regression
Predict the ore grade underground
It is the 1950s in the South African goldfields, and a mining engineer must estimate the ore grade at an unsampled point from a scatter of costly boreholes — and simple interpolation ignores that nearby samples are more informative than distant ones in a way the spatial data themselves reveal. Build a regression on geography: model the correlation between samples as a function of the distance between them, then predict each new location as a weighted average of the boreholes, with weights and an honest error variance from that structure. Get it wrong and you sink a shaft where the gold isn't, or walk away from a rich seam your interpolation smoothed into mediocrity — spatial prediction lives or dies on modeling the correlation, not ignoring it.
Who this problem belongs to
The two figures whose methods fit it best, out of 60 in contention.
Wiener's 1949 monograph 'Extrapolation, Interpolation, and Smoothing of Stationary Time Series,' developed from his wartime fire-control work, derived the optimal linear predictor for a random process from its own covariance structure, treating correlation between observations as a function of their separation, exactly the principle kriging would later formalize spatially rather than temporally. Independently, in the same decade, the mining engineer Danie Krige and the mathematician Georges Matheron adapted this same covariance-weighted-averaging logic to South African gold assays, but the mathematical core, weight observations by how informative their correlation makes them, is Wiener-Kolmogorov theory applied to space instead of time. He built the general framework kriging is a special case of, even without ever touching a borehole himself.
Wahba's smoothing splines and reproducing-kernel Hilbert space methods, developed from the 1970s onward, are mathematically equivalent under well-known correspondences to Gaussian-process regression and kriging: both predict an unsampled point as a weighted combination of observed values, with weights and an honest error variance derived from an assumed covariance or reproducing-kernel structure. Her cross-validation machinery for choosing smoothing parameters is precisely the honest-uncertainty apparatus this problem demands when deciding how much to trust an interpolated ore grade. She did not work with actual borehole or geostatistical data herself, and Matheron's specific mining formalization predates her major contributions by roughly a decade, but her mathematics is functionally the same method wearing different notation.
Fought here
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
60 figures are scored on this problem. Draw it in a battle to see where you land.