Arxiv cut

.gitignore

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+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
+*.so
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+pip-wheel-metadata/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
+.hypothesis/
+.pytest_cache/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+db.sqlite3
+db.sqlite3-journal
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
+.scrapy
+
+# Sphinx documentation
+docs/_build/
+
+# PyBuilder
+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# IPython
+profile_default/
+ipython_config.py
+
+# pyenv
+.python-version
+
+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
+# SageMath parsed files
+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
+venv.bak/
+
+# Spyder project settings
+.spyderproject
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+# Rope project settings
+.ropeproject
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+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+# Saved archives
+*.npz

LICENSE

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+MIT License
+
+Copyright (c) 2022 Adrien Corenflos
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+# Auxiliary Kalman and particle Gibbs samplers for generalised Feynman-Kac models
+
+This is the companion code for the paper [Auxiliary MCMC and particle Gibbs samplers for parallelisable
+inference in latent dynamical systems](TODO) by Adrien Corenflos and Simo Särkkä.
+
+The models considered here are of the form
+
+```math
+    \pi(x_{0:T}) \propto p_0(x_0) \prod_{t=1}^T p_t(x_t | x_{t-1}) g(x_{0:T})
+```
+
+for which the auxiliary Kalman sampler can be implemented as long as $g$ is differentiable and Gaussian approximations of
+$p_t(x_t | x_{t-1})$ can be computed.
+
+For separable potentials, for example, $g(x_{0:T}) = \prod_{t=0}^T g_t(x_t)$, the second order auxiliary Kalman sampler can be implemented. This
+is the case for the following models:
+
+```math
+    g(x_{0:T}) = \prod_{t=0}^T g_t(x_t) = \prod_{t=0}^T p(y_t | x_t)
+```
+
+Particle Gibbs samplers can be implemented for models of the form
+
+```math
+    \pi(x_{0:T}) \propto p_0(x_0)g_0(x_0) \prod_{t=1}^T p_t(x_t | x_{t-1}) g(x_t, x_{t-1}).
+```
+
+When $p_t(x_t | x_{t-1})$ is approximated by a Gaussian, and/or when $g$ is differentiable, improvements can be achieved as explained in the paper.
+
+To install this, be sure to follow the official JAX installation instructions, and then run
+```bash
+    pip install -e .
+```
+or any other way of installing a Python package from source of your preference.
+
+Examples can be found in the `examples` folder, together with scripts to reproduce the results described in the paper.

aux_samplers/__init__.py

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+from ._primitives.base import SamplerState
+from ._primitives.linearisation import extended, gauss_hermite, cubature
+from ._primitives.math import mvn
+from .common import delta_adaptation

aux_samplers/_primitives/base.py

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+from typing import Union
+
+from chex import Array, ArrayNumpy, dataclass, ArrayTree
+
+Array = Union[ArrayNumpy, Array, ArrayTree]
+
+
+@dataclass
+class SamplerState:
+    x: Array

aux_samplers/_primitives/csmc/__init__.py

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+from .csmc import get_kernel

aux_samplers/_primitives/csmc/base.py

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+import abc
+from typing import Optional
+
+import chex
+from chex import ArrayTree, dataclass, Array
+
+from aux_samplers._primitives.base import SamplerState
+
+_MSG = """
+The logpdf is not implemented for this {type(self).__name__} but was called.
+If you see this message, you likely are using a cSMC method relying on it. 
+Please implement this function or choose the standard cSMC with no backward pass.
+"""
+
+_EPS = 1e-10
+
+
+@dataclass
+class CSMCState(SamplerState):
+    x: ArrayTree
+    updated: Array
+
+
+@chex.dataclass
+class UnivariatePotential(abc.ABC):
+    """
+    Abstract class for univariate potential functions.
+    This is just a callable, but may have parameters.
+    """
+
+    def __call__(self, x):
+        raise NotImplementedError
+
+
+@chex.dataclass
+class Distribution(abc.ABC):
+    """
+    Abstract class for densities.
+    """
+
+    def sample(self, key, N):
+        raise NotImplementedError
+
+    def logpdf(self, x):
+        return NotImplemented(_MSG.format(type(self).__name__))
+
+
+@chex.dataclass
+class Potential(abc.ABC):
+    """
+    Abstract class for potential functions.
+    This is just a callable, but may have parameters.
+    """
+    params: Optional[ArrayTree] = None
+
+    def __call__(self, x_t_p_1, x_t, params):
+        raise NotImplementedError
+
+
+@chex.dataclass
+class Dynamics(abc.ABC):
+    """
+    Abstract class for conditional densities.
+    """
+    params: Optional[ArrayTree] = None
+
+    def sample(self, key, x_t, params):
+        raise NotImplementedError
+
+    def logpdf(self, x_t_p_1, x_t, params):
+        return NotImplemented(_MSG.format(type(self).__name__))