Mean pairwise L1 distance of each unit to the others (within a block)

For an outcome vector y of length n, returns, for each unit i, the mean absolute distance mean_{j != i} |y_i - y_j| with denominator n - 1. This is the energy/distance representation: units far from the rest of their block (in either tail) score high.

Usage

riposte_mean_dist(y)

Arguments

y

numeric vector (a single block's outcomes).

Value

numeric vector the same length as y. A block of length < 2 has no distances and returns zeros.

Details

The computation is the sorted closed form (no n-by-n distance matrix), made numerically stable by first subtracting the median. L1 distances are translation invariant, so the subtraction changes nothing about the answer; it keeps the prefix sums small so the fast form matches the definitional sum-of-distances on the same input to machine precision even when y carries a large location (dollars, populations). It does not recover precision already lost when y is stored as a large offset plus a small spread — no algorithm can — but unlike a plain cumsum-then-subtract it adds no error of its own.