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Bayesian learning and inference for state space models
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SSM: Bayesian learning and inference for state space models

Test status

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

  • Hidden Markov Models (HMM)
  • Auto-regressive HMMs (ARHMM)
  • Input-output HMMs (IOHMM)
  • Hidden Semi-Markov Models (HSMM)
  • Linear Dynamical Systems (LDS)
  • Switching Linear Dynamical Systems (SLDS)
  • Recurrent SLDS (rSLDS)
  • Hierarchical extensions of the above
  • Partial observations and missing data

We support the following observation models:

  • Gaussian
  • Student's t
  • Bernoulli
  • Poisson
  • Categorical
  • Von Mises

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


Here's a snippet to illustrate how we simulate from an HMM.

import ssm
T = 100  # number of time bins
K = 5    # number of discrete states
D = 2    # dimension of the observations

# make an hmm and sample from it
hmm = ssm.HMM(K, D, observations="gaussian")
z, y = hmm.sample(T)

Fitting an HMM is simple.

test_hmm = ssm.HMM(K, D, observations="gaussian")
zhat = test_hmm.most_likely_states(y)

The notebooks folder has more thorough, complete examples of HMMs, SLDS, and recurrent SLDS.


git clone
cd ssm
pip install numpy cython
pip install -e .

This will install "from source" and compile the Cython code for fast message passing and gradients.

To install with some parallel support via OpenMP, first make sure that your compiler supports it. OS X's default Clang compiler does not, but you can install GNU gcc and g++ with conda. Once you've set these as your default, you can install with OpenMP support using

USE_OPENMP=True pip install -e .
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