Which Input Actually Mattered

Last timeEach Tree Fixing the Last

A committee can be asked which inputs it leaned on, by three different methods that disagree, and the ranking that comes back is read wrongly in two standard ways.

The question that always arrives

A committee of three hundred trees predicts well and explains nothing. The

first question anybody asks is which inputs mattered, and there are three

answers to it, which disagree.

Counting what each input cleaned up

Every split in every tree was chosen because it reduced mixedness by some

amount. Add up those amounts for each input, across every split in every tree

where that input was the question. The totals rank the inputs.

It is free, since the numbers were computed during fitting, and it is the

ranking that implementations report by default.

It is also biased, in a way that matters.

FIG 1A forest fitted to pure noise, four inputs, no relationship at all

	distinct values the inpu	share of the cleanup cou	share by shuffling
yes or no	2	4	1
five categories	5	11	1
a whole number up to 100	100	31	1
a measurement with decim	400	54	2

Percentages, from a data set whose outcome is a coin flip independent of every input. The honest answer is that all four shares should be nothing, because nothing predicts anything here. The cleanup count gives the last input more than half the credit purely because it offers four hundred thresholds to try and one of them always looks good by luck. The shuffling measure, in the last column, correctly reports nothing.

The mechanism is worth stating because it generalises. An input with many

distinct values offers many candidate questions. The split search keeps the

best of them, so more candidates means a higher best by chance alone, and the

procedure rewards an input for having fine resolution rather than for being

informative. Identifier columns are the extreme case, and a customer number

reaching the top of a cleanup ranking is the classic sign of this.

The lesson stops here

7 more paragraphs to go

You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.

The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.

See the plan The contents

This is the reading half

Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.

The contents

Which Input Actually Mattered

The question that always arrives

Counting what each input cleaned up

7 more paragraphs to go

This is the reading half

Read alongside