Graphical model selection for a particular class of continuous-time processes

Mattia Zorzi

Kybernetika (2019)

  • Volume: 55, Issue: 5, page 782-801
  • ISSN: 0023-5954

Abstract

top
Graphical models provide an undirected graph representation of relations between the components of a random vector. In the Gaussian case such an undirected graph is used to describe conditional independence relations among such components. In this paper, we consider a continuous-time Gaussian model which is accessible to observations only at time T . We introduce the concept of infinitesimal conditional independence for such a model. Then, we address the corresponding graphical model selection problem, i. e. the problem to estimate the graphical model from data. Finally, simulation studies are proposed to test the effectiveness of the graphical model selection procedure.

How to cite

top

Zorzi, Mattia. "Graphical model selection for a particular class of continuous-time processes." Kybernetika 55.5 (2019): 782-801. <http://eudml.org/doc/295064>.

@article{Zorzi2019,
abstract = {Graphical models provide an undirected graph representation of relations between the components of a random vector. In the Gaussian case such an undirected graph is used to describe conditional independence relations among such components. In this paper, we consider a continuous-time Gaussian model which is accessible to observations only at time $T$. We introduce the concept of infinitesimal conditional independence for such a model. Then, we address the corresponding graphical model selection problem, i. e. the problem to estimate the graphical model from data. Finally, simulation studies are proposed to test the effectiveness of the graphical model selection procedure.},
author = {Zorzi, Mattia},
journal = {Kybernetika},
keywords = {sparse inverse covariance selection; regularization; graphical models; entropy; optimization},
language = {eng},
number = {5},
pages = {782-801},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Graphical model selection for a particular class of continuous-time processes},
url = {http://eudml.org/doc/295064},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Zorzi, Mattia
TI - Graphical model selection for a particular class of continuous-time processes
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 5
SP - 782
EP - 801
AB - Graphical models provide an undirected graph representation of relations between the components of a random vector. In the Gaussian case such an undirected graph is used to describe conditional independence relations among such components. In this paper, we consider a continuous-time Gaussian model which is accessible to observations only at time $T$. We introduce the concept of infinitesimal conditional independence for such a model. Then, we address the corresponding graphical model selection problem, i. e. the problem to estimate the graphical model from data. Finally, simulation studies are proposed to test the effectiveness of the graphical model selection procedure.
LA - eng
KW - sparse inverse covariance selection; regularization; graphical models; entropy; optimization
UR - http://eudml.org/doc/295064
ER -

