The Living Thing / Notebooks :

Contagion processes and their statistics

The spread of quantities of things - earthquakes/diseases/innovations/credit defaults - between different georegions/populations/vertices/banks/variates.

In my own internal taxonomy, I file about contagion -like growth within a single population as branching processes, and care about multivariate issues here.

For now this is a mere collection of contagion research links because I am hunting for data sets; no fancy analysis for the moment.

I’ll annotate a couple of useful models here, and hopefully talk about identifiability and noisy/incomplete data issues using a graphical model formalism.

Dirichlet Hawkes process

I don’t know anything about these, but have had them referred to me as a plausible multivariate something something. See DFAS15, YaZh13, PiCh14 and compare with the Dirichlet Poisson process.

Refs

AhEl07
Ahmed, E., & Elgazzar, A. S.(2007) On fractional order differential equations model for nonlocal epidemics. Physica A: Statistical Mechanics and Its Applications, 379(2), 607–614. DOI.
AmCM13
Amini, H., Cont, R., & Minca, A. (2013) Resilience to Contagion in Financial Networks. Mathematical Finance, n/a-n/a. DOI.
Arag12
Aragón, T. J.(2012) Applied epidemiology using R. . MedEpi Publishing. http://www. medepi. net/epir/index. html. Calendar Time. Accessed
ArMS09
Aral, S., Muchnik, L., & Sundararajan, A. (2009) Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks. Proceedings of the National Academy of Sciences, 106(51), 21544–21549. DOI.
AzGO08
Azizpour, S., Giesecke, K., & others. (2008) Self-exciting corporate defaults: contagion vs frailty. . Stanford University working paper series
BaMu14
Bacry, E., & Muzy, J.-F. (2014) Second order statistics characterization of Hawkes processes and non-parametric estimation. arXiv:1401.0903 [Physics, Q-Fin, Stat].
BaBS09
Barnett, L., Barrett, A. B., & Seth, A. K.(2009) Granger causality and transfer entropy are equivalent for Gaussian variables. Physical Review Letters, 103(23), 238701.
BaBS10
Barrett, A. B., Barnett, L., & Seth, A. K.(2010) Multivariate Granger causality and generalized variance. Phys. Rev. E, 81(4), 041907. DOI.
BaSa13
Battey, H., & Sancetta, A. (2013) Conditional estimation for dependent functional data. Journal of Multivariate Analysis, 120, 1–17. DOI.
BrLB00
Brault, R., Lim, N., & d’Alché-Buc, F. (n.d.) Scaling up Vector Autoregressive Models With Operator-Valued Random Fourier Features.
CSMF12
Caccioli, F., Shrestha, M., Moore, C., & Farmer, J. D.(2012) Stability analysis of financial contagion due to overlapping portfolios. arXiv:1210.5987.
CaFe08
Cauchemez, S., & Ferguson, N. M.(2008) Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London. Journal of The Royal Society Interface, 5(25), 885–897. DOI.
CeMa07
Centola, D., & Macy, M. W.(2007) Complex contagions and the weakness of long ties. American Journal of Sociology, 113(3), 702.
Chon08
Chongsuvivatwong, V. (2008) Analysis of epidemiological data using R and Epicalc. . Book Unit, Faculty of Medicine, Prince of Songkla University Thailand
COMG07
Cook, A. R., Otten, W., Marion, G., Gibson, G. J., & Gilligan, C. A.(2007) Estimation of multiple transmission rates for epidemics in heterogeneous populations. Proceedings of the National Academy of Sciences, 104(51), 20392–20397. DOI.
DaEi03
Dahlhaus, R., & Eichler, M. (2003) Causality and graphical models in time series analysis. Oxford Statistical Science Series, 115–137.
DGSS14
Daneshmand, H., Gomez-Rodriguez, M., Song, L., & Schölkopf, B. (2014) Estimating Diffusion Network Structures: Recovery Conditions, Sample Complexity & Soft-thresholding Algorithm. In ICML.
DDTU16
Du, N., Dai, H., Trivedi, R., Upadhyay, U., Gomez-Rodriguez, M., & Song, L. (2016) Recurrent Marked Temporal Point Processes: Embedding Event History to Vector. In Proceedings of the 22Nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 1555–1564). New York, NY, USA: ACM DOI.
DFAS15
Du, N., Farajtabar, M., Ahmed, A., Smola, A. J., & Song, L. (2015) Dirichlet-Hawkes Processes with Applications to Clustering Continuous-Time Document Streams. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 219–228). New York, NY, USA: ACM DOI.
DSGZ13
Du, N., Song, L., Gomez-Rodriguez, M., & Zha, H. (2013) Scalable influence estimation in continuous-time diffusion networks. In Advances in neural information processing systems (pp. 3147–3155).
