pyfilter

pyfilter is a package designed for joint parameter and state inference in (mainly) non-linear state space models using Sequential Monte Carlo and variational inference. It is similar to pomp, but implemented in Python leveraging pytorch. The interface is heavily inspired by pymc3.

Example

from pyfilter.timeseries import AffineEulerMaruyama, LinearGaussianObservations
import torch
from pyfilter.distributions import DistributionWrapper
from torch.distributions import Normal
import matplotlib.pyplot as plt
from pyfilter.filters.particle import APF, proposals as p
from math import sqrt


def drift(x, gamma, sigma):
    return torch.sin(x.values - gamma)


def diffusion(x, gamma, sigma):
    return sigma


dt = 0.1
parameters = 0.0, 1.0
init_dist = DistributionWrapper(Normal, loc=0.0, scale=1.0)
inc_dist = DistributionWrapper(Normal, loc=0.0, scale=sqrt(dt))

sine_diffusion = AffineEulerMaruyama(
    (drift, diffusion),
    parameters,
    init_dist,
    inc_dist,
    dt=dt,
    num_steps=int(1 / dt)
)
ssm = LinearGaussianObservations(sine_diffusion, scale=0.1)

x, y = ssm.sample_path(1000)

fig, ax = plt.subplots(2)
ax[0].plot(x.numpy(), label="True")
ax[1].plot(y.numpy())

filt = APF(ssm, 1000, proposal=p.Bootstrap())
result = filt.longfilter(y)

ax[0].plot(result.filter_means.numpy(), label="Filtered")
ax[0].legend()

plt.show()

Installation

Install the package by typing the following in a git shell or similar

pip install git+https://github.com/tingiskhan/pyfilter.git

Implementations

Below is a list of implemented algorithms/filters.

Filters

The currently implemented filters are

1. SISR
2. APF
3. UKF

For filters 1. and 2. there exist different proposals, s.a.

1. Optimal proposal when observations are linear combinations of states, and normally distributed.
2. Locally linearized observation density, mainly used for models having log-concave observation density.

Algorithms

The currently implemented algorithms are

1. NESS
2. SMC2 (see here for one of the original authors' implementation)
3. Variational Bayes
4. SMC2FW
5. PMMH

Caveats

Please note that this is a project I work on in my spare time, as such there might be errors in the implementations and sub-optimal performance. You are more than welcome to report bugs should you try out the library.