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Forward and Backward Inference in Spatial Cognition

Figure 2

Generative model for spatial cognition.

The agent's dynamical model is embodied in the red arrows, , and its observation model in the blue arrows, . All of the agent's spatial computations are based on statistical inference in this same probabilistic generative model. The computations are defined by what variables are known (gray shading) and what the agent wishes to estimate. Sensory Imagery Given a known initial state, , and virtual motor commands , the agent can generate sensory imagery . Decision Making Given initial state , a sequence of putative motor commands (eg. left turn), and sensory goals , an agent can compute the likelihood of attaining those goals given and , . This computation requires a single sweep of forward inference. The agent can then repeat this for a second putative motor sequence (eg. right turn), and decide which turn to take based on the likelihood ratio. Model Selection Here, the agent has made observations and computes the likelihood ratio under two different models of the environment. Planning can be formulated as estimation of a density over actions given current state and desired sensory states, . This requires a forward sweep to compute the hidden states that are commensurate with the goals, and a backward sweep to compute the motor commands that will produce the required hidden state trajectory.

doi: https://doi.org/10.1371/journal.pcbi.1003383.g002