---
title: "probabilistic-inference — Mova code model"
description: "Mova code model of models/probabilistic-inference.groupant: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/models/probabilistic-inference.groupant/"
---
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# probabilistic-inference

The groupant beside models/probabilistic-inference.groupant 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

- **kind:** groupant_group
- **status:** partial source bound group
- **bound sources:** 10
- **repository folder:** [`models/probabilistic-inference.groupant`](https://github.com/ElamurAI/mova-free/tree/main/models/probabilistic-inference.groupant)
- **repository commit:** `855da7bd4a7b`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | partial source model | [forward](#forward) |
| **ast** | not materialized |  |
| **composition** | partial source model | [composition](#composition) |
| **cost** | partial source model | [cost](#cost) |
| **descriptant** | partial source model | [epoch-memory](#epoch-memory) |
| **invariant** | partial source model | [invariant](#invariant) |
| **tests** | bounded executed | [wave26-evidence](#wave26-evidence) |

## 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.

| id | type | label | where |
|---|---|---|---|
| `probabilistic-inference-behavior-complement` | behavior_complement | partial relational specification | [behavior-complement](#behavior-complement) |
| `probabilistic-inference-reverse-reconstruction` | reverse_reconstruction | partial relational specification | [reverse-reconstruction](#reverse-reconstruction) |
| `probabilistic-inference-max_sum_separation` | max_sum_separation | partial relational specification | [max_sum_separation](#max-sum-separation) |
| `probabilistic-inference-sampling_mass` | sampling_mass | partial relational specification | [sampling_mass](#sampling-mass) |
| `probabilistic-inference-support_convergence` | support_convergence | partial relational specification | [support_convergence](#support-convergence) |
| `probabilistic-inference-weight_normalization` | weight_normalization | partial relational specification | [weight_normalization](#weight-normalization) |

## Model text


### model

## probabilistic-inference

### forward

Tagged weighted observations: alias-table sampling decisions, most-probable sequence decoding, forward/backward posterior mass, Sinkhorn matrix scaling and weighted covariance. Deterministic supplied uniforms and probability normalization are separate from external randomness. HMM w(s)=pi(s0) product_t emission_t(st) product_{t>0}transition(st-1,st); Z=sum_s w(s),V=max_s w(s),0<=V<=Z. Posterior path sums divide by Z when Z>0. Sinkhorn X=diag(u)Kdiag(v),X1=r,X^T1=c. Population covariance=sum_i w_i(x_i-mu)(x_i-mu)^T/sum_i w_i under leaf denominator rules.

### invariant

Nonnegative mass, finite values, support, zero-total handling, sequence-state indexes and normalization/status conventions remain leaf-specific. Maximum-path score is not summed evidence; posterior marginal consistency is not joint-path optimality.

### cost

Alias preparation is linear and lookup constant within leaf bounds. Viterbi/forward-backward cost sequence length times transition work; Sinkhorn cost iterations times matrix cells plus marginal checks; weighted covariance includes sample/feature accumulation. Costs of producing random draws or building upstream models are outside these kernels.

### composition

Alias may sample a normalized posterior row only after row validity and index mapping are checked; a sampled marginal sequence is not a joint HMM sample. Viterbi and forward/backward can share initial/transition/emission data but compare max versus sum semantics, with consistent log/scaled conventions. Sinkhorn outputs can represent couplings only under its support/marginal convergence conditions. Weighted covariance consumes weights, not probabilities necessarily summing to one; normalization must match its population/sample convention.

### limitations

Successful allocations and each leaf's finite domain/error precedence. These are tagged relations, not automatic production adoption. Floating residuals are not solution-error guarantees. No generic 1/2/5/10% composition-wide profile; finite evidence remains separate from analytical claims.

### epoch-memory

Wave26, 2026-10-30. Tagged library tools; no automatic training adoption, source-volume quality claim or generic numerical profile.

### checks

["cargo test -p mova-algorithms alias_method::tests","cargo test -p mova-algorithms viterbi::tests","cargo test -p mova-algorithms forward_backward::tests","cargo test -p mova-algorithms sinkhorn_scaling::tests","cargo test -p mova-algorithms weighted_covariance::tests"]

### wave26-executed-checks

## probabilistic-inference: wave26 checks

15 source-local test declarations across five modules. Every module has a compiled failing production mutation followed by exact restoration. The final whole library passed 877 checks twice debug and twice release. See [integrated evidence](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave26-evidence) for scopes and limitations. These tagged APIs are not an invented serial pipeline.

### catalog

## Typed family relations

### behavior-complement

Type: behavior_complement.

Exclude V>Z for identical nonnegative path weights beyond documented rounding tolerance; posterior normalization at Z=0 contrary to status/error rules; invalid alias variates; exhausted Sinkhorn residuals treated as exact marginals; covariance with a substituted denominator.

### reverse-reconstruction

Type: reverse_reconstruction.

Z admits all HMMs with that path-weight sum; Viterbi constrains maximizing path/score but leaves other weights ambiguous. Alias outcomes do not reconstruct random source. Sinkhorn u->a*u,v->v/a preserves X for a>0. Covariance retains moments; many weighted multisets share them.

### max_sum_separation

Type: max_sum_separation.

Viterbi optimizes a path; forward/backward sums paths. Their scores generally differ even when the selected path is valid.

### sampling_mass

Type: sampling_mass.

Alias thresholds and supplied variates preserve their discrete mass model only under specified endpoints; no random-number source quality is certified.

### support_convergence

Type: support_convergence.

Zero support can make desired marginals unattainable. Sinkhorn residual/exhaustion statuses cannot be recast as a successful exact coupling.

### weight_normalization

Type: weight_normalization.

Weighted covariance normalization and effective degrees of freedom must match the consumer; uniform rescaling and zero mass need explicit handling.

### wave26-evidence

#### probabilistic-inference: wave26 checks

15 source-local test declarations across five modules. Every module has a compiled failing production mutation followed by exact restoration. The final whole library passed 877 checks twice debug and twice release. See [integrated evidence](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave26-evidence) for scopes and limitations. These tagged APIs are not an invented serial pipeline.