Outlier detection refers to the identification of data points that deviate from a general data distribution. Existing unsupervised approaches often suffer from high computational cost, complex hyperparameter tuning, and limited interpretability, especially when working with large, high-dimensional datasets. To address these issues, we present a simple yet effective algorithm calledECOD(Empirical-Cumulative-distribution-based Outlier Detection), which is inspired by the fact that outliers are often the “rare events” that appear in the tails of a distribution. In a nutshell,ECODfirst estimates the underlying distribution of the input data in a nonparametric fashion by computing the empirical cumulative distribution per dimension of the data.ECODthen uses these empirical distributions to estimate tail probabilities per dimension for each data point. Finally,ECODcomputes an outlier score of each data point by aggregating estimated tail probabilities across dimensions. Our contributions are as follows: (1) we propose a novel outlier detection method calledECOD, which is both parameter-free and easy to interpret; (2) we perform extensive experiments on 30 benchmark datasets, where we find thatECODoutperforms 11 state-of-the-art baselines in terms of accuracy, efficiency, and scalability; and (3) we release an easy-to-use and scalable (with distributed support) Python implementation for accessibility and reproducibility.

Outlier detection refers to the identification of rare items that are deviant from the general data distribution. Existing approaches suffer from high computational complexity, low predictive capability, and limited interpretability. As a remedy, we present a novel outlier detection algorithm called COPOD, which is inspired by copulas for modeling multivariate data distribution. COPOD first constructs an empirical copula, and then uses it to predict tail probabilities of each given data point to determine its level of “extremeness”. Intuitively, we think of this as calculating an anomalous p-value. This makes COPOD both parameter-free, highly interpretable, and computationally efficient. In this work, we make three key contributions, 1) propose a novel, parameter-free outlier detection algorithm with both great performance and interpretability, 2) perform extensive experiments on 30 benchmark datasets to show that COPOD outperforms in most cases and is also one of the fastest algorithms, and 3) release an easy-to-use Python implementation for reproducibility.

Abstract We present the starting elements of a mathematical theory of policy advice and avoidability. More specifically, we formalize a cluster of notions related to policy advice, such as policy , viability , reachability , and propose a novel approach for assisting decision making, based on the concept of avoidability . We formalize avoidability as a relation between current and future states, investigate under which conditions this relation is decidable and propose a generic procedure for assessing avoidability. The formalization is constructive and makes extensive use of the correspondence between dependent types and logical propositions, decidable judgments are obtained through computations. Thus, we aim for a computational theory, and emphasize the role that computer science can play in global system science.

We present an interdisciplinary effort in the field of global environmental change, related to the understanding of the concept of ‘vulnerability’. We have used functional programming to capture the generic aspects of the myriad of definitions of vulnerability, and have used the resulting formalization to learn something new about vulnerability and to write some better software for vulnerability assessment. In the process, we have also found out something about formalization in general, about the advantages and disadvantages of dependent types, and about the role of computing science in the larger intellectual landscape.