📐algorithm-weighted-covariance

The groupant beside algorithms/src/weighted_covariance/mod.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

Facts

Components

Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

Model text

descriptant

weighted_covariance algorithm

Original std-only implementation and fixtures; source citations appear in module documentation.

Dimension1..64; finite |coordinates|<=1e100, weight[0,1e100]. Push validates dimension then point then weight before zero-weight no-op. Merge validates equal dimensions before empty neutrality. W=A+B, delta=meanB-meanA, mean=meanA+delta*B/W, M2=M2A+M2B+outer(delta)A(B/W). Population covariance M2/W; empty None.

Epoch 2026-10-30: independent tiny-domain oracle, repeated debug/release and compiled production mutation. No timing or end-to-end Mova claims.

model

Invariants and state

Dimension1..64; finite |coordinates|<=1e100, weight[0,1e100]. Push validates dimension then point then weight before zero-weight no-op. Merge validates equal dimensions before empty neutrality. W=A+B, delta=meanB-meanA, mean=meanA+delta*B/W, M2=M2A+M2B+outer(delta)A(B/W). Population covariance M2/W; empty None.

Reported arithmetic failures exclude partial updates; invalid zero-weight observations still error. Negative input weights and mismatched dimensions exclude success. Covariance is population rather than unbiased sample estimator.

O(dd) push/merge/storage; getters mean/weight O(1), covariance O(dd) allocation.

All allocations follow standard Rust process policy, not fallible allocation APIs. No callbacks or external effects. f64 roundoff and underflow remain explicit limitations.

approximant

Forward and cost approximant

Dimension1..64; finite |coordinates|<=1e100, weight[0,1e100]. Push validates dimension then point then weight before zero-weight no-op. Merge validates equal dimensions before empty neutrality. W=A+B, delta=meanB-meanA, mean=meanA+delta*B/W, M2=M2A+M2B+outer(delta)A(B/W). Population covariance M2/W; empty None.

O(dd) push/merge/storage; getters mean/weight O(1), covariance O(dd) allocation.

No executable cheaper surrogate or supported generic 1/2/5/10% profile is claimed. Residuals and floating estimates are not solution-error certificates.

models

behavior_complement

Reported arithmetic failures exclude partial updates; invalid zero-weight observations still error. Negative input weights and mismatched dimensions exclude success. Covariance is population rather than unbiased sample estimator.

reverse_reconstruction

Many weighted point multisets share W, mean, M2; permutations and splitting one observation into same-point weights preserve real moments. Original sample count and points are not reconstructible. Grouping can change floating results.

merge_moments

The between-group rank-one correction restores centered second moments. Independent two-pass weighted moments checks this recurrence over all small weight choices and all split points.

zero_mass

Zero-weight points are validated then ignored. Empty merge is neutral only after dimension agreement. Empty covariance/mean returns None.

atomic_failure

Compute temporary mean/M2/total and validate finiteness before assigning; arithmetic rejection leaves source state byte-equivalent by PartialEq.

population_policy

Covariance divides M2 by total mass, not W-1. No unbiased estimator or effective-sample-size interpretation; standard allocations can abort and no callback is invoked.

tests

Validation

Run cargo test -p mova-algorithms weighted_covariance::tests. Evidence in $MOVA_DATA/runs/octopus-wave26-probability-2026-10-30: repeated profiles, mutation logs and restored positive runs. Three named tests per module. See receipt.json for evidence hashes. No allocator fault injection, timing or full-school measurement.

prospective

Probability batch prospective math

Written before implementation. All code original, std-only. Bounded allocations use standard Vec; allocator failure follows Rust process policy, no callbacks or RNG.

Alias: Walker (1977), An efficient method for generating discrete random variables with general distributions; Vose (1991), A linear algorithm for generating random numbers with a given distribution. n 1..4096, finite nonnegative weights, positive maximum. Scale by maximum then total to avoid overflow. Small/large work lists conserve total scaled mass. Column uniform and coin uniform [0,1) produce the specified categorical distribution in real arithmetic; caller explicitly supplies coordinates. O(n) build/storage, O(1) draw. No probabilistic draw generation or numeric percentage guarantee.

HMM: Rabiner (1989), A tutorial on hidden Markov models and selected applications in speech recognition; Viterbi (1967), Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. n1..64, T0..4096; finite probabilities in [0,1], initial/transition rows sum to one within 1e-10. Emissions time-major likelihoods in [0,1], need not sum across states. Validate structure then numeric values before empty sequence. Empty log likelihood0/path empty. Viterbi log max-plus recurrence, predecessor ties lowest index and terminal ties lowest index (not global lexicographic). No positive path =>None. Forward/backward log-sum-exp, posterior proportional exp(alpha+beta-logZ); per-row normalization corrects rounding. O(Tn²) time/O(Tn) space. Tiny exhaustive state-sequence enumeration is independent oracle. Log scales avoid direct-product underflow; no general floating error bound.

Sinkhorn: Sinkhorn and Knopp (1967), Concerning nonnegative matrices and doubly stochastic matrices. Positive matrix entries and marginals restricted [1e-100,1e100], dims1..64, equal marginal totals within tolerance1e-12 relative. Alternate row and column multiplication to target marginals; residual max absolute marginal discrepancy. Budget0..10000, finite tolerance>0. Stop on residual<=tolerance or budget; overflow/underflow to zero explicit arithmetic error. O(iterationsrc) time/O(rc) space. Residual is feasibility evidence, not solution distance/optimality guarantee. Scale-invariant input fibers and budget status explicit.

Weighted covariance: West (1979), Updating mean and variance estimates: an improved method; Chan, Golub, LeVeque (1983), Algorithms for computing the sample variance. dimension1..64; finite coordinates |x|<=1e100, weights[0,1e100]. Population covariance M2/W, not unbiased sample covariance. Zero weight validates coordinates then does nothing. Merge dimensions must match, empty neutral. Merge W=A+B; delta=muB-muA; mu=muA+deltaB/W; M2=M2A+M2B+delta outer deltaA*(B/W). Atomic error updates, finite intermediates required. O(d²) push/merge/storage. Independent batch weighted centered moments oracle, partition merge equivalence within tolerance. No order-bitwise identity or universal covariance error certificate.

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