar
Mandelbrot, B. B. Fractals: form, chance and dimension. W. H. Freeman and Company, San Francisco, 1977.Google Scholar
Mandelbrot, B. B. Fractals and scaling in finance: discontinuity, concentration, risk. Selecta volume E. Springer Science and Business Media, 1997.CrossRefGoogle Scholar
Mandelbrot, B. B. and Mandelbrot, B. B.. The fractal geometry of nature, volume 1. WH Freeman, 1982.Google Scholar
Markowitz, H. Portfolio selection. The Journal of Finance, 7:77–91, 1952.Google Scholar
Markowitz, H. M. Portfolio selection. Yale University Press, 1968.Google Scholar
Laplace, P. S.marquis de. Théorie Analytique des Probabilitiés, volume 7. Courcier, 1820.Google Scholar
Marsaglia, G. and Marsaglia, J.. Evaluating the anderson–darling distribution. Journal of Statistical Software, 9(1):1–5, 2004.CrossRefGoogle Scholar
Marti, G., Nielsen, F., Bińkowski, M., and Donnat, P.. A review of two decades of correlations, hierarchies, networks and clustering in financial markets. In Nielsen, F., editor, Progress in Information Geometry: Theory and Applications, pages 245–274. Springer International Publishing, 2021.CrossRefGoogle Scholar
Marčenko, V. A. and Pastur, L. A.. Distribution of eigenvalues for some sets of random matrices. Matematicheskii Sbornik, 114(4):507–536, 1967.Google Scholar
Massara, G. P. and Aste, T.. Learning clique forests. arXiv preprint arXiv:1905.02266, 2019.Google Scholar
Massara, G. P., Di Matteo, T., and Aste, T.. Network filtering for big data: triangulated maximally filtered graph. Journal of Complex Networks, 5(2):161–178, 2017.Google Scholar
Massey, F. J. Jr The kolmogorov-smirnov test for goodness of fit. Journal of the American statistical Association, 46(253):68–78, 1951.CrossRefGoogle Scholar
MathWorks, . fitdist. MATLAB Version R2024a Available at: https://www.mathworks.com/help/matlab/ref/plot.html, 2024. [Accessed 10 June 2024].Google Scholar
Matsuda, H. Physical nature of higher-order mutual information: intrinsic correlations and frustration. Physical Review E, 62(3):3096, 2000.Google Scholar
Mayfield, M. M. and Stouffer, D. B.. Higher-order interactions capture unexplained complexity in diverse communities. Nature Ecology and Evolution, 1(3):1–7, 2017.CrossRefGoogle ScholarPubMed
McElreath, R. Statistical rethinking: a Bayesian course with examples in R and Stan. Chapman and Hall/CRC, 2018.CrossRefGoogle Scholar
McGillem, C. D. and Cooper, G. R.. Continuous and discrete signal and system analysis. Harcourt School, 1991.Google Scholar
Metzler, R. and Klafter, J.. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 339(1):1–77, 2000.CrossRefGoogle Scholar
Meyn, S. P. and Tweedie, R. L.. Markov chains and stochastic stability. Springer Science & Business Media, 2012.Google Scholar
Minh, D., Wang, H. X., Li, Y. F., and Nguyen, T. N.. Explainable artificial intelligence: a comprehensive review. Artificial Intelligence Review, 55(5):1–66, 2022.CrossRefGoogle Scholar
Mirlin, A. D., Fyodorov, Y. V., Dittes, F.-M., Quezada, J., and Seligman, T. H.. Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices. Physical Review E, 54(4):3221, 1996.Google Scholar
Mulder, D. and Bianconi, G.. Network geometry and complexity. Journal of Statistical Physics, 173:783–805, 2018.CrossRefGoogle Scholar
Myers, R. H. and Myers, R. H.. Classical and modern regression with applications, volume 2. Duxbury press Belmont, CA, 1990.Google Scholar
Nakkiran, P. More data can hurt for linear regression: sample-wise double descent. arXiv preprint arXiv:1912.07242, 2019.Google Scholar
Natekin, A. and Knoll, A.. Gradient boosting machines, a tutorial. Frontiers in neurorobotics, 7:21, 2013.CrossRefGoogle ScholarPubMed
Nava, N., Di Matteo, T., and Aste, T.. Anomalous volatility scaling in high frequency financial data. Physica A: Statistical Mechanics and its Applications, 447:434–445, 2016a.CrossRefGoogle Scholar
Nava, N., Di Matteo, T., and Aste, T.. Time-dependent scaling patterns in high frequency financial data. The European Physical Journal Special Topics, 225(10):1997–2016, 2016b.CrossRefGoogle Scholar
