Anomaly Detection Under Uncertainty Using Distributionally Robust
  Optimization Approach
Amir Hossein Noormohammadia Seyed Ali MirHassania Farnaz Hooshmand Khaligh
Anomaly detection is defined as the problem of finding data points that do
not follow the patterns of the majority. Among the various proposed methods for
solving this problem, classification-based methods, including one-class Support
Vector Machines (SVM) are considered effective and state-of-the-art. The
one-class SVM method aims to find a decision boundary to distinguish between
normal data points and anomalies using only the normal data. On the other hand,
most real-world problems involve some degree of uncertainty, where the true
probability distribution of each data point is unknown, and estimating it is
often difficult and costly. Assuming partial distribution information such as
the first and second-order moments is known, a distributionally robust
chance-constrained model is proposed in which the probability of
misclassification is low. By utilizing a mapping function to a higher
dimensional space, the proposed model will be capable of classifying
origin-inseparable datasets. Also, by adopting the kernel idea, the need for
explicitly knowing the mapping is eliminated, computations can be performed in
the input space, and computational complexity is reduced. Computational results
validate the robustness of the proposed model under different probability
distributions and also the superiority of the proposed model compared to the
standard one-class SVM in terms of various evaluation metrics.