How can you handle ML data with spatial dependencies?

While methods like Moran's I and Geary's C are useful for quantifying spatial autocorrelation, they often assume a stationary process, meaning the spatial relationship is consistent across the entire study area. In many real-world applications, spatial processes are non-stationary. For example, urban areas may exhibit different spatial autocorrelation patterns compared to rural areas within the same dataset. Failure to account for non-stationarity can introduce bias or inefficiency in the model. Techniques such as Geographically Weighted Regression (GWR) may be more appropriate for handling non-stationary spatial data.

Incorporating spatial lag can improve model accuracy but it also introduces the risk of multicollinearity, especially when other explanatory variables in the model are themselves spatially dependent or correlated with the spatial lag variable. High multicollinearity can make it difficult to interpret the individual contributions of explanatory variables and may inflate the variance of the model estimates. Techniques such as Variance Inflation Factor (VIF) analysis can be employed to detect multicollinearity and one may consider using ridge or lasso regression as a remedy.

When I run into spatial heterogeneity, I will typically run a multiscale geographically weighted regression analysis a few times over. I'll experiment by removing explanatory variables with higher variance inflation factors (from the global model), one at a time and compare the models. Esri's guidance states that one should be concerned with variance inflation factors above 7.5, although I've had multicollinearity issues with values as low as 2. Then I'll make sure the condition numbers across the study area are within normal limits.

Spatial heterogeneity may not only vary in space but also in scale, meaning different variables or processes may operate effectively at different spatial scales. Failing to account for scale can lead to a phenomenon known as the Modifiable Areal Unit Problem (MAUP), where the results of an analysis are sensitive to the scale of the spatial units used. Techniques like multi-scale analysis or wavelet transforms can be employed to identify the most appropriate scale for each variable or process, thereby minimizing scale-induced biases and improving model robustness.

While spatial features can enhance model performance, they may also introduce data leakage if not handled carefully. For instance, including future environmental conditions as features for past events, or using features that indirectly include information about the target variable, can lead to overly optimistic performance metrics that are not representative of the model's true predictive capability. It's crucial to ensure that the spatial features used are appropriate for the temporal scope and independent from the target variable to obtain a model that generalizes well to unseen data.

Some spatial tools and libraries, like PySAL or ArcGIS, may have limitations in handling very large datasets efficiently due to memory constraints. For instance, PySAL's spatial autocorrelation methods may become computationally expensive with millions of data points, leading to longer runtimes or even failures due to memory errors. A specific remedy for this is to employ a divide-and-conquer strategy: partitioning the data into smaller, manageable subsets for parallelized analysis and later aggregating the results. Alternatively, one could consider cloud-based solutions like Google Earth Engine, which is designed to handle large-scale geospatial data, to circumvent local hardware limitations.