Nešetřil, J., Milková, E., and Nešetřilová, H.. Otakar Boruvka on minimum spanning tree problem translation of both the 1926 papers, comments, history. Discrete Mathematics, 233(1–3):3–36, 2001.CrossRefGoogle Scholar
Newman, M. Networks. Oxford University Press, 2018.CrossRefGoogle Scholar
Neyman, J. and Pearson, E. S.. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 231:289–337, 1933.Google Scholar
Nocedal, J. and Wright, S.. Numerical optimization. Springer Science & Business Media, 2006.Google Scholar
Nolan, J. P. Univariate stable distributions. Springer, 2020.CrossRefGoogle Scholar
Nourdin, I. Selected aspects of fractional Brownian motion, volume 4. Springer, 2012.CrossRefGoogle Scholar
Novikov, E. Intermittency and scale similarity in the structure of a turbulent plow. Journal of Applied Mathematics and Mechanics, 35(2):231–241, 1971.CrossRefGoogle Scholar
Nuzzo, R. Scientific method: Statistical errors. Nature, 506(7487):150–152, 2014.CrossRefGoogle ScholarPubMed
Oksendal, B. Stochastic differential equations. Springer, 2003.CrossRefGoogle Scholar
Olbrich, E., Bertschinger, N., Ay, N., and Jost, J.. How should complexity scale with system size? The European Physical Journal B, 63(3):407–415, 2008.CrossRefGoogle Scholar
Omori, F. On the aftershocks of earthquakes. Journal of the College of Science, Imperial University of Tokyo, 7:111–120, 1894.Google Scholar
Orey, S. Limit theorems for Markov chain transition probabilities. van Nostrand London, 1971.Google Scholar
Parisi, G. Complex systems: a physicist’s viewpoint. arXiv preprint arXiv:cond-mat/0205297, 2002.Google Scholar
Pearl, J. Models, reasoning and inference. Cambridge, UK: CambridgeUniversityPress, 19, 2000.Google Scholar
Pearl, J. The seven tools of causal inference, with reflections on machine learning. Communications of the ACM, 62(3):54–60, 2019.CrossRefGoogle Scholar
Pearl, J. and Mackenzie, D.. Ai can’t reason why. Wall Street Journal, 2018.Google Scholar
Pearson, K. Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London A, 185:71–110, 1894.Google Scholar
Pearson, K. X. Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material. Philosophical Transactions of the Royal Society of London A, 186: 343–414, 1895.Google Scholar
Pearson, K. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11):559–572, 1901.CrossRefGoogle Scholar
Pearson, K. The problem of the random walk. Nature, 72(1867):342–342, 1905.CrossRefGoogle Scholar
Pemmaraju, S. and Skiena, S.. Computational Discrete Mathematics: combinatorics and Graph Theory with Mathematica®. Cambridge University Press, 2003.CrossRefGoogle Scholar
Perry, M. J. A birthday tribute to the ‘sage of baltimore’ – H.L. Mencken, 09 2022. https://www.aei.org/carpe-diem/a-birthday-tribute-to-the-sage-of-baltimore-h-l-mencken/. [Accessed 10 July 2024].Google Scholar
Popper, K. The logic of scientific discovery. Julius Springer, 1934.Google Scholar
Pozzi, F., Di Matteo, T., and Aste, T.. Exponential smoothing weighted correlations. The European Physical Journal B, 85(6):1–21, 2012.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.. Numerical recipes 3rd edition: the art of scientific computing. Cambridge University Press, 2007.Google Scholar
Prim, R. C. Shortest connection networks and some generalizations. The Bell System Technical Journal, 36(6):1389–1401, 1957.CrossRefGoogle Scholar
Procacci, P. F. and Aste, T.. Forecasting market states. Quantitative Finance, 19(9):1491–1498, 2019.CrossRefGoogle Scholar
Protter, P. E. Stochastic differential equations. Springer, 2005.Google Scholar
Quine, W. V. O. Two dogmas of empiricism. The Philosophical Review, 60:20–43, 1951.CrossRefGoogle Scholar
Rényi, A. On the dimension and entropy of probability distributions. Acta Mathematica Academiae Scientiarum Hungarica, 10(1–2):193–215, 1959a.CrossRefGoogle Scholar
Rényi, A. On measures of dependence. Acta Mathematica Academiae Scientiarum Hungarica, 10(3–4):441–451, 1959b.CrossRefGoogle Scholar
