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State Space Models: A Modern Approach

This is an interactive textbook on state space models (SSM) using the JAX Python library. Some of the content is covered in other books such as [Sar13] and [Mur23]. However, we go into more detail, and focus on how to efficiently implement the various algorithms in a “modern” computing environment, exploiting recent progress in automatic differentiation and parallel computing.

• State Space Models
  • What are State Space Models?
  • Hidden Markov Models
  • Linear Gaussian SSMs
  • Nonlinear Gaussian SSMs
  • States estimation (inference)
  • Parameter estimation (learning)
• Hidden Markov Models
  • HMM filtering (forwards algorithm)
  • HMM smoothing (forwards-backwards algorithm)
  • Viterbi algorithm
  • Parallel HMM smoothing
  • Forwards-filtering backwards-sampling algorithm
• Linear-Gaussian SSMs
  • Kalman filtering
  • Kalman (RTS) smoother
  • Parallel Kalman Smoother
  • Forwards-filtering backwards sampling
• Extended (linearized) methods
  • Extended Kalman filtering
  • Extended Kalman smoother
  • Parallel extended Kalman smoothing
• Unscented methods
  • Unscented filtering
  • Unscented smoothing
• Quadrature and cubature methods
• Posterior linearization
• Assumed Density Filtering
• Variational inference
• Particle filtering
• Sequential Monte Carlo
• Offline parameter estimation (learning)
• Multi-target tracking
• Data assimilation using Ensemble Kalman filter
• Bayesian non-parametric SSMs
• Changepoint detection
• Timeseries forecasting
• Markovian Gaussian processes
• Differential equations and SSMs
• Optimal control
• Bibliography

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State Space Models