PySR

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

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

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Check out SymbolicRegression.jl for the pure-Julia backend of this package.

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.)

You can install PySR with:

pip install pysr

The first launch will automatically install the Julia packages required.

Quickstart

Here is some demo code (also found in example.py)

import numpy as np
from pysr import pysr, best

# 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", #Pre-defined library of operators (see https://pysr.readthedocs.io/en/latest/docs/operators/)
      "inv(x) = 1/x"]) # Define your own operator! (Julia syntax)

...# (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.