Literature on GWRF #2
Description
Some relevant literature
GWRF - this paper outlines the implementation (independent local model fitted around each focal) we use here https://www.tandfonline.com/doi/full/10.1080/10106049.2019.1595177#d1e967
As such, we extend RF as a disaggregation consisting of several local sub-models. The principle idea is similar to that of GWR (Fotheringham et al. Citation2003), in which we move to local computation rather than global one. This means that for each location i, a local RF is computed but only including a n number of nearby observations. Essentially, this leads to the calculation of an RF in each training data point, with its own performance, predictive power and feature importance. In that way, we increase the flexibility of RF to be calibrated locally rather than globally
Few more interesting bits:
For predicting, we fuse the global and local estimates using a weight parameter (a). Fusing the predictions allows us to extract the locally heterogeneous signal (low bias) from the local sub-model and merging it to that of a global model which uses more data (low variance).
Worth considering and should be fairly straightforward to implement.
To predict on new spatial locations, the closest available GRF model is used.
I am doing this differently, more costly but I believe more robustly. For any new location, we define its neighborhood based on model's bandwidth and weights based on its kernel. We then gather prediction from each of the models and return weighted average. I believe that is what Fotheringham suggested for GWR but I can't tell if that is what mgwr is doing.
It is implemented in SpatialML R package - https://stamatisgeoai.eu/spatialml/ I didn't find the repo so the code from CRAN will have to do :).
@ljwolf I do remember talking with @u3ks about the RF where each tree is local rather than each focal having its own ensemble but can't find a reference. Do you have the paper you mentioned somewhere at hand?