Overfitting — where it appears
Named by 12 essays across 2 fields — each of them below, with the objects they name alongside it.
The chart decides the profile
A camera's colour matrix is nine numbers fitted to a set of patches somebody chose, and the number that comes with it is the error on those patches. On a chart with no chromatic range that number is 0.19 ΔE00 and the matrix delivers 1.65 — and a second matrix, indistinguishable on the chart, delivers 2.03.
A fit can be exact and empty
Every fitted object here reports one number, the residual on the data it was fitted to, and every one of them has two more that nobody publishes — how many of its parameters the data actually determine, and how large the family of equally good answers is. The third column is where the failures live.
Two stages catch the tube and bill the lamps they misplace
A narrow-channel estimate of a camera's colour error missed the halophosphate tube because the census held nothing like it, and a line that learned the tube's family from four siblings cost every other lamp. The proposed cure was two stages: recognise a lamp's family, then apply that family's own line. Given each lamp's family, it works as predicted and better — the tube missed by 0.011 ΔE₀₀, the fifty-four lamps estimated to ±0.133 against the ratio's ±0.141. Found by the nearest other lamp in the sensor's departures, the family is right for the tube and wrong for five lamps, and those five, missed by ±0.41, take the whole census back to ±0.162. The gain is real; the classifier is where it is lost.
A classifier that abstains gives up the tube
Found by the nearest other lamp, a lamp's family cost a two-stage estimate of a camera's colour error more than it bought, because five lamps were placed confidently in the wrong family. The proposed repair was a classifier that abstains — falls back on the census-wide line — unless a lamp's three nearest neighbours agree. It abstains on the wrong lamps. The misplaced ones have three agreeing neighbours, all white LEDs; the lamp it gives up is the halophosphate tube the two stages were built to catch, whose third neighbour is a cyan LED, and its miss returns from 0.011 to 0.445. Two agreeing neighbours look better than knowing every family. Chosen without looking at the lamp being estimated, the rule is worth exactly what the ratio alone is worth.
A family's line runs through its neighbours
The halophosphate tubes differ from one another by one number — where their main phosphor band sits — and so lie along a line in the three departures an ambient-light sensor reads. The proposal was to classify a lamp by the family whose line passes nearest, which would keep the tube a vote of neighbours gives up. It keeps the tube, under every version that does not rescale the distances. It also places eighteen white LEDs on the radiators' line, because that line — fitted to six radiators close together — runs along the LEDs' own and, extended, straight through the violet-pumped ones; and the radiators' estimate, extrapolated to them, misses the triphosphor tube by 7.6. Clamped to the stretch each family spans, the lines still cost ±0.285; given to the halophosphate family alone, its line claims a cyan LED and costs ±0.179. The one line classifier that comes in under the ratio line's ±0.141 does so by two thousandths, having placed the tube with the LEDs.
Radiators and LEDs are one family to the sensor
An ambient-light sensor's three narrow departures see the collection's six smooth radiators and forty-four white LEDs along one line: the radiators' own short line lies on the LEDs' long one. Estimating a camera's colour error family by family, the census had treated them as two, and every classifier that tried to tell them apart paid for it. Merged into one family of smooth broadband sources, found by the nearest other lamp as before, the two-stage estimate comes to ±0.127 over fifty-four lamps held out — below the ratio line's ±0.141, and below the ±0.133 the separate families managed when every lamp's family was simply given. The halophosphate tube is still caught. The radiators, which the prediction said the merge would cost a little, are estimated better inside it than inside their own family, because a three-coefficient line fitted over five radiators was worse for them than the census-wide ratio line.
New LEDs miss the line their cousins drew
An ambient-light sensor's three departures can estimate a camera's colour error under a lamp, and merging radiators and white LEDs into one smooth family brought that estimate to ±0.127 over fifty-four lamps, each left out in turn. Every one of those lamps had relatives in the pool. Fourteen lamps the census never saw test what the relatives were worth. The prediction was that new smooth lamps would land on the line and tinted incandescents fall off it by four tenths or more. The radiators and daylights land on it, within ±0.13 each. The tinted lamps do too — the pink-glass incandescent, placed among the LEDs by its nearest neighbour, misses by 0.12. The lamps that fall off are the new white LEDs: ±0.20, half again the census's error, two of them by a quarter. Their misses follow the sensor's 640 nm channel at a slope of −0.72, explaining four fifths of their scatter, because the line learned what that channel means from LEDs varied only in their blue pump. Adding the fourteen to the pool does not help.