References

top
  1. Alpago, D., Zorzi, M., Ferrante, A., 10.1109/lcsys.2018.2845943, IEEE Control Systems Lett. 2 (2018), 4, 659-664. DOI10.1109/lcsys.2018.2845943
  2. Avventi, E., Lindquist, A., Wahlberg, B., 10.1109/tac.2012.2231551, IEEE Trans. Automat. Control 58 (2013), 1167-1178. MR3047919DOI10.1109/tac.2012.2231551
  3. Baggio, G., 10.1109/tac.2018.2794407, IEEE Trans. Automat- Control 63 (2018), 10, 3510-3515. MR3866257DOI10.1109/tac.2018.2794407
  4. Banerjee, O., Ghaoui, L. El, d'Aspremont, A., Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data., J. Machine Learning Res. 9 (2008), 485-516. MR2417243
  5. Boyd, S., Vandenberghe, L., 10.1017/cbo9780511804441, Cambridge Univ. Press, Cambridge 2004. Zbl1058.90049MR2061575DOI10.1017/cbo9780511804441
  6. Byrnes, C., Gusev, S., Lindquist, A., 10.1137/s0363012997321553, SIAM J. Optim. 37 (1998), 211-229. MR1642019DOI10.1137/s0363012997321553
  7. Byrnes, C. I., Georgiou, T. T., Lindquist, A., 10.1109/78.875475, IEEE Trans. Signal Process. 48 (2000), 3189-3205. MR1791083DOI10.1109/78.875475
  8. Candes, E., Plan, Y., 10.1109/jproc.2009.2035722, Proc. IEEE 98 (2010), 925-936. DOI10.1109/jproc.2009.2035722
  9. Candes, E., Recht, B., 10.1145/2184319.2184343, Comm. ACM 55 (2012), 111-119. MR2565240DOI10.1145/2184319.2184343
  10. Chandrasekaran, V., Parrilo, P., Willsky, A., 10.1214/12-aos1020, Ann. Statist. 40 (2010), 1935-2013. MR3059067DOI10.1214/12-aos1020
  11. Chandrasekaran, V., Shah, P., 10.1007/s10107-016-0998-2, Math. Program. 161 (2017), (1-2), 1-32. MR3592772DOI10.1007/s10107-016-0998-2
  12. Cover, T., Thomas, J., 10.1002/0471200611, Wiley, New York 1991. DOI10.1002/0471200611
  13. d'Aspremont, A., Banerjee, O., Ghaoui, L. El, 10.1137/060670985, SIAM J. Matrix Analysis Appl. 30 (2008), 56-66. MR2399568DOI10.1137/060670985
  14. Dempster, A., 10.2307/2528966, Biometrics 28 (1972), 157-175. MR3931974DOI10.2307/2528966
  15. Ferrante, A., Pavon, M., 10.1109/tit.2011.2143970, IEEE Trans. Inform. Theory 57 (2011), 3925-3931. MR2817064DOI10.1109/tit.2011.2143970
  16. Ferrante, A., Pavon, M., Ramponi, F., 10.1109/tac.2008.920238, IEEE Trans. Autom. Control 53 (2008), 954-967. MR2419442DOI10.1109/tac.2008.920238
  17. Friedman, J., Hastie, T., Tibshirani, R., 10.1093/biostatistics/kxm045, Biostatistics 9 (2008), 432-441. DOI10.1093/biostatistics/kxm045
  18. Grant, M., Boyd, S., CVX: Matlab software for disciplined convex programming, version 2.1., 2014. 
  19. Gu, S., Betzel, R., Mattar, M., Cieslak, M., Delio, P., Grafton, S., Pasqualetti, F., Bassett, D., 10.1016/j.neuroimage.2017.01.003, NeuroImage 148 (2017), 305-317. DOI10.1016/j.neuroimage.2017.01.003
  20. Huang, J., Liu, N., Pourahmadi, M., Liu, L., 10.1093/biomet/93.1.85, Biometrika 93 (2006), 85-98. MR2277742DOI10.1093/biomet/93.1.85
  21. Huotari, N., Raitamaa, L., Helakari, H., Kananen, J., Raatikainen, V., Rasila, A., Tuovinen, T., Kantola, J., Borchardt, V., Kiviniemi, V., Korhonen, V., 10.3389/fnins.2019.00279, Frontiers Neurosci. 13 (2019), 279. DOI10.3389/fnins.2019.00279
  22. Jalali, A., Sanghavi, S., Learning the dependence graph of time series with latent factors., In: International Conference on Machine Learning Edinburgh 2012. 
  23. Koller, D., Friedman, N., Probabilistic Graphical Models: Principles and Techniques., MIT Press, 2009. MR2778120
  24. Lauritzen, S., Graphical Models., Oxford University Press, Oxford 1996. MR1419991
  25. Meinshausen, N., Bühlmann, P., 10.1214/009053606000000281, Annals Statist. 34 (2006), 1436-1462. MR2278363DOI10.1214/009053606000000281
  26. Pearl, J., 10.1007/978-94-017-1735-9_12, In: Quantified representation of uncertainty and imprecision, Springer 1998, pp. 367-389. MR1743892DOI10.1007/978-94-017-1735-9_12
  27. Ringh, A., Karlsson, J., Lindquist, A., 10.1137/17m1127922, SIAM J. Control Optim. 56 (2018), 2, 913-944. MR3775123DOI10.1137/17m1127922
  28. Songsiri, J., Dahl, J., Vandenberghe, L., Graphical models of autoregressive processes., In: Convex Optimization in Signal Processing and Communications (D. Palomar and Y. Eldar, eds.), Cambridge Univ. Press, Cambridge 2010, pp. 1-29. MR2767565
  29. Songsiri, J., Vandenberghe, L., Topology selection in graphical models of autoregressive processes., J. Machine Learning Res. 11 (2010), 2671-2705. MR2738780
  30. Yue, Z., Thunberg, J., Ljung, L., Gonçalves, J., Identification of sparse continuous-time linear systems with low sampling rate: Exploring matrix logarithms., arXiv preprint arXiv:1605.08590, 2016. 
  31. {Zhu}, B., {Baggio}, G., 10.1109/tac.2018.2836984, IEEE Trans. Automat. Control 64 (2019), 2, 820-825. MR3912133DOI10.1109/tac.2018.2836984
  32. Zorzi, M., 10.1109/tac.2013.2293218, IEEE Trans. Automat. Control 59 (2014), 892-904. MR3199341DOI10.1109/tac.2013.2293218
  33. Zorzi, M., 10.1007/s00498-013-0118-2, Math. Control Signals Systems 26 (2014), 259-278. MR3201948DOI10.1007/s00498-013-0118-2
  34. Zorzi, M., 10.1016/j.automatica.2015.09.023, Automatica 62 (2015), 87-92. MR3423974DOI10.1016/j.automatica.2015.09.023
  35. Zorzi, M., 10.1109/tac.2014.2359713, IEEE Trans. Automat. Control 60 (2015), 1647-1652. MR3353402DOI10.1109/tac.2014.2359713
  36. Zorzi, M., 10.1016/j.automatica.2019.108516, Automatica 109 (2019), 108516. MR3989933DOI10.1016/j.automatica.2019.108516
  37. Zorzi, M., Sepulchre, R., 10.1109/tac.2015.2491678, IEEE Trans. Automat. Control 61 (2016), 2327-2340. MR3545056DOI10.1109/tac.2015.2491678

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.