PySR.jl

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

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 https://arxiv.org/abs/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. Then, at the command line, install the Optim and SpecialFunctions packages via:

julia -e 'import Pkg; Pkg.add("Optim"); Pkg.add("SpecialFunctions")'

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

# 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"])

...

print(equations)

which gives:

   Complexity       MSE                                                Equation
0           5  1.947431                          plus(-1.7420927, mult(x0, x0))
1           8  0.486858           plus(-1.8710494, plus(cos(x3), mult(x0, x0)))
2          11  0.000000  plus(plus(mult(x0, x0), cos(x3)), plus(-2.0, cos(x3)))

The newest version of PySR also returns three additional columns:

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.