Welcome to ssm’s documentation!#

Important

We’re working full time on a JAX refactor of SSM that will take advantage of JIT compilation, GPU and TPU support, automatic differentation, etc. Please stay tuned for updates soon!

This package has fast and flexible code for simulating, learning, and performing inference in a variety of state space models. Currently, it supports:

  1. Hidden Markov Models (HMM)

  2. Auto-regressive HMMs (ARHMM)

  3. Input-output HMMs (IOHMM)

  4. Hidden Semi-Markov Models (HSMM)

  5. Linear Dynamical Systems (LDS)

  6. Switching Linear Dynamical Systems (SLDS)

  7. Recurrent SLDS (rSLDS)

  8. Hierarchical extensions of the above

  9. Partial observations and missing data

We support the following observation models:

  1. Gaussian

  2. Student’s t

  3. Bernoulli

  4. Poisson

  5. Categorical

  6. Von Mises

HMM inference is done with either expectation maximization (EM) or stochastic gradient descent (SGD). For SLDS, we use stochastic variational inference (SVI).

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SSM Notebooks#

Notebooks to accompany the State Space Models (SSM) library.

Simple HMM Demo

Simple HMM Demo

Simple HMM Demo
Simple Linear Dynamical System Demo

Simple Linear Dynamical System Demo

Simple Linear Dynamical System Demo
Input Driven HMM

Input Driven HMM

Input Driven HMM
Input Driven Observations (GLM-HMM)

Input Driven Observations (GLM-HMM)

Input Driven Observations (GLM-HMM)
Switching Linear Dynamical System

Switching Linear Dynamical System

Switching Linear Dynamical System
Recurrent SLDS

Recurrent SLDS

Recurrent SLDS
Poisson SLDS

Poisson SLDS

Poisson SLDS
Poisson fLDS

Poisson fLDS

Poisson fLDS
Variational Laplace EM for SLDS

Variational Laplace EM for SLDS

Variational Laplace EM for SLDS
HMM State Clustering

HMM State Clustering

HMM State Clustering
Multi-Population rSLDS

Multi-Population rSLDS

Multi-Population rSLDS

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Indices and tables#