Abstract
Maintaining the a-posteriori distribution of categorical states given a sequence of noisy and ambiguous observations, e.g. sensor data, can lead to situations where one observation can correspond to a large number of different states. We call these states symmetrical as they cannot be distinguished given the observation. Considering each of them during the inference is computationally infeasible, even for small scenarios. However, the number of situations (called hypotheses) can be reduced by abstracting from particular ones and representing all symmetrical in a single abstract state. We propose a novel Bayesian Filtering algorithm that performs this abstraction. The algorithm that we call Lifted Marginal Filtering (LiMa) is inspired by Lifted Inference and combines techniques known from Computational State Space Models and Multiset Rewriting Systems to perform efficient sequential inference on a parametric multiset state description. We demonstrate that our approach is working by comparing LiMa with conventional filtering.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
We use the term density to refer to densities over continuous domains as well as probability distributions over finite domains.
- 2.
A multiset over some set S is defined as a partial map from S to \(\mathbb {N}\). We use \([\![\, n_1s_1,n_2s_s,n_3s_3 \,]\!]\) to denote the multiset containing \(s_1,s_2\) and \(s_3\) with the corresponding cardinalities. We use \(\mathcal {M}(S)\) to refer to the set of all multisets over S.
References
Ahmadi, B., Kersting, K., Sanner, S.: Multi-evidence lifted message passing, with application to pagerank and the kalman filter. In: Proceedings-International Joint Conference on Artificial Intelligence, p. 1152 (2011)
Baker, C.L., Saxe, R., Tenenbaum, J.B.: Action understanding as inverse planning. Cognition 113(3), 329–349 (2009)
Barbuti, R., Levi, F., Milazzo, P., Scatena, G.: Maximally parallel probabilistic semantics for multiset rewriting. Fundam. Inform. 112(1), 1–17 (2011)
Berry, G., Boudol, G.: The chemical abstract machine. In: POPL, pp. 81–94. ACM, San Francisco(1990)
Bistarelli, S., Cervesato, I., Lenzini, G., Marangoni, R., Martinelli, F.: On representing biological systems through multiset rewriting. In: Moreno-Díaz, R., Pichler, F. (eds.) EUROCAST 2003. LNCS, vol. 2809, pp. 415–426. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45210-2_38
Boutilier, C., Reiter, R., Price, B.: Symbolic dynamic programming for first-order MDPs. In: Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, vol. 1, pp. 690–700 (2001)
Choi, J., Amir, E., Xu, T., Valocchi, A.J.: Learning relational kalman filtering. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, pp. 2539–2546 (2015)
Choi, J., Hill, D.J., Amir, E.: Lifted inference for relational continuous models. In: Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, UAI 2010, pp. 126–134. AUAI Press (2010)
Fox, V., Hightower, J., Liao, L., Schulz, D., Borriello, G.: Bayesian filtering for location estimation. IEEE Pervasive Comput. 2(3), 24–33 (2003)
Geier, T., Biundo, S.: Approximate online inference for dynamic Markov logic networks. In: 23rd IEEE International Conference on Tools with Artificial Intelligence, pp. 764–768. IEEE (2011)
Huang, J., Guestrin, C., Jiang, X., Guibas, L.: Exploiting probabilistic independence for permutations. In: AISTATS, Clearwater, USA, pp. 248–255 (2009)
Kersting, K., Ahmadi, B., Natarajan, S.: Counting belief propagation. In: UAI, Montreal, Canada, pp. 277–284 (2009)
Kersting, K.: Lifted probabilistic inference. In: 20th European Conference on Artificial Intelligence, ECAI 2012. Frontiers in Artificial Intelligence and Applications, vol. 242. IOS Press (2012)
Khardon, R., Sanner, S.: Stochastic planning and lifted inference. arXiv preprint arXiv:1701.01048 (2017)
Kimmig, A., Mihalkova, L., Getoor, L.: Lifted graphical models: a survey. Mach. Learn. 99, 1–45 (2015)
Kondor, R., Howard, A., Jebara, T.: Multi-object tracking with representations of the symmetric group. In: AISTATS, vol. 2, pp. 211–218 (2007)
Krüger, F., Nyolt, M., Yordanova, K., Hein, A., Kirste, T.: Computational state space models for activity and intention recognition. A feasibility study. PLOS ONE 9(11), e109381 (2014)
Poole, D.: First-order probabilistic inference. In: IJCAI, pp. 985–991 (2003)
Ramírez, M., Geffner, H.: Goal recognition over POMDPs: inferring the intention of a POMDP agent. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, pp. 2009–2014, July 2011
Sanner, S., Boutilier, C.: Practical solution techniques for first-order MDPs. Artif. Intell. 173, 748–788 (2009)
Schröder, M., Lüdtke, S., Bader, S., Krüger, F., Kirste, T.: An office scenario dataset for benchmarking observation-equivalent entities (2016). http://dx.doi.org/10.18453/rosdok_id00000138
Schröder, M., Lüdtke, S., Bader, S., Krüger, F., Kirste, T.: Abstracting from observation-equivalent entities in human behavior modeling. In: AAAI Workshop: Plan, Activity, and Intent Recognition, February 2017
Van Den Broeck, G., Taghipour, N., Meert, W., Davis, J., De Raedt, L.: Lifted probabilistic inference by first-order knowledge compilation. In: IJCAI, pp. 2178–2185 (2011)
Venugopal, D., Gogate, V.: Evidence-based clustering for scalable inference in Markov logic. In: Calders, T., Esposito, F., Hüllermeier, E., Meo, R. (eds.) ECML PKDD 2014. LNCS, vol. 8726, pp. 258–273. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44845-8_17
Wilson, D.H., Atkeson, C.: Simultaneous tracking and activity recognition (STAR) using many anonymous, binary sensors. In: Gellersen, H.-W., Want, R., Schmidt, A. (eds.) Pervasive 2005. LNCS, vol. 3468, pp. 62–79. Springer, Heidelberg (2005). doi:10.1007/11428572_5
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Schröder, M., Lüdtke, S., Bader, S., Krüger, F., Kirste, T. (2017). LiMa: Sequential Lifted Marginal Filtering on Multiset State Descriptions. In: Kern-Isberner, G., Fürnkranz, J., Thimm, M. (eds) KI 2017: Advances in Artificial Intelligence. KI 2017. Lecture Notes in Computer Science(), vol 10505. Springer, Cham. https://doi.org/10.1007/978-3-319-67190-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-67190-1_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-67189-5
Online ISBN: 978-3-319-67190-1
eBook Packages: Computer ScienceComputer Science (R0)