DSYS12
Du, N., Song, L., Yuan, M., & Smola, A. J.(2012) Learning networks of heterogeneous influence. In Advances in Neural Information Processing Systems (pp. 2780–2788).
Eich00
Eichler, M. (2000) Graphical Models in Time Series Analysis.
Eich01
Eichler, Michael. (2001) Granger-causality graphs for multivariate time series. Granger-Causality Graphs for Multivariate Time Series.
Eich07
Eichler, Michael. (2007) Granger causality and path diagrams for multivariate time series. Journal of Econometrics, 137(2), 334–353. DOI.
EiDD16
Eichler, Michael, Dahlhaus, R., & Dueck, J. (2016) Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions. Journal of Time Series Analysis, n/a-n/a. DOI.
FeLO06
Ferland, R., Latour, A., & Oraichi, D. (2006) Integer-Valued GARCH Process. Journal of Time Series Analysis, 27(6), 923–942. DOI.
GiRe01
Gibson, G. J., & Renshaw, E. (2001) Likelihood estimation for stochastic compartmental models using Markov chain methods. Statistics and Computing, 11(4), 347–358. DOI.
GlYo16
Glasserman, P., & Young, H. P.(2016) Contagion in Financial Networks. Journal of Economic Literature, 54(3), 779–831. DOI.
GLBS14
Gomez-Rodriguez, M., Leskovec, J., Balduzzi, D., & Schölkopf, B. (2014) Uncovering the structure and temporal dynamics of information propagation. Network Science, 2(01), 26–65. DOI.
GoLS13
Gomez-Rodriguez, M., Leskovec, J., & Schölkopf, B. (2013) Structure and Dynamics of Information Pathways in Online Media. In Proceedings of the Sixth ACM International Conference on Web Search and Data Mining (pp. 23–32). New York, NY, USA: ACM DOI.
Gran63
Granger, C. W. J.(1963) Economic processes involving feedback. Information and Control, 6(1), 28–48. DOI.
Gran04
Granger, C. W. J.(2004) Time series analysis, cointegration, and applications. American Economic Review, 421–425.
GIKM16
Greenhill, C., Isaev, M., Kwan, M., & McKay, B. D.(2016) The average number of spanning trees in sparse graphs with given degrees. arXiv:1606.01586 [Math].
GrPR99
Greenland, S., Pearl, J., & Robins, J. M.(1999) Causal diagrams for epidemiologic research. Epidemiology, 10(1), 37.
GHFZ13
Guille, A., Hacid, H., Favre, C., & Zighed, D. A.(2013) Information Diffusion in Online Social Networks: A Survey. SIGMOD Rec., 42(2), 17–28. DOI.
HaSä10
Hartikainen, J., & Särkkä, S. (2010) Kalman filtering and smoothing solutions to temporal Gaussian process regression models. In 2010 IEEE International Workshop on Machine Learning for Signal Processing (pp. 379–384). DOI.
IrMo11
Iribarren, J. L., & Moro, E. (2011) Branching dynamics of viral information spreading. Physical Review E, 84(4), 046116. DOI.
IyVV11
Iyengar, R., Van den Bulte, C., & Valente, T. W.(2011) Opinion leadership and social contagion in new product diffusion. Marketing Science, 30(2), 195–212. DOI.
KoDu00
Koopman, S. J., & Durbin, J. (2000) Fast Filtering and Smoothing for Multivariate State Space Models. Journal of Time Series Analysis, 21(3), 281–296. DOI.
KrGH14
Kramer, A. D. I., Guillory, J. E., & Hancock, J. T.(2014) Experimental evidence of massive-scale emotional contagion through social networks. Proceedings of the National Academy of Sciences, 111(24), 8788–8790. DOI.
KrPa14
Kraus, A., & Panaretos, V. M.(2014) Frequentist estimation of an epidemic’s spreading potential when observations are scarce. Biometrika, 101(1), 141–154. DOI.
LSTB15
Lakshmanan, K. C., Sadtler, P. T., Tyler-Kabara, E. C., Batista, A. P., & Yu, B. M.(2015) Extracting Low-Dimensional Latent Structure from Time Series in the Presence of Delays. Neural Computation, 27(9), 1825–1856. DOI.
LiLR16
Li, Y., Liang, Y., & Risteski, A. (2016) Recovery Guarantee of Non-negative Matrix Factorization via Alternating Updates. In D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, & R. Garnett (Eds.), Advances in Neural Information Processing Systems 29 (pp. 4988–4996). Curran Associates, Inc.
LiKB10
Liu, K.-Y., King, M., & Bearman, P. S.(2010) Social influence and the autism epidemic. American Journal of Sociology, 115(5), 1387.
OgMK93
Ogata, Y., Matsu’ura, R. S., & Katsura, K. (1993) Fast likelihood computation of epidemic type aftershock-sequence model. Geophysical Research Letters, 20(19), 2143–2146. DOI.
PiCh14
