The Christoffel-Darboux Kernel and the associated Christoffel function are well-known tools from the theory of approximation and orthogonal polynomials. Although they have been largely ignored in analysis of discrete data, recent results show that they have many potential uses in data analysis, including several applications in machine learning [1][2][3]. In particular, some peculiar properties of the CF can be leveraged for anomaly detection, a subject of great interest. Anomalies, also defined as outliers or out-of-distribution observations, are essential to be detected in data as they can indicate data corruption or faulty behavior. Trust in Artificial Intelligence (AI) systems depends on this because their reliability relies on inputs lying in the training distribution. On the other hand, anomaly detection plays a crucial role in certifying data obtained from sensors or images, as well as in identifying symptoms that can be used to drive diagnosis reasoning and health management. This talk presents two methods devised for anomaly detection in streaming data. The first one is DyCF (Dynamic Christoffel Function method) that benefits from incrementality and the ability of dealing with concept drift, i.e., of updating the model so that it adapts to the distribution. The second method, called DyCG (Dynamic Christoffel Growth method), leverages convergence properties of the Christoffel function so that it is downright tuning-free. Those two methods benefit from a clean algebraic framework and nicely fulfil the data stream requirements related to non-stationarity of the distributions and infinitely growing data. An evaluation against state-of-the-art methods using synthetic and real industrial datasets will show that DyCF and DyCG outperform more often than not finetuned methods and are clearly better with respect to execution time and memory use [4][5]. [1] Lasserre, J. B., & Pauwels, E. (2019). The empirical Christoffel function with applications in data analysis. Advances in Computational Mathematics, 45, 1439-1468. doi: 10.1007/s10444-019-09673- 1. URL https://hal.science/hal-01511624. [2] Lasserre,J.B.,Pauwels,E.,&Putinar,M.(2022).TheChristoffel–DarbouxKernelforDataAnalysis (Vol. 38). Cambridge University Press. https://doi.org/10.1017/9781108937078 URL https://hal.laas.fr/hal-03590829. [3] Pauwels, E., Putinar, M., & Lasserre, J. B. (2021). Data analysis from empirical moments and the Christoffel function. Foundations of Computational Mathematics, 21, 243-273. doi: 10.1007/s10208-020-09451-2. URL https://hal.science/hal-01845137. [4] Ducharlet, K., Travé-Massuyès, L., Lasserre, J. B., Le Lann, M. V., & Miloudi, Y., Leveraging the Christoffel-Darboux kernel for online outlier detection. 2022. URL https://hal.science/hal-03562614. [5] Ducharlet, K., Travé-Massuyès, L., Lasserre, J. B., Le Lann, M. V., & Miloudi, Y., Leveraging the Christoffel-Darboux Kernel for Online Outlier Detection in data streams. Submitted to Data Mining and Knowledge Discovery.