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Moment-Based Variational Inference for Markov Jump Processes Christian Wildner and Heinz Koeppl Department of Electrical Engineering and Information Technology Technische Universitt Darmstadt, Germany June 11, 2019 | Moment-Based

  1. Moment-Based Variational Inference for Markov Jump Processes Christian Wildner and Heinz Koeppl Department of Electrical Engineering and Information Technology Technische Universität Darmstadt, Germany June 11, 2019 | Moment-Based Variational Inference for Markov Jump Processes | Christian Wildner, Heinz Koeppl | 1

  2. Introduction Model Class: Markov jump process / continuous time Markov chain • Applications in many domains (finance, social networks, healthcare, systems biology, etc.) • Data-driven modelling requires latent state estimation June 11, 2019 | Moment-Based Variational Inference for Markov Jump Processes | Christian Wildner, Heinz Koeppl | 2

  3. Introduction Model Class: Markov jump process / continuous time Markov chain • Applications in many domains (finance, social networks, healthcare, systems biology, etc.) • Data-driven modelling requires latent state estimation Problem: Hard/intractable for large state spaces June 11, 2019 | Moment-Based Variational Inference for Markov Jump Processes | Christian Wildner, Heinz Koeppl | 3

  4. Introduction Model Class: Markov jump process / continuous time Markov chain • Applications in many domains (finance, social networks, healthcare, systems biology, etc.) • Data-driven modelling requires latent state estimation Problem: Hard/intractable for large state spaces Proposed solution: new variational inference approach based on • transition space partitioning • gradient-based optimization June 11, 2019 | Moment-Based Variational Inference for Markov Jump Processes | Christian Wildner, Heinz Koeppl | 4

  5. Markov Jump Processes An MJP is fully defined by • an initial distribution • a transition function with June 11, 2019 | Moment-Based Variational Inference for Markov Jump Processes | Christian Wildner, Heinz Koeppl | 5

  6. Markov Jump Processes An MJP is fully defined by • an initial distribution • a transition function with June 11, 2019 | Moment-Based Variational Inference for Markov Jump Processes | Christian Wildner, Heinz Koeppl | 6

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