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The second level encodes the probability of choosing a concrete policy: P (Q2t = π|St−1 = s, Q1t = π ) = σπ (s, π). The third level encodes the probability of choosing a concrete action: P (At = a|St−1 = s, Q2t = π) = σπ (s, a). The last level encodes the world model: P (St = s |St−1 = s, At = a). authors are interested in inferring what policy an agent is following by observing its effects in the world. ) A (stochastic) policy is a (probabilistic) mapping from (fully observed) states to actions: σ π (s, a) = P (do action a|in state s).

We therefore need to use approximate inference. 1. 4 Fault diagnosis in hybrid systems One of the most important applications of hybrid systems is fault diagnosis. 32: A DBN for blind deconvolution. 33: The two-tank system. The goal is to infer when pipes are blocked or have burst, or sensors have broken, from (noisy) observations of the flow out of tank 1, F 1o, out of tank 2, F 2o, or between tanks 1 and 2, F 12. R1o is a hidden variable representing the resistance of the pipe out of tank 1, P 1 is a hidden variable representing the pressure in tank 1, etc.

10), but are always flattened into a single level state space for speed and ease of processing. Simiarly, combinations of weighted transducers [Moh96, PR97b] are always flattened into a single transducer before use. Although it is always possible to convert an HHMM to an HMM, just as with any DBN, there are several disadvantages to doing so: • Flattening loses modularity, since the parameters of the sub-HMMs get combined in a complex way, as we have just seen. , [JLM92, JM00]), takes O(T 3 ) no matter what the grammar is.

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Dynamic Bayesian Networks Representation, Inference And Learning by Kevin Patrick Murphy


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