**PySR: parallel symbolic regression built on Julia, and interfaced by Python.** Uses regularized evolution, simulated annealing, and gradient-free optimization. | **Docs** | **pip** | |---|---| |[](https://pysr.readthedocs.io/en/latest/?badge=latest)|[](https://badge.fury.io/py/pysr)| (pronounced like *py* as in python, and then *sur* as in surface) [Cite this software](https://github.com/MilesCranmer/PySR/blob/master/CITATION.md) ### Test status: | **Linux** | **Windows** | **macOS** | **Coverage** | |---|---|---|---| |[](https://github.com/MilesCranmer/PySR/actions/workflows/CI.yml)|[](https://github.com/MilesCranmer/PySR/actions/workflows/CI_Windows.yml)|[](https://github.com/MilesCranmer/PySR/actions/workflows/CI_mac.yml)|[](https://coveralls.io/github/MilesCranmer/PySR)| Check out [SymbolicRegression.jl](https://github.com/MilesCranmer/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](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](https://www.creativemachineslab.com/eureqa.html), 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](https://julialang.org/downloads/), and then instructions for [mac](https://julialang.org/downloads/platform/#macos) and [linux](https://julialang.org/downloads/platform/#linux_and_freebsd). (Don't use the `conda-forge` version; it doesn't seem to work properly.) You can install PySR with: ```bash pip install pysr ``` The first launch will automatically install the Julia packages required. Most common issues at this stage are solved by [tweaking the Julia package server](https://github.com/MilesCranmer/PySR/issues/27). to use up-to-date packages. # Quickstart Here is some demo code (also found in `example.py`) ```python 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=["+", "*"], unary_operators=[ "cos", "exp", "sin", # Pre-defined library of operators (see docs) "inv(x) = 1/x", # Define your own operator! (Julia syntax) ], ) ...# (you can use ctl-c to exit early) print(best(equations)) ``` which gives: ```python 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: ```python 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.