Interpretable AI Software Modules

Transparent and automated predictive and prescriptive machine learning algorithms from cutting-edge research that empower you to push the boundary of data science

Machine Learning Under a Modern Optimization Lens

The recent book by co-founders Bertsimas and Dunn details many recent advances in machine learning and optimization, including all of the Interpretable AI algorithms.

Available for purchase from:

Book cover

Optimal Decision Trees

Insight and understanding alongside accurate predictions

Simple to Understand

Optimal Decision Trees delivers state-of-the-art predictive performance that is on par with blackbox methods.

It produces a single tree that users can follow and validate, enabling trust in the decision-making process.

It has been applied in 20+ research and industry projects in the past year alone, covering a wide range of fields including health care, banking, and insurance.

≥ 0.62< 0.62≥ 1.5< 1.5≥ -0.011< -0.011≥ 32< 32Risk: 4.80%875 patientsTotal_bilirubinRisk: 1.74%115 patientsRisk: 28.57%56 patientsRisk: 10.53%171 patientsHematocritRisk: 10.77%65 patientsRisk: 0.00%516 patientsRisk: 13.82%123 patientsRisk: 2.66%639 patientsChange in weightRisk: 3.41%704 patientsDextrose

A tree output from a cancer mortality prediction study.

Superior Accuracy

In a large computational study, Optimal Decision Trees outperforms CART and is comparable to random forest and XGBoost, as averaged across 66 real-world datasets.

Breakthrough in Research

With the power of modern optimization, Optimal Decision Trees builds the entire tree holistically, rather than split-by-split like existing methods, closing the performance gap with black-boxes.

Our approach enables unprecedented flexibility in model construction:

  • Sparse hyperplane splits
  • Regression in the leaves
  • Customized constraints
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Automated Regression

Transform regression from art to science
Optimal Regressions
  • ✓ Variable transformations
  • ✓ Statistical significance
  • ✓ Number of variables selected
  • ✓ Multicolinearity
  • ✓ Robustness to outliers and uncertainty
  • ✓ And many more

One Step to Optimal Regression

Regression models are widely used for their simplicity, but are built manually over many iterations of trial-and-error to accommodate multiple objectives.

We offer an algorithmic approach to find the optimal regression model in a single step that incorporates all relevant considerations, fast and scalable.

Selection of Optimal Features

Automated Regression leverages superior performance from cutting-edge research in Optimal Feature Selection.

This method improves upon Lasso, a popular state-of-the-art variable selection algorithm, with higher accuracy and lower false alarm rate. With more exact selection of variables, we ensure better performance and higher interpretability.

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Optimal Imputation

Unlock the full power of data with missing values or quality issues

Better data preprocessing leads to stronger predictive performance

Optimal Imputation as a preprocessing step delivers consistent performance gains in prediction tasks:

  • Regression: 0.05 increase in R2
  • Classification: 2% higher accuracy

It serves as the basis for a novel data quality assessment tool that identifies outliers and automates the cleaning and validation process.

Missing data imputation Prediction tasks

Highly Accurate Imputations

Compared against benchmark methods across 84 datasets, Optimal Imputation achieves the best imputation accuracy in the majority of datasets under all scenarios, with a significant reduction of 10-15% in imputation errors.

Exploit Feature Relationships

Traditional imputation approaches compromise the quality of data, resulting in biases and limiting the predictive power.

Optimal Imputation uses global optimization to find the best imputed values by exploiting the relationship across features.

In the example to the right,

  • Complete cases: left with only 50% observations; biased and less powerful.
  • Mean impute: imputes 25 years of employment; nonsensical given age.
  • Optimal Imputation: uses age and gender to estimate the years of employment. More sensible, accurate and leads to better final predictions.
Age Gender Years of Employment
60 M 30
45 F 20
20 M ?
25 F ?

Optimal Prescription

From data to decisions with state-of-the-art optimization
Models Decisions Data Machine Learning Statistics Optimization

Optimal Data-Driven Prescription derives actionable decisions directly from data

Data to Decisions Directly

Typical data-to-decisions analytics use point predictions from machine learning to feed into optimization. However, the uncertainty is not captured and the models are subject to error magnification.

Our Optimal Data-Driven Prescription combines machine learning and optimization by using data directly in optimization to incorporate estimates and uncertainties. In many case studies, this leads to significantly better outcomes.

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Optimal Prescriptions (red) outperforms the predict-then-prescribe (purple), baseline (gray), and is closest to oracle (black dotted) in an inventory management case.

Contact us for more information or to request a demo or academic license