Anomaly Detection via Mean Shift Density Enhancement

Unsupervised anomaly detection stands as an important problem in machine learning, with applications in financial fraud prevention, network security and medical diagnostics. Existing unsupervised anomaly detection algorithms rarely perform well across different anomaly types, often excelling only under specific structural assumptions. This lack of robustness also becomes particularly evident under noisy settings. We propose Mean Shift Density Enhancement (MSDE), a fully unsupervised framework that detects anomalies through their geometric response to density-driven manifold evolution. MSDE is based on the principle that normal samples, being well supported by local density, remain stable under iterative density enhancement, whereas anomalous samples undergo large cumulative displacements as they are attracted toward nearby density modes. To operationalize this idea, MSDE employs a weighted mean-shift procedure with adaptive, sample-specific density weights derived from a UMAP-based fuzzy neighborhood graph. Anomaly scores are defined by the total displacement accumulated across a small number of mean-shift iterations. We evaluate MSDE on the ADBench benchmark, comprising forty six real-world tabular datasets, four realistic anomaly generation mechanisms, and six noise levels. Compared to 13 established unsupervised baselines, MSDE achieves consistently strong, balanced and robust performance for AUC-ROC, AUC-PR, and Precision@n, at several noise levels and on average over several types of anomalies. These results demonstrate that displacement-based scoring provides a robust alternative to the existing state-of-the-art for unsupervised anomaly detection.

Fast Iterative and Task-Specific Imputation with Online Learning

Missing feature values are a significant hurdle for downstream machine-learning tasks such as classification and regression. However, they are pervasive in multiple real-life use cases, for instance, in drug discovery research. Moreover, imputation methods might be time-consuming and offer few guarantees on the imputation quality, especially for not-missing-at-random mechanisms. We propose an imputation approach named F3I based on the iterative improvement of a K-nearest neighbor imputation that learns the weights for each neighbor of a data point, optimizing for the most likely distribution of points over data points. This algorithm can also be jointly trained with a downstream task on the imputed values. We provide a theoretical analysis of the imputation quality by F3I for several types of missing mechanisms. We also demonstrate the performance of F3I on both synthetic data sets and real-life drug repurposing and handwritten-digit recognition data.

Multivariate Functional Linear Discriminant Analysis for the Classification of Short Time Series with Missing Data

Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete data, statistical dependencies between features must be estimated in a computationally tractable way, while also dealing with missing data. There is a need for a computationally tractable approach that considers the statistical dependencies between features and can handle missing values. We here develop a multivariate version of FLDA (MUDRA) to tackle this issue and describe an efficient expectation/conditional-maximization (ECM) algorithm to infer its parameters. We assess its predictive power on the "Articulary Word Recognition" data set and show its improvement over the state-of-the-art, especially in the case of missing data. MUDRA allows interpretable classification of data sets with large proportions of missing data, which will be particularly useful for medical or psychological data sets.