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PhD / EXPLAINABLE AI / DECEMBER 2025

Mining Patterns
on Tabular Data.

Turning the hidden logic of relational data into rules you can read, verify, and question.

François AmatInstitut Polytechnique de Paris
Download thesis Defence slides
research.graphOVERVIEW
From relational tables to explainable rulesConnected tables are mined for candidate rules. Support and confidence provide auditable evidence for evaluating them.RELATION_1RELATION_2RELATION_3∀ → ∃RULE MININGEXPLICIT RULESbody ⇒ headAUDITABLE EVIDENCEsupport · confidence01 / DATA02 / PATTERNS
tables → patterns → explanations
NNT: 2025IPPAT046Explore the research

// 00 / THE RESEARCH QUESTION

The schema isn’t
the whole story.

Relational databases form the backbone of modern information systems. But much of their business logic remains in the data itself: implicit regularities that a schema cannot capture. This thesis introduces a deterministic framework for mining those patterns.

MATILDA and MAHILDA discover expressive Tuple-Generating Dependencies and Horn Rules directly from relational tables. The result is a set of verifiable, explicit rules for auditing, data quality, and logical imputation.

Inspect the rule. Trace the evidence. Understand the result.

// THE CONTRIBUTIONS

Two systems. Readable rules.

Explore a schema, switch to a concrete example, then walk through the mining pipeline.

CHAPTER 0401 / 02

MATILDA

Tuple-Generating Dependencies

Discover the rules between tables.

A scalable algorithm for mining first-order dependencies with multi-atom heads and existential witnesses. It captures implications that span several relational tables.

  • Multi-table joins, represented in a constraint graph.
  • New existential variables, such as a shared location.
  • Auditable, closed-world support and confidence.
View MATILDA on GitHub
BODYMARRIAGE(x,y)observed tuplesRESIDENCE(x,l,s)head atom 01RESIDENCE(y,l,s)head atom 02same l, s∃ l, sone implication → shared witnesses
One body, two head atoms. Both residences share the same existential witnesses l and s.
tuple-generating dependency
∀x,y: MARRIAGE(x,y)
  ⇒ ∃l,s: RESIDENCE(x,l,s) ∧ RESIDENCE(y,l,s)
Explore the algorithm04 steps
STEP 01 / 04

Constraint Graph Construction

Compile the database schema into a graph where nodes represent joinable attributes.

Lineage.parentattributeMarriage.partner1attributeResidence.personattributejoinable
illustrative example
Lineage.parent = Marriage.partner1

Joinable attributes define the search space.

CHAPTER 0502 / 02

MAHILDA

Horn Rules · Disjoint Semantics

Find recursive patterns. Skip trivial loops.

A specialized system for mining recursive Horn rules. Disjoint semantics prevents vacuous self-loops, providing a rigorous baseline for inductive logic programming.

  • Foreign-key paths guide the search space.
  • Distinct tuple bindings rule out trivial self-loops.
  • Support-based pruning discards unpromising branches.
View MAHILDA on GitHub
Table Abody bindingTable A′head binding≠disjoint checkdifferent primary-key bindings
A relation can occur on both sides of a rule. Disjoint bindings prevent the same tuple from proving itself.
disjoint Horn rule
LINEAGE(p,c₁) ∧ MARRIAGE(p,s)
  ⇒ LINEAGE(p,c₂)    where c₁ ≠ c₂
Explore the algorithm04 steps
STEP 01 / 04

Schema Analysis

Focus the search space on meaningful paths defined by foreign keys.

Lineage.parentforeign keyPerson.idprimary keyFK → PKselect meaningful schema paths
illustrative example
Lineage.parent → Person.id

Foreign-key relationships guide path selection.

// KEEP EXPLORING

The full research,
down to the details.

Definitions, algorithms, and experiments in the dissertation. A shorter route through the work in the defence slides.

Doctoral dissertationMining Patterns on Tabular DataDefence slidesResearch presentation · December 2025

// 03 / DEFENCE COMMITTEE

The people behind the questions.

Directeur de thèse

Fabian Suchanek

Télécom Paris

Co-directeur de thèse

Pierre-Henri Paris

Université Paris-Saclay

Rapporteur

Fatiha Sais

Université Paris-Saclay

Rapporteur

Pierre Senellart

ENS Paris

Examinateur

Bernd Amann

Sorbonne Université

Examinatrice

Nathalie Pernelle

Université Sorbonne Paris Nord

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