lhcb / experiments

A repository to demonstrate new data analysis packages and techniques

LHCb data analysis experiments

This is a repository for demonstrating that cool new data analysis method you came up with, or to show how we might use that new library you found.

Contents

Likelihood fits with automatic differentiation

Author: Igor Babuschkin

Automatic differentiation (AD) allows you to calculate the derivatives of a function more precisely, and possibly faster than the commonly used finite differences method. This is achieved by exploiting the exact structure of the code that implements the function.

Reverse mode AD is particularly useful if you need to calculate the derivatives of a scalar-valued function with many inputs, as is the case for the log-likelihood function of a statistical model.

The autograd package implements reverse mode AD for the Python programming language, and makes it particularly easy to experiment with AD, as it is a drop-in package that seamlessly integrates with idiomatic Python code using the numpy and scipy packages.

In this notebook, I demonstrate how autograd can be used to provide the gradient of a simple model consisting of a mixture of two normal distributions, and minimize the log-likelihood for a randomly generated dataset using this gradient.

In addition, I demonstrate how to apply transformations on some of the parameters to remove physical boundaries from the minimization process.

[Link to Jupyter notebook](/Likelihood with autodiff.ipynb)