Interpreting Deepkriging for spatial interpolation in geostatistics
Bibliographic record
Abstract
In the current era marked by an unprecedented abundance of data, the usage of conventional methods such as kriging persists in some applications of geostatistics, despite their limitations in adequately capturing the intricate relationships found in contemporary, multivariate datasets. Although deep neural networks (DNNs) have demonstrated remarkable efficacy in capturing complex nonlinear feature relationships across various domains, their success in geostatistical applications has been limited. This can be partly attributed to two significant challenges. Firstly, the opaque nature of these black box models raises concerns about the dependability of their outputs for critical decision-making, as the inner workings of the model remain less interpretable. Secondly, DNNs do not explicitly capture spatial dependencies within data. To address these shortcomings, we employ a methodology to interpret the recently proposed spatial DNNs known as Deepkriging, and we apply it to dry bulk rock density estimation, an often-overlooked aspect in mineral resource estimation. Through our adaptation of Shapley values—Batched Shapley—we overcome significant computational challenges to quantify feature importance for Deepkriging. This approach takes into account feature interactions, which is crucial for DNNs, as they rely on high-order interactions, especially in a complex application like mineral resource estimation. Additionally, we demonstrate in the 3D case that Deepkriging outperforms ordinary kriging and regression kriging in terms of mean squared errors, in both the purely spatial case and in the presence of auxiliary variables. Our study produces the first methodology to interpret Deepkriging, which is suitable for any model with a large number of features; it reaffirms the efficacy of Deepkriging through several comparisons in a 3D application, and most importantly; it underscores the adaptability and broader potential of DNNs to cater to various challenges in geostatistics.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".