Tree-Values: Selective Inference for Regression Trees

Area of Science:

• Statistics
• Machine Learning
• Data Mining

Background:

• Inference on Classification and Regression Trees (CART) requires specialized methods.
• Naive inference approaches fail to provide standard statistical guarantees like Type 1 error control.

Purpose of the Study:

• To develop a selective inference framework for fitted CART models.
• To ensure valid statistical inference, including error rate control and coverage, for CART outputs.

Main Methods:

• Proposing a selective inference framework by conditioning on the data used for tree estimation.
• Developing a test for mean response differences between terminal nodes controlling selective Type 1 error rate.
• Creating a confidence interval for mean response within a terminal node achieving nominal selective coverage.
• Providing efficient algorithms for computing necessary conditioning sets.

Main Results:

• The proposed framework successfully controls the selective Type 1 error rate for hypothesis tests.
• Confidence intervals achieve nominal selective coverage for mean responses within terminal nodes.
• Methods were validated through simulation studies and application to a real-world dataset.

Conclusions:

• The selective inference framework offers a statistically sound approach for analyzing CART models.
• These methods enhance the reliability of statistical inference in the context of machine learning algorithms.
• The approach is applicable to various datasets, including those in health and nutrition research.