Spatial and spatiotemporal model evaluation

[sigmafelix]

This issue is about spatial and spatiotemporal cross-validation for model performance evaluation, and is possibly related to ropensci/chopin#1 .

Paper

• Area of Applicability (AOA, Meyer and Pebesma 2021)
  • New observations ($\tilde{X}$) are assessed based on the lowest Euclidean distance:
    $$d(\tilde{X}_{j \cdot}, X_{i \cdot})$$
    from the existing training data (X) on the multivariate predictor space, say,
    $$d_{j} = \arg \min_{k} d(\tilde{X}_{j\cdot}, X_{k\cdot})$$
  • Dissimilarity index is assessed based on the formula
    $$\text{DI}_{j} = d_{j} / \bar{d}$$
    where $\bar{d}$ is the average pairwise distance from the training data
    • With a user-defined threshold, the user can identify the new observations that are not suitable for applying the model (or gives low expectation on finding good prediction accuracy)
  • Questions
    • Does AOA unintentionally prefer the spatiotemporally closer features to others, especially when the high spatial and spatiotemporal autocorrelation exists?
    • What if one employs other distance metrics?
    • Quite surely it is computationally demanding O(n^2) as AOA relies on full distance matrix of the training data -> how to make it scalable?
      • Further question: how to assess spatial or spatiotemporal autocorrelation efficiently with the sizable datasets?

R packages

🔍

• CAST: spatiotemporal extension of caret. By Meyer, the author of AOA paper.
• waywiser: spatial model evaluation in tidymodels ecosystem
• targets: workflow management tool in R. Provides code examples for HPC utilization.

[sigmafelix]

Spatial/temporal/spatiotemporal splitting functions for cross-validation are implemented in NRTAPmodel. I think these functions are also useful for this package either.