Tighten The Lasso: A Convex Hull Volume-based Anomaly Detection Method

The rapid advancements in data-driven methodologies have underscored the critical importance of ensuring data quality. Consequently, detecting out-of-distribution (OOD) data has emerged as an essential task to maintain the reliability and robustness of data-driven models, in general, and machine and deep learning models, in particular. In this study, we leveraged the convex hull property of a dataset and the fact that anomalies highly contribute to the increase of the CH's volume to propose a novel anomaly detection algorithm. Our algorithm computes the CH's volume as an increasing number of data points are removed from the dataset to define a decision line between OOD and in-distribution data points. We compared the proposed algorithm to seven widely used anomaly detection algorithms over ten datasets, showing comparable results for state-of-the-art (SOTA) algorithms. Moreover, we show that with a computationally cheap and simple check, one can detect datasets that are well-suited for the proposed algorithm which outperforms the SOTA anomaly detection algorithms.

Parametric PDF for Goodness of Fit

The goodness of fit methods for classification problems relies traditionally on confusion matrices. This paper aims to enrich these methods with a risk evaluation and stability analysis tools. For this purpose, we present a parametric PDF framework.

Goodness of Fit Metrics for Multi-class Predictor

The multi-class prediction had gained popularity over recent years. Thus measuring fit goodness becomes a cardinal question that researchers often have to deal with. Several metrics are commonly used for this task. However, when one has to decide about the right measurement, he must consider that different use-cases impose different constraints that govern this decision. A leading constraint at least in \emph{real world} multi-class problems is imbalanced data: Multi categorical problems hardly provide symmetrical data. Hence, when we observe common KPIs (key performance indicators), e.g., Precision-Sensitivity or Accuracy, one can seldom interpret the obtained numbers into the model's actual needs. We suggest generalizing Matthew's correlation coefficient into multi-dimensions. This generalization is based on a geometrical interpretation of the generalized confusion matrix.