Pinto, J. C. L., & Chahed, T. (2014) Modeling Multi-topic Information Diffusion in Social Networks Using Latent Dirichlet Allocation and Hawkes Processes. In Proceedings of the 2014 Tenth International Conference on Signal-Image Technology and Internet-Based Systems (pp. 339–346). Washington, DC, USA: IEEE Computer Society DOI.
PiTV12
Pinto, P. C., Thiran, P., & Vetterli, M. (2012) Locating the Source of Diffusion in Large-Scale Networks. Physical Review Letters, 109(6), 068702. DOI.
PoRT11
Pooseh, S., Rodrigues, H. S., & Torres, D. F. M.(2011) Fractional derivatives in Dengue epidemics. arXiv:1108.1683 [Math, Q-Bio], 739–742. DOI.
PoHo15
Pouget-Abadie, J., & Horel, T. (2015) Inferring Graphs from Cascades: A Sparse Recovery Framework. In Proceedings of The 32nd International Conference on Machine Learning.
RMAR07
Rasmussen, J. G., Møller, J., Aukema, B. H., Raffa, K. F., & Zhu, J. (2007) Continuous time modelling of dynamical spatial lattice data observed at sparsely distributed times. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69(4), 701–713. DOI.
RoDH11
Roca, C. P., Draief, M., & Helbing, D. (2011) Percolate or die: Multi-percolation decides the struggle between competing innovations.
SaSo11a
Saichev, A., & Sornette, D. (2011a) Generating functions and stability study of multivariate self-excited epidemic processes. arXiv:1101.5564 [Cond-Mat, Physics:physics].
SaSo11b
Saichev, A., & Sornette, D. (2011b) Hierarchy of temporal responses of multivariate self-excited epidemic processes. arXiv:1101.1611 [Cond-Mat, Physics:physics].
SäSH13
Särkkä, S., Solin, A., & Hartikainen, J. (2013) Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering. IEEE Signal Processing Magazine, 30(4), 51–61. DOI.
ScCV10
Schoenberg, F. P., Chu, A., & Veen, A. (2010) On the relationship between lower magnitude thresholds and bias in epidemic-type aftershock sequence parameter estimates. Journal of Geophysical Research: Solid Earth, 115(B4), B04309. DOI.
ShTh11
Shalizi, C. R., & Thomas, A. C.(2011) Homophily and Contagion Are Generically Confounded in Observational Social Network Studies. Sociological Methods & Research, 40(2), 211–239. DOI.
ShBG16
Shen, Y., Baingana, B., & Giannakis, G. B.(2016) Nonlinear Structural Vector Autoregressive Models for Inferring Effective Brain Network Connectivity. arXiv:1610.06551 [Stat].
SDKD13
Solé-Ribalta, A., De Domenico, M., Kouvaris, N. E., Díaz-Guilera, A., Gómez, S., & Arenas, A. (2013) Spectral properties of the Laplacian of multiplex networks. Physical Review E, 88(3), 032807. DOI.
Sorn05
Sornette, D. (2005) Constraints on the size of the smallest triggering earthquake from the epidemic-type aftershock sequence model, Båth’s law, and observed aftershock sequences. Journal of Geophysical Research, 110(B8). DOI.
StHL16
Stegehuis, C., van der Hofstad, R., & van Leeuwaarden, J. S. H.(2016) Epidemic spreading on complex networks with community structures. Scientific Reports, 6, 29748. DOI.
Stig10
Stiglitz, J. E.(2010) Contagion, liberalization, and the optimal structure of globalization. Journal of Globalization and Development, 1(2), 2. DOI.
SMYH12
Sugihara, G., May, R., Ye, H., Hsieh, C., Deyle, E., Fogarty, M., & Munch, S. (2012) Detecting Causality in Complex Ecosystems. Science, 338(6106), 496–500. DOI.
Verm14
Verma, I. M.(2014) Editorial Expression of Concern: Experimental evidence of massivescale emotional contagion through social networks. Proceedings of the National Academy of Sciences, 201412469. DOI.
WXDL00
Wang, Y., Xie, B., Du, N., Le Song, E. D. U., & EDU, G. (n.d.) Isotonic Hawkes Processes.
WaDo07
Watts, D. J., & Dodds, P. S.(2007) Influentials, Networks, and Public Opinion Formation. Journal of Consumer Research, 34(4), 441–458. DOI.
YLWS11
Yang, D.-P., Lin, H., Wu, C.-X., & Shuai, J. (2011) Topological conditions of scale-free networks for cooperation to evolve. arXiv:1106.5386.
YaZh13
Yang, S.-H., & Zha, H. (2013) Mixture of Mutually Exciting Processes for Viral Diffusion. In Proceedings of The 30th International Conference on Machine Learning (Vol. 28, pp. 1–9).
Youn09
Young, H. P.(2009) Innovation diffusion in heterogeneous populations: Contagion, social influence, and social learning. The American Economic Review, 99(5), 1899–1924.
ZhZS13
Zhou, K., Zha, H., & Song, L. (2013) Learning triggering kernels for multi-dimensional Hawkes processes. In Proceedings of the 30th International Conference on Machine Learning (ICML-13) (pp. 1301–1309).