FFX: Fast Function Extraction

FFX is a technique for symbolic regression. It is:

Fast - runtime 5-60 seconds, depending on problem size (1GHz cpu)
Scalable - 1000 input variables, no problem!
Deterministic - no need to "hope and pray".

Installation

To install from PyPI, simply run:

pip install ffx

Usage

FFX can either be run in stand-alone mode, or within your existing Python code using its own API or a Scikit-learn style API. It installs both a command-line utility ffx and the Python module ffx.

Standalone

ffx test train_X.csv train_y.csv test_X.csv test_y.csv

Use ffx help for more information on using the command-line utility.

Python Module (run interface)

The FFX Python module exposes a function, ffx.run(). The following snippet is a simple example of how to use FFX this way. Note that all arguments are expected to be of type numpy.ndarray or pandas.DataFrame.

import numpy as np
import ffx

train_X = np.array( [ (1.5,2,3), (4,5,6) ] ).T
train_y = np.array( [1,2,3])

test_X = np.array( [ (5.241,1.23, 3.125), (1.1,0.124,0.391) ] ).T
test_y = np.array( [3.03,0.9113,1.823])

models = ffx.run(train_X, train_y, test_X, test_y, ["predictor_a", "predictor_b"])
for model in models:
    yhat = model.simulate(test_X)
    print(model)

Scikit-Learn interface

The FFX Python module also exposes a class, ffx.FFXRegressor which provides a Scikit-learn API, in particular fit(X, y), predict(X), and score(X, y) methods. In this API, all of the models produced by FFX (the whole Pareto front) are accessible after fit()ing as _models, but predict() and score() will use only the model of highest accuracy and highest complexity. Here is an example of usage.

import numpy as np
import ffx

# This creates a dataset of 2 predictors
X = np.random.random((20, 2))
y = 0.1 * X[:, 0] + 0.5 * X[:, 1]

train_X, test_X = X[:10], X[10:]
train_y, test_y = y[:10], y[10:]

FFX = ffx.FFXRegressor()
FFX.fit(train_X, train_y)
print("Prediction:", FFX.predict(test_X))
print("Score:", FFX.score(test_X, test_y))

Technical details

Circuits-oriented description: Slides Paper (CICC 2011)
AI-oriented description Slides Paper (GPTP 2011)

References

McConaghy, FFX: Fast, Scalable, Deterministic Symbolic Regression Technology, Genetic Programming Theory and Practice IX, Edited by R. Riolo, E. Vladislavleva, and J. Moore, Springer, 2011.
McConaghy, High-Dimensional Statistical Modeling and Analysis of Custom Integrated Circuits, Proc. Custom Integrated Circuits Conference, Sept. 2011