Rényi, A. On measures of entropy and information. In Proceedings of the fourth Berkeley Symposium on Mathematical Statistics and Probability, volume 1, pages 547–561. Berkeley, California, USA, 1961.Google Scholar
Ringel, G. Map color theorem, volume 209. Springer Science & Business Media, 1974.CrossRefGoogle Scholar
Rokach, L. and Maimon, O.. Clustering methods. In Data mining and knowledge discovery handbook, pages 321–352. Springer, 2005.CrossRefGoogle Scholar
Rosas, F. E., Mediano, P. A., Gastpar, M., and Jensen, H. J.. Quantifying high-order interdependencies via multivariate extensions of the mutual information. Physical Review E, 100(3): 032305, 2019.CrossRefGoogle ScholarPubMed
Ross, S. M. Introduction to probability models. Academic Press, 2014.Google Scholar
Sanchez, S. M. and Lucas, T. W.. Exploring the world of agent-based simulations: simple models, complex analyses. In Proceedings of the Winter Simulation Conference, volume 1, pages 116–126. IEEE, 2002.CrossRefGoogle Scholar
Santosa, F. and Symes, W. W.. Linear inversion of band-limited reflection seismograms. SIAM Journal on Scientific and Statistical Computing, 7(4):1307–1330, 1986.CrossRefGoogle Scholar
Scalas, E. Continuous-time statistics and generalized relaxation equations. The European Physical Journal B, 90:1–5, 2017.CrossRefGoogle Scholar
Schreiber, T. Measuring information transfer. Physical Review Letters, 85(2):461, 2000.CrossRefGoogle ScholarPubMed
Schwarz, G. Estimating the dimension of a model. The Annals of Statistics, pages 461–464, 1978.Google Scholar
Shannon, C. E. A mathematical theory of communication. The Bell System Technical Journal, 27(3):379–423, 1948.CrossRefGoogle Scholar
Silverman, B. W. Density estimation for statistics and data analysis. Routledge, 2018.CrossRefGoogle Scholar
Smoluchowski, M. The kinetic theory of Brownian molecular motion and suspensions. Annalen der Physik, 21:756–780, 1906.CrossRefGoogle Scholar
Song, W.-M., Di Matteo, T., and Aste, T.. Nested hierarchies in planar graphs. Discrete Applied Mathematics, 159(17):2135–2146, 2011.CrossRefGoogle Scholar
Song, W.-M., Di Matteo, T., and Aste, T.. Building complex networks with platonic solids. Physical Review E, 85(4):046115, 2012a.CrossRefGoogle ScholarPubMed
Song, W.-M., Di Matteo, T., and Aste, T.. Hierarchical information clustering by means of topologically embedded graphs. PLoS ONE, 7(3):e31929, 2012b.CrossRefGoogle ScholarPubMed
Song, Y.-Y. and Ying, L.. Decision tree methods: applications for classification and prediction. Shanghai Archives of Psychiatry, 27(2):130, 2015.Google ScholarPubMed
StanfordEncyclopedia, . https://plato.stanford.edu/entries/causation-probabilistic/. [Accessed 10 July 2024].Google Scholar
Student, . The probable error of a mean. Biometrika, 6(1):1–25, 1908.CrossRefGoogle Scholar
Sturges, H. A. The choice of a class interval. Journal of the American Statistical Association, 21(153):65–66, 1926.CrossRefGoogle Scholar
Tibshirani, R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B, 58(1):267–288, 1996.CrossRefGoogle Scholar
Tikhonov, A. N. On the stability of inverse problems. In Doklady akademii nauk (Comptes Rendus de l’Academie des Sciences de l’URSS), volume XXXIX, pages 176–179. Russian Academy of Sciences, 1943.Google Scholar
Tikhonov, A. N. On the solution of ill-posed problems and the method of regularization. In Doklady akademii nauk, volume 151, pages 501–504. Russian Academy of Sciences, 1963.Google Scholar
Tikk, D., Kóczy, L. T., and Gedeon, T. D.. A survey on universal approximation and its limits in soft computing techniques. International Journal of Approximate Reasoning, 33(2):185–202, 2003.CrossRefGoogle Scholar
Ting, H. K. On the amount of information. Theory of Probability and Its Applications, 7(4): 439–447, 1962.CrossRefGoogle Scholar
Tsallis, C. Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52(1):479–487, 1988.CrossRefGoogle Scholar
Tsallis, C. Introduction to nonextensive statistical mechanics: approaching a complex world, volume 1. Springer, 2009a.Google Scholar
