Welcome to EPI’s documentation!

EPI - Euler Parameter Inference

Euler Parameter Inference (EPI) is a Python package for inverse parameter inference. It provides an implementation of the EPI algorithm, which takes observed data and a model as input and returns a parameter distribution consistent with the observed data by solving the inverse problem directly. In the case of a one-to-one mapping, this is the true underlying distribution.

Features

EPI supports

SBML ode models
User provided models
Models with automatic differentation using jax

Installation

The package is available on pypi and can be installed with:

pip install eulerpi

or

pip install eulerpi[sbml]

for the support of sbml models.

Make sure that you have the following C++ libraries installed:

sudo apt install -y swig libblas-dev libatlas-base-dev libhdf5-dev

You can also build the library from the latest source code by following the Development Quickstart Guide.

How to start

To use EPI, derive your model from the Model class and implement the abstract functions. Here’s an example code snippet:

# my_model.py
import jax.numpy as jnp

from eulerpi.core.model import Model

class MyModel(Model):

    param_dim = N # The dimension of a parameter point
    data_dim = M # The dimension of a data point

    def forward(self, param):
        return jnp.array(...)

    def jacobian(self, param):
        return jnp.array(...)

To evaluate the model and infer the parameter distribution, call:

from eulerpi.core.inference import inference

from my_model import MyModel

# This line is needed for multiprocessing in python
if __name__ == "__main__":
    central_param = np.array([0.5, -1.5, ...])
    param_limits = np.array([[0.0, 1.0], [-3.0, 0.0], ...])

    model = MyModel(central_param, param_limits)
    inference(model=model, data="my_data.csv")

The parameter data can be a numpy-2d-array or a PathLike object that points to a CSV file. In the example shown above, the CSV file my_data.csv should contain the data in the following format:

datapoint_dim1, datapoint_dim2, datapoint_dim3, ..., datapoint_dimN
datapoint_dim1, datapoint_dim2, datapoint_dim3, ..., datapoint_dimN
datapoint_dim1, datapoint_dim2, datapoint_dim3, ..., datapoint_dimN
...
datapoint_dim1, datapoint_dim2, datapoint_dim3, ..., datapoint_dimN

This corresponds to a matrix with the shape nSamples x data_dim. For more available options and parameters for the inference method, please refer to the API documentation. Note that the inference can be done with grid-based methods (dense grids, sparse grids) or sampling methods (mcmc).

The results are stored in the following locations

./Applications/<ModelName>/.../OverallParams.csv
./Applications/<ModelName>/.../OverallSimResults.csv
./Applications/<ModelName>/.../OverallDensityEvals.csv

These files contain the sampled parameters, the corresponding data points obtained from the model forward pass, and the corresponding density evaluation.

Note

Please read the documentation for our Examples.

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