Geodetic Theory provides a rigorous mathematical framework for parameter estimation and statistical testing, e.g., such as Gauss-Markov models, Maximum Likelihood Estimation (MLE), and Detection-Identification-Adaptation (DIA). Meanwhile, the increasing availability of data from terrestrial and space-geodetic techniques (e.g., GNSS, InSAR, VLBI, SLR, altimetry and gravimetry) has accelerated the adoption of Machine Learning (ML) and Deep Learning (DL), creating new opportunities to integrate model-based and data-driven approaches.

In this short course, we bridge Geodetic Theory and Machine Learning by exploring their mathematical foundations, thus highlighting relationships and complementary capabilities. We first introduce established geodetic estimation and statistical testing methods, defining their connections with statistical learning and modern ML techniques. Through representative geodetic examples, we illustrate the connections between model-based and data-driven paradigms, discussing their underlying assumptions, along with main advantages and limitations.

Particular attention will be given to the challenges of adopting ML as a black-box solution, including uncertainty quantification, statistical reliability, and model validation. Finally, we emphasize the importance of 'explainability' and 'reproducibility' in scientific ML applications.

The course targets geodesists and Earth-science researchers interested in understanding, applying or evaluating ML methods in their research.

Prerequisites: basic linear algebra; no prior ML/DL knowledge is required.