marginals

std.stats.marginals · Level L0

The two marginals of a finite joint distribution given as a table of masses P(X = i, Y = j): P(X = i) = Σⱼ, and P(Y = j) = Σᵢ.

P(X = i) = Σⱼ pᵢⱼ, P(Y = j) = Σᵢ pᵢⱼ

Signature

marginals(joint: f64[m, n]) → f64[m], f64[n]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference joint.sum(axis=1), joint.sum(axis=0) in exact rational arithmetic, on all 40 test cases.
All 302 float64 results inside the running error bound; the closest uses 86% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 93% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 87%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 1.24

Identity

Calls

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Called by

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sha256:5d98f30e5b586853f23ab9e1bc62a352dcc54c7e9140d46ce9b53c20f837634c

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.marginals · Ω:marginals
Pins: sha256:33658008e9fe31639f29a9ad773dbddc15a11af5942406100be92416db8e4f4fthis graph alone
Evidence: sha256:7d7ea84dc955751436e98258035a4cfe188a8bb0ea6bf4130f8781617d377bacthe hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.