# The ALAMO approach to machine learning

## TL;DR

ALAMO is a computational method that learns simple, accurate algebraic models from data, using adaptive sampling and constraints to improve model quality for complex processes.

## Contribution

The paper introduces ALAMO, a novel approach combining algebraic modeling, adaptive sampling, and constraint enforcement for improved data-driven model building.

## Key findings

- ALAMO produces simple, accurate models for reaction data.
- Error maximization sampling outperforms Latin hypercube designs.
- Constrained regression improves model validation performance.

## Abstract

ALAMO is a computational methodology for leaning algebraic functions from data. Given a data set, the approach begins by building a low-complexity, linear model composed of explicit non-linear transformations of the independent variables. Linear combinations of these non-linear transformations allow a linear model to better approximate complex behavior observed in real processes. The model is refined, as additional data are obtained in an adaptive fashion through error maximization sampling using derivative-free optimization. Models built using ALAMO can enforce constraints on the response variables to incorporate first-principles knowledge. The ability of ALAMO to generate simple and accurate models for a number of reaction problems is demonstrated. The error maximization sampling is compared with Latin hypercube designs to demonstrate its sampling efficiency. ALAMO's constrained regression methodology is used to further refine concentration models, resulting in models that perform better on validation data and satisfy upper and lower bounds placed on model outputs.