The bin's curve holds between its points and breaks beyond them
A camera's colour error under a white LED was read from an ambient sensor across a manufacturing bin by a line with a slope and a curve in Duv for each colour temperature, fitted at three Duv values — on the locus and 0.003 either side — and reading the LEDs beside the locus within ±0.056 and ±0.048 ΔE₀₀. A curve through three points passes through them whatever happens between them. The prediction was that 119 new LEDs built at ±0.0015 are read within ±0.06, and those at ±0.006 worse than ±0.10. Both halves hold: ±0.045 and ±0.043 inside, ±0.153 and ±0.161 outside. But the error's own mean course stays on its parabola within 0.02 out to ±0.006. The line's bend is not the error's: it is the gap the line leaves between the locus LEDs and the bin's edges, and a gap spent as a curvature quadruples at twice the distance.
A level for each temperature lets the curve be the error's
An error line with a slope and a curve in Duv for each colour temperature read white LEDs inside a manufacturing bin within ±0.045 ΔE₀₀ and LEDs at twice the bin's edge only within ±0.16, though the camera's own error stays on its parabola there. Its curve was borrowed: the line's shared terms could not place each temperature's level, and the square of the Duv absorbed the gap. The prediction was that one more number a pump, the square of the mireds, brings the locus LEDs within ±0.05 and those at ±0.006 within ±0.08. It brings the locus to ±0.025 — three times better than the locus-only line that started this run of essays — and the outer LEDs to ±0.049 and ±0.058. The curvature the line now implies at each temperature is the error's own within a fifth; what it leaves is the warm whites' scatter at the bin's edges.
The red phosphor tilts the warm whites and bends nothing
An error line with a level, a slope and a curve in Duv for each colour temperature reads white LEDs at 4,000 and 6,500 K within ±0.04 ΔE₀₀ across and beyond a manufacturing bin, but warm whites at twice the bin's edge only within ±0.087. The prediction was that the red phosphor sets a warm white's bend, so that one term more a pump — the square of the Duv times the estimated red — brings them within ±0.05. It moves them by a thousandth. The red phosphor enters the slope instead: the Duv times the red takes them to ±0.046 below the locus and ±0.067 above. And the rest points upstream. The first stage reads a warm white's red phosphor squeezed toward the middle of its range, the warm misses follow that misreading times the Duv at r = 0.79, and given the red each LED was built with the warm whites come within ±0.05 — though the same substitution doubles the error at 4,000 K.
The line had already undone the squeeze
An ambient sensor's first stage reads a 2,700 K white LED's red phosphor squeezed about a third toward the middle of its range, and the camera-error line's warm misses outside the bin follow that misreading times the Duv. The prediction was that giving the first stage the Duv times its 600 nm departure and times the mireds would undo the squeeze. It changes nothing: the squeeze belongs to the temperature, and a level and a departure slope for each temperature read the warm red four times better, within ±0.035. But the eleven-term error line does not move — no warm LED by more than 0.006 — because at one temperature a squeeze is a rescaling its red and red-times-mireds terms had already undone. Only the red-slope line, whose one coefficient a pump spans three temperatures, gains: to ±0.034 below the locus, within 0.002 of the red known. And the cold whites pay for it.
Two estimates of one red each read their own end
Two first stages read a white LED's red phosphor from an ambient sensor: one squeezes the warm whites' red a third toward the middle, the other reads it four times better, and a camera-error line with a red slope prefers the first for cold whites and the second for warm. The prediction was that a line handed both — the eleven-term line on the squeezed estimate, the red slope on the faithful one — keeps each end's gain. It does, within 0.004 at the cold end. But the second estimate is not needed: the squeezed red alone, its red slope multiplied by the mireds, reads every LED within a ten-thousandth of the split line. And the two estimates' difference is worth a term of its own. Added to the line, it reads the cold whites within ±0.016 at every Duv and on the locus within a thousandth, and moves the warm whites and the middle by nothing.
Named alongside it
The objects these essays reach for when they reach for this one.
Held-out validationCamera rawWhite LEDLeast-squaresLinear modelPlanckian locusPredictionFluorescentModelling assumptionCalibrationDegrees of freedomIdentifiability