Simultaneous feature selection and outlier detection with optimality guarantees.

Area of Science:

• Biostatistics
• Computational Biology
• Genomics

Background:

• Biomedical research generates vast datasets with numerous features, increasing the risk of redundant or contaminated data.
• Small sample sizes exacerbate challenges posed by data redundancy and outliers in high-dimensional studies.
• Robust sparse estimation methods are crucial for accurate analysis in data-rich biomedical research.

Purpose of the Study:

• To develop a general framework for robust sparse estimation in high-dimensional regressions.
• To simultaneously perform feature selection and outlier detection in the presence of mean-shift outliers in both response and design matrices.
• To provide a method with provably optimal guarantees for feature selection and outlier detection.

Main Methods:

• Utilized mixed-integer programming for simultaneous feature selection and outlier detection.
• Developed a framework to address multiple mean-shift outliers in high-dimensional regression models.
• Proved theoretical properties including the robustly strong oracle property, optimal parameter estimation, and breakdown point.

Main Results:

• Demonstrated a necessary and sufficient condition for the robustly strong oracle property, allowing feature count to grow exponentially with sample size.
• Achieved optimal estimation of parameters and established the breakdown point of the developed estimates.
• Showcased superior performance against existing heuristic methods via simulations.

Conclusions:

• The proposed mixed-integer programming framework offers a robust and optimal solution for feature selection and outlier detection in high-dimensional biomedical data.
• The method provides theoretical guarantees and demonstrates superior performance, making it valuable for analyzing complex datasets.
• Applied the method to investigate links between childhood obesity and the human microbiome, highlighting its practical utility.