Lifted Marginal Inference

Lifted Marginal Inference is a Bayesian Filtering approach that exploits symmetries in the state space that arise due to the observation data to make probabilistic inference feasible for large scenarios that exhibit such symmetries.


Bayesian Filtering in discrete state spaces resulting from symbolic models (e.g. models of human behaviour) is a challenging task because the state space space can grow very lare due to redundancies and symmetries. One of these symmetries is observation-equivalence, i.e. multiple states that are distinct, but cannot be distinguished based on the sensor data. This is for instance the case in multiple person tracking by use of anonymous sensors or assisted manufacturing, where the identity of different tools and parts is uncertain, but cannot be discarded completely. Lifted Marginal Filtering is a Bayesian Filtering algorithm that exploits these symmetries by representing symmetrical states by a single, parametric state representation. The representation, and the state dynamics is based on Probabilistic Multiset Rewriting Systems. The concept to exploit the symmetries is inspired by Lifted Probabilistic Inference algorithms. Bayesian Filtering tasks that exhibit such symmetries occur for example in the context of smart environments, assisted living, and security.

Example of the abstract state representation in the Lifted Marginal Filtering approach (LiMa)
The left part describes the LiMa representation of a situation with three agents (named A, B and C) being at one location. The representation is separated into (1) the structure of the entities in the situation and (b) the actual values that can be inserted into that structure. In the right part, one of the agents has moved to the second location. Different to the grounded representation, LiMa describes with this single representation the following three situations: (1) agent A being at the right location and the other agents being at the left location, (2) agent B being at the right location, or (3) agent C being at the right location.