tesuract

tesuract, which stands for tensor surrogate automation and computation, is a software library to perform automated supervised (and semi-unsupervised via data-driven reduced order modeling) machine learning tasks with single and multi-target output data.1 One of the key features is that it is fully compatible with scikit-learn’s API, e.g., their set, fit, predict functionality, allowing flexibility and modularity. It also contains tools to quickly and easily implement multi-variate Legendre polynomial (the original universal approximator!) regression models.

Installation

The code is easy to install with pip. Simply run

pip install tesuract

and this will install the pypi version of tesuract. For the latest development build, just clone and install the repo. Make sure you have numpy and scikit-learn. You might also need the alive-progress bar library. Then

git clone git@github.com:kennychowdhary/tesuract.git
cd tesuract

and simple run

pip install .

You can also run a suite of unit tests and regression tests before installation by typing

python -m pytest -v -s tesuract/tests

to check that the library works. Note that the python -m allows you to automatically add the current path to the Python path, without having to change any environmental variables. That’s it! Now you are ready to use tesuract.

Usage/ Quickstart

Let’s see how easy it is to create a multivariate polynomial regression model. Let’s create a \(4^{th}\) order polynomial regression model2 on the \([-1,1]^5\) hypercube, using sklearn’s LassoCV (\(\ell_1\) sparsity constraint) fitting.3

import tesuract
from sklearn.datasets import make_friedman1

X,y = make_friedman1(n_samples=100,n_features=5)
pce = tesuract.PCEReg(order=8, fit_type='LassoCV') # create an 8th order polynomial
pce.fit(X,y)

That’s it! 4 You’ve fit your first polynomial chaos expansion (PCE) using tesuract (with a linear least squares solver). You can try changing the type of solver, e.g., LassoCV or ElasticNetCV, getting feature importances, etc.

Introduction

• Main features
• Installation

User Guide

• Fitting with sklearn’s API
• Model comparison
  • Setup
• Hyper-parameter tuning
  • Setup
  • Grid search tuning
• Feature Importances
  • Setup
  • Total order Sobol sensitivities
• Tensor or field surrogates
  • PCA target transform
  • Scoring tensor surrogate estimators
  • Custom scorer for field functions
  • More advanced hyper-parameter tuning

API

• PCE Base Class
• PCE Regression Class

Indices and tables

• Index

• Module Index

• Search Page

1

Python 3+ is required and tesuract has been tested for 3.7.6 and 3.8.10 so far.

2

In short, a \(4^{th}\) order polynomial means that the terms are no higher than an \(x_i^4\) for each dimension.

3

Don’t worry! There are a lot more customization options that we will get into later

4

The dimensionality is automatically determined by looking at the size of the data matrix columns.