Conformal prediction based on principal component analysis for high-dimensional outlier detection

Current outlier detection methods exhibit many limitations in high-dimensional settings. Traditional statistical approaches rely on strong assumptions and lack practicality and generality. Meanwhile, despite the better performance, machine learning methods suffer from low interpretability and reliability due to their complex mechanisms and the absence of confidence estimation. Although outlier detection methods based on principal component analysis (PCA) have shown some advantages by extracting important features from high-dimensional data, they have not entirely solved these problems. Conformal prediction, a finite-sample distribution-free uncertainty quantification method recently applied to outlier detection, produces a set-valued prediction with a Type-I error guarantee and false discovery rate control. This paper proposes a new distribution-free method for high-dimensional outlier detection, PCA-CP, combining principal component analysis and conformal prediction. PCA-CP overcomes the shortcomings of previous methods, demonstrating high generality and reliability while achieving high performance. Experiments on simulation and real data show that PCA-CP outperforms previous methods, achieving higher power and lower False Discovery Rate, thus proving its significant advantages.