Scan-Parallel Variational Inference for event-driven Latent Jump Models

Key points

• Continuous-time latent state-space models are widely used for irregularly observed time series, typically representing uncertainty through a random initial state followed by smooth ordinary differential equation (ODE) dynamics, or Brownian perturbations accumulated by a stochastic differential equation (SDE).1
• This defines a time-homogeneous Markov process whose jumps are intrinsic state transitions rather than numerical integration steps.1
• For training, we derive a tractable event-augmented path-space evidence lower bound (ELBO) and introduce Scan-Parallel Variational Inference (SPVI): an observation-conditioned variational posterior samples the complete latent event configuration before the state recurrence is evaluated using triangular affine scans.1
• Across synthetic stochastic systems and real irregular time series, LJMs remain competitive with continuous-time latent baselines in forecast accuracy, often with fewer latent updates than numerical solver evaluations, while training one to two orders of magnitude faster than the sequential baselines.1

Sources (1)

• [1]Scan-Parallel Variational Inference for event-driven Latent Jump Models
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 9, 04:39 AM

  We instead introduce latent jump models (LJMs): the latent state follows closed-form deterministic dynamics between Poisson-driven event times and undergoes a learned instantaneous jump at each event, with state-dependent intensity and mark distributions.

  Continuous-time latent state-space models are widely used for irregularly observed time series, typically representing uncertainty through a random initial state followed by smooth ordinary differential equation (ODE) dynamics, or Brownian perturbations accumulated by a stochastic differential equation (SDE).

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