johannbrehmer / PySR

Simple, fast, and parallelized symbolic regression in Python/Julia via regularized evolution and simulated annealing

PySR.jl

(pronounced like py as in python, and then sur as in surface)

Parallelized symbolic regression built on Julia, and interfaced by Python. Uses regularized evolution, simulated annealing, and gradient-free optimization.

Cite this software

Documentation

Symbolic regression is a very interpretable machine learning algorithm for low-dimensional problems: these tools search equation space to find algebraic relations that approximate a dataset.

One can also extend these approaches to higher-dimensional spaces by using a neural network as proxy, as explained in 2006.11287, where we apply it to N-body problems. Here, one essentially uses symbolic regression to convert a neural net to an analytic equation. Thus, these tools simultaneously present an explicit and powerful way to interpret deep models.

Backstory:

Previously, we have used eureqa, which is a very efficient and user-friendly tool. However, eureqa is GUI-only, doesn't allow for user-defined operators, has no distributed capabilities, and has become proprietary (and recently been merged into an online service). Thus, the goal of this package is to have an open-source symbolic regression tool as efficient as eureqa, while also exposing a configurable python interface.

Installation

PySR uses both Julia and Python, so you need to have both installed.

Install Julia - see downloads, and then instructions for mac and linux. (Don't use the conda-forge version; it doesn't seem to work properly.) Then, at the command line, install and precompile the Optim and SpecialFunctions packages via:

julia -e 'using Pkg; pkg"add Optim; add SpecialFunctions; precompile;"'

For python, you need to have Python 3, numpy, sympy, and pandas installed.

You can install this package from PyPI with:

pip install pysr

Quickstart

import numpy as np
from pysr import pysr, best, get_hof

# Dataset
X = 2*np.random.randn(100, 5)
y = 2*np.cos(X[:, 3]) + X[:, 0]**2 - 2

# Learn equations
equations = pysr(X, y, niterations=5,
        binary_operators=["plus", "mult"],
        unary_operators=["cos", "exp", "sin"])

...# (you can use ctl-c to exit early)

print(best(equations))

which gives:

x0**2 + 2.000016*cos(x3) - 1.9999845

One can also use best_tex to get the LaTeX form, or best_callable to get a function you can call. This uses a score which balances complexity and error; however, one can see the full list of equations with:

print(equations)

This is a pandas table, with additional columns:

• MSE - the mean square error of the formula
• score - a metric akin to Occam's razor; you should use this to help select the "true" equation.
• sympy_format - sympy equation.
• lambda_format - a lambda function for that equation, that you can pass values through.