Tsallis, C. Nonadditive entropy and nonextensive statistical mechanics-an overview after 20 years. Brazilian Journal of Physics, 39:337–356, 2009b.CrossRefGoogle Scholar
Tumminello, M., Aste, T., Di Matteo, T., and Mantegna, R. N.. A tool for filtering information in complex systems. Proceedings of the National Academy of Sciences, 102(30):10421–10426, 2005.CrossRefGoogle ScholarPubMed
Tumminello, M., Di Matteo, T., Aste, T., and Mantegna, R. N.. Correlation based networks of equity returns sampled at different time horizons. The European Physical Journal B, 55(2): 209–217, 2007.CrossRefGoogle Scholar
Tumminello, M., Micciche, S., Lillo, F., Piilo, J., and Mantegna, R. N.. Statistically validated networks in bipartite complex systems. PloS ONE, 6(3):e17994, 2011.CrossRefGoogle ScholarPubMed
Umarov, S., Tsallis, C., and Steinberg, S.. On a q-central limit theorem consistent with nonextensive statistical mechanics. Milan Journal of Mathematics, 76(1):307–328, 2008.CrossRefGoogle Scholar
Verdu, S. and Weissman, T.. The information lost in erasures. IEEE Transactions on Information Theory, 54(11):5030–5058, 2008.CrossRefGoogle Scholar
Viterbi, A. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory, 13(2):260–269, 1967.CrossRefGoogle Scholar
Vrbik, J. Small-sample corrections to Kolmogorov-Smirnov test statistic. Pioneer Journal of Theoretical and Applied Statistics, 15(1–2):15–23, 2018.Google Scholar
Wang, Y., Briola, A., and Aste, T.. Homological neural networks: A sparse architecture for multivariate complexity. In Proceedings of 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML), volume 221 of PMLR , pages 228–241. PMLR, 28 Jul 2023.Google Scholar
Wasserman, L. Topological data analysis. Annual Review of Statistics and Its Application, 5: 501–532, 2018.CrossRefGoogle Scholar
Wasserstein, R. L. and Lazar, N. A.. The asa statement on p-values: Context, process, and purpose, 2016.CrossRefGoogle Scholar
Whitney, H. Planar graphs. In Hassler Whitney Collected Papers, pages 135–146. Springer, 1933.Google Scholar
Wiener, N. The theory of prediction. Modern mathematics for engineers, 1956.Google Scholar
Wiener, N. Cybernetics or Control and Communication in the Animal and the Machine. MIT press, 2019.CrossRefGoogle Scholar
Wilkinson, J. H. Modern error analysis. SIAM Review, 13(4):548–568, 1971.CrossRefGoogle Scholar
Wilkinson, J. H. Rounding errors in algebraic processes. Courier Corporation, 1994.Google Scholar
Wilks, S. S. Certain generalizations in the analysis of variance. Biometrika, 24(3/4):471–494, 1934.CrossRefGoogle Scholar
Williams, P. L. and Beer, R. D.. Nonnegative decomposition of multivariate information. arXiv preprint arXiv:1004.2515, 2010.Google Scholar
Williams, P. L. and Beer, R. D.. Generalized measures of information transfer. arXiv preprint arXiv:1102.1507, 2011.Google Scholar
Yeung, R. W. A new outlook on shannon’s information measures. IEEE Transactions on Information Theory, 37(3):466–474, 1991.CrossRefGoogle Scholar
Young, N. An introduction to Hilbert space. Cambridge University Press, 1988.CrossRefGoogle Scholar
Zou, H. and Hastie, T.. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society Series B: Statistical Methodology, 67(2):301–320, 2005.CrossRefGoogle Scholar

Accessibility standard: Unknown

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Tomaso Aste, University College London
  • Book: Probabilistic Data-Driven Modeling
  • Online publication: 17 May 2025
  • Chapter DOI: https://doi.org/10.1017/9781009221887.033
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Tomaso Aste, University College London
  • Book: Probabilistic Data-Driven Modeling
  • Online publication: 17 May 2025
  • Chapter DOI: https://doi.org/10.1017/9781009221887.033
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Tomaso Aste, University College London
  • Book: Probabilistic Data-Driven Modeling
  • Online publication: 17 May 2025
  • Chapter DOI: https://doi.org/10.1017/9781009221887.033
Available formats
×