Spatial data is ubiquitous, encompassing a wide range of applications from environmental observations and biological measurements to more recent fields like computer vision. A critical challenge in the analysis of spatial data is spatial prediction, which involves estimating unobserved values based on nearby observations under the assumption of certain correlations. Among parametric algorithms, Kriging is particularly notable ((Matheron (1963))). Described as the best linear unbiased estimator (BLUE), Kriging employs a weighted average of nearby observations, with weights determined by a covariance function typically presumed to be stationary. However, this assumption does not hold in many real-world scenarios, such as data from satellites, monitoring stations, and urban streets, which tend to exhibit nonstationarity (Katzfuss (2013)).

Dynamic Bayesian Networks (DBNs) bring efficient tools to model complex multivariate dynamical systems learned from collected data and/or expert knowledge. Notwithstanding, the underlying generative Markov model is supposed homogeneous; neither its topology nor its parameters evolve over time. Thus, learning a DBN to model a non-stationary process with this belief will lead to poor prediction capabilities. In order to account for nonstationary processes, we build on a framework to identify transitions between underlying models and a framework to learn them in real time, without making hypothesis about their evolution. We present the tool performances on simulated datasets. Since we aim to use this to model and predict incongruities within an Intrusion Detection System (IDS) in near real-time, great care is ascribed to the capability to correctly detect transition times. Our prior results display the precision of our algorithm in the choice of transitions and therefore the quality of identified networks. At last we suggest future work.

When dealing with time series with complex non-stationarities, low retrospective regret on individual realizations is a more appropriate goal than low prospective risk in expectation. Online learning algorithms provide powerful guarantees of this form, and have often been proposed for use with non-stationary processes because of their ability to switch between different forecasters or ``experts''. However, existing methods assume that the set of experts whose forecasts are to be combined are all given at the start, which is not plausible when dealing with a genuinely historical or evolutionary system. We show how to modify the ``fixed shares'' algorithm for tracking the best expert to cope with a steadily growing set of experts, obtained by fitting new models to new data as it becomes available, and obtain regret bounds for the growing ensemble.