Chapter 07
The ML problem
You now know the industry, the geology, the workflow and the schema. This chapter is the hinge: it takes all of that and states precisely why the obvious machine learning formulation — binary classification over a map — is a trap, and what to reach for instead.
What the funnel does to a model
Chapter 3 walked the exploration workflow stage by stage. Two properties of that staging drive everything in this part of the primer.
First, the data changes type at every stage — you go from 2-D raster geophysics over a whole belt to sparse 3-D point samples in one prospect, and a model trained on one is not a model of the other. Second, the decision changes too. Early on you are ranking ground and the output is an ordering. Later you are answering a single binary question about one orebody: is there enough of it, at high enough grade, to justify building a mine? Those need different models, different metrics, and different notions of what "correct" means.
Base rates, and what they do to your metrics
Take a province-scale grid at 1 km resolution — say 500,000 cells. The number of known economic deposits in it might be 20. That is a positive class prevalence of 4 × 10⁻⁵.
At that prevalence, a model that predicts "no deposit" everywhere scores 99.996% accuracy. Accuracy is meaningless here, and so — more subtly — is a good ROC-AUC. ROC uses the false positive rate, whose denominator is the 500,000 negatives; you can move tens of thousands of cells across the threshold and barely dent it. Use precision-recall, and report performance at the top-k the business can actually drill — because you will drill ten targets, not ten thousand.
The right framing of the output is a ranking with calibrated probabilities, evaluated as: if I take the top 50 cells this model proposes, how many known deposits do I capture, and how much area did I have to accept to do it? That is a capture-efficiency curve, and it is the closest thing the field has to a standard evaluation.
The costs are wildly asymmetric
Standard classification loss assumes some fixed cost for each error type. Here the asymmetry spans orders of magnitude, and it flips depending on the stage.
| Error | What it means | Rough cost |
|---|---|---|
| False positive | You drill a target that turns out barren | One to a few hundred k$ — plus weeks |
| False negative | You walk away from ground that hosts a tier-one deposit | 10⁸–10¹⁰ $ of forgone NPV |
| Miscalibrated confidence | You raise money, or don't, on a resource number that moves | Existential — and a securities-law problem |
A false negative can be five orders of magnitude worse than a false positive. That is the economic reason exploration tolerates so many dry holes: the payoff distribution is extremely heavy-tailed, and the optimal policy against a heavy-tailed payoff is to buy a lot of cheap options. Your model's job is usually not to avoid dry holes — it is to make the options cheaper, by getting more information per dollar spent.
This is why the objective is information gain per dollar, not classification loss. Formally the field borrows from Bayesian optimal experimental design and decision analysis: choose the observation that maximises expected reduction in uncertainty about the quantity that drives the decision. Chapter 10 develops this properly. Hold the thought that a perfectly accurate model can have zero value of information — if it never changes what you would have done anyway.
Why the obvious formulation is a trap
Here is the naive pipeline nearly everyone writes first, and the four places it breaks.
known_deposits -> positive labels
everywhere_else -> negative labels
geophysics + geochem rasters -> features
RandomForest().fit(X, y)
predict_proba over the grid -> "prospectivity map"- Your negatives are fiction. "Everywhere else" contains undiscovered deposits. You are training the model to call real deposits negative. This is a positive-unlabeled problem, and treating it as supervised binary classification biases everything downstream. (Chapter 9.)
- Your positives encode where people looked. Known deposits cluster near roads, near historical camps, near outcrop, in permissive jurisdictions. A model fed this learns accessibility, which correlates with discovery but is not geology. Sampling-bias correction is a first-class concern, not a refinement.
- Random cross-validation leaks. Geological fields are spatially autocorrelated over kilometres. A random 80/20 split puts cells from the same deposit in both train and test, and your held-out score becomes a measure of interpolation, not generalisation. You need spatial block or leave-one-region-out CV, and your honest numbers will be much worse.
- A map is not a decision. Even a well-built map answers "where is it prospective?" The company needs to answer "given a $4M budget and this fixed rig, what is the next hole, and when do I stop?" Those are different objects. (Chapter 10.)
The prior is a story, and it is falsifiable
Geologists do not approach a blank map with a uniform prior. They work from deposit models — well-characterised recipes for how a particular class of orebody forms. A porphyry copper system implies a specific intrusion, a specific alteration zoning pattern, a specific magnetic and resistivity signature at a specific scale. A sediment-hosted copper system implies a basin, a redox boundary, and a plumbing system to move brine.
This is a genuinely strong, genuinely informative prior — a mineral systems model — and encoding it is where domain knowledge earns its keep. It is also, crucially, frequently wrong, and the frontier of the field is about handling that.
A team commits to a hypothesis — "this is a fault-controlled replacement body dipping north" — plans a drill programme to test it, and after four holes discovers the geometry is nothing like that. Under a Bayesian framing, this is not a posterior update. The hypothesis space itself was wrong. Data acquisition planned under a wrong prior can reduce nothing at all, because you are efficiently resolving uncertainty about the wrong variable.
Mern, Corso, Burch, House and Caers make exactly this the subject of Intelligent Prospector v2.0: plan optimally across multiple competing geological hypotheses, and equip the agent with a method to detect early that the human-stated hypotheses have all been falsified — so you can stop spending against a dead model. That is epistemic uncertainty, as distinct from the aleatoric variability within any single hypothesis, and keeping the two separate is the conceptual move that makes this field click.
The frontier is blind and deep
One last structural fact. The deposits that outcrop have largely been found. What remains is under cover — sediment, weathering, ice — with no surface expression. Exploration under cover is inference through a screen: you are inverting sparse, noisy, physically-entangled remote measurements for a target that may be several hundred metres down.
That is bad news for prospectors and good news for you. When the signal is obvious, geologists find it without help. The regime where the signal is weak, multi-modal, and buried in a decade of heterogeneous survey data is exactly the regime where careful statistical machinery pays.
- Prevalence ~10⁻⁴–10⁻⁵ → precision-recall and top-k capture, never accuracy or ROC-AUC alone.
- Negatives are unlabeled, not negative → PU learning (Ch. 9).
- Positives encode human attention → sampling-bias correction (Ch. 9).
- Spatial autocorrelation → block CV or your scores are fantasy (Ch. 9).
- Payoffs are heavy-tailed and asymmetric → optimise information per dollar (Ch. 10).
- The prior is a falsifiable human hypothesis → model epistemic uncertainty explicitly (Ch. 10).
Sources for this chapter
- MinEx Consulting (Richard Schodde) — the discovery-rate and discovery-cost statistics that set the base rates used throughout this chapter. See also Chapter 1.
- Saito & Rehmsmeier, "The precision-recall plot is more informative than the ROC plot when evaluating binary classifiers on imbalanced datasets", PLoS ONE 10(3), 2015. The citation to hand someone who wants to report ROC-AUC on a 10⁻⁴ prevalence problem.
- Davis & Goadrich, "The relationship between Precision-Recall and ROC curves", ICML 2006. The formal version of the same argument.
- Hüllermeier & Waegeman, "Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods", Machine Learning 110 (2021). The cleanest general treatment of the distinction that Chapter 10 turns into money.
- Caers, Modeling Uncertainty in the Earth Sciences (Wiley, 2011). Uncertainty quantification and decision-making framed for geoscience specifically.