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)
• 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

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.

from ssm.models import HMM
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 = HMM(K, D, observations="gaussian")
z, y = hmm.sample(T)

Fitting an HMM is simple.

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

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

git clone git@github.com:slinderman/ssm.git
cd ssm
pip install -e .

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