Computationally Efficient Outlier Detection for High-Dimensional Data Using the MDP Algorithm

Outlier detection, or anomaly detection as it is known in the machine learning community, has gained interest in recent years, and it is commonly used when the sample size is smaller than the number of variables. In 2015, an outlier detection procedure was proposed 7 for this high-dimensional setting, replacing the classic minimum covariance determinant estimator with the minimum diagonal product estimator. Computationally speaking, their method has two drawbacks: (a) it is not computationally efficient and does not scale up, and (b) it is not memory efficient and, in some cases, it is not possible to apply due to memory limits. We address the first issue via efficient code written in both R and C++, whereas for the second issue, we utilize the eigen decomposition and its properties. Experiments are conducted using simulated data to showcase the time improvement, while gene expression data are used to further examine some extra practicalities associated with the algorithm. The simulation studies yield a speed-up factor that ranges between 17 and 1800, implying a successful reduction in the estimator's computational burden.