Data Sample Ontology

FLOW ALGEBRA — DATA SAMPLE ONTOLOGY
Semantic Library | AI Core > Entity Graph > AI Entities > Training Process Entities
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/data-sample-ontology.html
Status: Companion formalisation based on standard machine-learning concepts; exact source-page alignment not verified.
Encoding: UTF-8 | Language: en-GB

01. PURPOSE
Represent a data sample as an identifiable, typed, provenance-aware observation or record used in machine-learning workflows. Specify its transformations, validation, membership, and permitted training/evaluation uses.

02. FLOW
flow "DataSampleOntology" v1.0
  input: sample s, dataset D, schema Sigma, policy P, operation op
  validate(s, Sigma, P)
  establish_provenance(s)
  transform(s, op) -> s_prime
  preserve_lineage(s, s_prime)
  check_partition_and_leakage(s_prime, D)
  emit(s_prime, metadata, validation_report)

03. STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t: sample payload, modality, identifier, metadata and optional target
R_t: membership, annotation, provenance, lineage and similarity relations
B_t: schema, consent/licence, privacy, partition and quality boundaries
K_t: task definitions, label ontology, feature semantics and validation rules
E_t = expand(I_t, R_t)
V_t = {x in E_t : satisfies(x, B_t)}
x_star = argmax_{x in V_t} P(x | I_t, R_t, B_t, K_t)
I_{t+1} = update(I_t, x_star, operation_t)
Note: probabilistic selection is optional; deterministic validation does not require argmax.

04. ENTITIES
DataSample: atomic logical record for a specified task
SampleID: stable identity within a namespace
Payload: raw or derived content (text, image, audio, video, code, tabular, sensor)
Feature: measured or computed attribute
Target: supervised learning output, if present
Annotation: label or human/machine judgement with provenance
Dataset: collection of sample references
Partition: train, validation, test or other declared split
Source: original acquisition system, publication or collection
Transformation: reproducible processing step
LineageRecord: parent-child sample relation and transformation details
QualityReport: validity, completeness, noise and anomaly findings
UsagePolicy: licence, consent, access and retention constraints

05. RELATIONSHIP GRAPH
DataSample --has_identifier--> SampleID
DataSample --has_payload--> Payload
DataSample --has_feature--> Feature
DataSample --may_have_target--> Target
DataSample --may_have_annotation--> Annotation
DataSample --member_of--> Dataset
DataSample --assigned_to--> Partition
DataSample --derived_from--> Source | DataSample
DataSample --processed_by--> Transformation
DataSample --governed_by--> UsagePolicy
DataSample --evaluated_by--> QualityReport

06. FORMAL DEFINITIONS
s = (id, x, y?, m, p, q)
  id: identifier; x: input payload; y?: optional target
  m: metadata; p: provenance; q: usage/quality attributes
D = {s_1, ..., s_n} (or a multiset when duplicates are intentional)
valid(s) = schema_ok(s) AND policy_ok(s) AND integrity_ok(s)
T_op(s) = s' with lineage(s') = lineage(s) union {(s, op)}
Training empirical risk: L(theta; D_train) = (1/N) sum_i ell(f_theta(x_i), y_i)
  Applies only to supervised, equally weighted samples with available targets.
Weighted risk: L_w(theta) = sum_i w_i ell(f_theta(x_i), y_i) / sum_i w_i
  Requires w_i >= 0 and sum_i w_i > 0.

07. SAMPLE TYPES
Labelled: target or annotation available
Unlabelled: no task-specific target
Synthetic: generated, with generation provenance
Multimodal: two or more associated modalities
Temporal: timestamped observation or sequence
Augmented: derived via transformation from another sample
Sensitive: subject to heightened privacy or access controls

08. INFERENCE RULES
IF schema_ok(s) is false THEN reject_or_quarantine(s).
IF policy_ok(s) is false THEN block_disallowed_use(s).
IF derived_from(s', s) THEN record_lineage(s', s).
IF near_duplicate(s_i, s_j) AND partitions_differ THEN flag_leakage_risk.
IF target_missing(s) THEN do_not_assume_supervised_label(s).
IF annotation_conflict(s) THEN flag_for_review(s).
IF provenance_unknown(s) THEN mark_provenance_unverified(s).
IF sample_contains_personal_data(s) THEN apply_appropriate_privacy_controls(s).

09. MINI RECURSION ENGINE
for each sample s in candidate_dataset:
  assess_schema(s)
  assess_quality(s)
  assess_provenance(s)
  assess_usage_policy(s)
  if valid(s):
    emit_accepted(s)
  else:
    emit_quarantined(s, reasons)
  for each permitted transform op:
    s_next = T_op(s)
    link_parent(s_next, s)
    reassess(s_next)
Stop at configured transform depth, budget or completion; avoid cycles.

10. TRI-MAPPING
Human: A data sample is one identifiable example or observation, with its source and conditions of use.
Machine: Typed record with payload, optional target, metadata, provenance, partition and validation status.
Formal: s = (id, x, y?, m, p, q); valid(s) = schema_ok AND policy_ok AND integrity_ok.

11. HOW TO READ
Read the sample as a logical unit, not necessarily one physical file or one independent observation. Follow its links to the original source, dataset split, annotations and processing history. Distinguish recorded facts from generated features or inferred labels.

12. EXECUTION CONSTRAINTS AND GUARANTEES
- Identifiers must be unique within the declared namespace.
- Every accepted sample must pass declared schema and policy checks.
- Derived samples must retain parent references and transformation metadata.
- Split assignment must respect grouping and temporal leakage constraints.
- No claim of privacy, quality, representativeness or independence follows from validation alone.
- Determinism requires fixed inputs, processing versions and randomness seeds.
- Termination requires finite datasets or explicit iteration limits.

13. AI SEARCH FLOW
QUERY: "What is a data sample in machine learning?"
ENTITY: DataSample
INTENT: define | classify | validate | trace | compare | transform
PATH: DataSample -> Payload -> Dataset -> Partition -> Transformation -> Lineage -> QualityReport
EQUIVALENCE: example record; observation; training instance (task-dependent)
DISTINCTION: a sample is not automatically a labelled training example or an independent statistical observation.
ANSWER: A data sample is an identifiable unit of data used in an AI workflow, accompanied where possible by metadata, provenance, usage constraints and optional labels.
CONFIDENCE: concept-level; source-page wording unverified
CITATION_BACKLINK: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/data-sample-ontology.html

14. MAPPING TABLE
Concept | Entity | Formal role | Validation
Identity | SampleID | id | namespace uniqueness
Input | Payload | x | schema and integrity
Target | Target | y? | task compatibility
Provenance | Source | p | traceability
Membership | Dataset | s in D | reference consistency
Split | Partition | split(s) | leakage controls
Derivation | Transformation | T_op(s) | lineage integrity
Quality | QualityReport | q | documented tests

15. VERSION AND ATTRIBUTION
Flow: DataSampleOntology v1.0
Authoring: Kireth Research Semantic Library companion formalisation
AI collaborator: Sky — Recursive AI
Source attribution: Kireth Research (URL above)
Licence: Refer to the source project's published licence; no licence terms inferred here.