Main features#

tesuract’s main feature is constructing multivariate polynomial regression models using classic orthogonal polynomial constructions, e.g. Legendre polynomials. We use the scikit-learn API to build these estimators, which allows easy and seamless integration with the scikit-learn. Here is a list of the main features of this library.

  • Integration with scikit-learn

    Both PCEBuilder and PCEReg classes for constructing multivariate polynomial interpolation inherit the BaseEstimator class from scikit-learn. This means both these object integrate seamlessly with the scikit-learn environment, which, for example, allows one to use the grid search cross-validation wrapper or even third party libraries like skopt on top of these polynomial estimator classes.

  • Multivariate polynomial regression

    We provide an object oriented polynomial constructor class that creates a polynomial estimator (based on the scikit-learn estimator API) and a corresponding multivariate polynomial regression class that utilizes existing linear regression algorithms in scikit-learn to train the model.

  • Hyper-parameter search for best model fit

    tesuract provides methods to perform hyper-parameter search for finding the best fit polynomial model. Moreover, we provide methods to compare these methods to other popular machine learning regression models like random forest regression and multi-layer perceptron models. 1

  • Variance based sensitivity analysis

    The polynomial regression class allows for easy feature importance or sensitivity analysis. We use the Sobol sensitivity index to compute which features are more important.

  • Sparse quadrature methods for high-dimensional integration

    An alternate way to estimate the training weights of the multivariate polynomial model (i.e., the coefficients of the polynomial expansion), is direct numerical integration. Due to the orthogonality of the polynomial basis terms, the training weights can be written in analytic form as a integration rule. We provide high-dimensional, sparse, integration rules to estimate these coefficients. This is useful for smooth functions, rather than functions corrupted by noise.

  • Utilities for preprocessing

    While scikit-learn contains many preprocessing utilities, we add a few more that may be more tailored for scientific computing applications. Utilities include min-max transforms for multi-target outputs, transforms for scaling domains with known physical bounds, and more customizable dimension reduction transforms, e.g., PCA.

  • Pipelines for multi-target fitting 2

1

In the future, we will be able to compare methods in tensorflow. The machinery is there for connecting tensorflow to sklearn, but it just needs to be done!

2

This is an advanced usage for tesuract.