Anomalies, also defined as outliers or out-of-distribution observations, are essential to be detected in data as they may signal data corruption or faulty behavior. Trust in Artificial Intelligence (AI) systems hinges on this capability because their reliability is contingent upon inputs that align with 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 presentation introduces two innovative approaches for detecting anomalies in streaming data. These methods leverage the unique characteristics of the Christoffel function, a well-known tool in approximation theory and orthogonal polynomials with numerous potential applications in data analysis [1][2][3]. The first method, DyCF (Dynamic Christoffel Function method), harnesses incrementality and the capability to handle concept drift, allowing the model to be updated and to adapt to changing distributions. The second approach, termed DyCG (Dynamic Christoffel Growth method), exploits the growth properties of the Christoffel function, rendering it entirely tuning-free. Both of these methods benefit from a clear algebraic framework and effectively address the challenges presented by data streams, particularly in handling non-stationary distributions and continuously growing data. Evaluation against state-of-the-art methods using synthetic and real industrial datasets demonstrates that DyCF outperforms fine-tuning methods, displaying superior performance in terms of execution time and memory usage. While DyCG may exhibit lower performance, it possesses a significant advantage in that it requires no tuning whatsoever [4][5][6]. [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).The Christoffel-Darboux Kernel for Data Analysis (Vol. 38). Cambridge University Press. https://doi.org/10.1017/9781108937078 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. (2023). Détection d'anomalies dans les flux de données pour une application dans les réseaux de capteurs (Doctoral dissertation, INSA de Toulouse, In French). [5] 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. [6] Ducharlet, K., Travé-Massuyès, L., Lasserre, J. B., Le Lann, M. V., & Miloudi, Y., Leveraging the Christoffel function for outlier detection in data streams. Submitted to Int. J. of Data Science and Analytics.