Online Drift Detection with Maximum Concept Discrepancy

Continuous learning from an immense volume of data streams becomes exceptionally critical in the internet era. However, data streams often do not conform to the same distribution over time, leading to a phenomenon called concept drift. Since a fixed static model is unreliable for inferring concept-drifted data streams, establishing an adaptive mechanism for detecting concept drift is crucial. Current methods for concept drift detection primarily assume that the labels or error rates of downstream models are given and/or underlying statistical properties exist in data streams. These approaches, however, struggle to address high-dimensional data streams with intricate irregular distribution shifts, which are more prevalent in real-world scenarios. In this paper, we propose MCD-DD, a novel concept drift detection method based on maximum concept discrepancy, inspired by the maximum mean discrepancy. Our method can adaptively identify varying forms of concept drift by contrastive learning of concept embeddings without relying on labels or statistical properties. With thorough experiments under synthetic and real-world scenarios, we demonstrate that the proposed method outperforms existing baselines in identifying concept drifts and enables qualitative analysis with high explainability.

On the properties of Gaussian Copula Mixture Models

Gaussian copula mixture models (GCMM) are the generalization of Gaussian Mixture models using the concept of copula. Its mathematical definition is given and the properties of likelihood function are studied in this paper. Based on these properties, extended Expectation Maximum algorithms are developed for estimating parameters for the mixture of copulas while marginal distributions corresponding to each component is estimated using separate nonparametric statistical methods. In the experiment, GCMM can achieve better goodness-of-fitting given the same number of clusters as GMM; furthermore, GCMM can utilize unsynchronized data on each dimension to achieve deeper mining of data.