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Cognacy Queries over Dependence Graphs for Transparent Visualisations

Joseph Bond, Cristina David, Minh Nguyen, Dominic Orchard, Roly Perera

TL;DR

A new program analysis framework which supports interactive exploration of fine-grained I/O relationships directly through computed outputs, making use of dynamic dependence graphs, and shows how Jonsson and Tarski's concept of conjugate operators on Boolean algebras appropriately characterises the notion of cognacy in a dependence graph.

Abstract

Charts, figures, and text derived from data play an important role in decision making, from data-driven policy development to day-to-day choices informed by online articles. Making sense of, or fact-checking, outputs means understanding how they relate to the underlying data. Even for domain experts with access to the source code and data sets, this poses a significant challenge. In this paper we introduce a new program analysis framework which supports interactive exploration of fine-grained I/O relationships directly through computed outputs, making use of dynamic dependence graphs. Our main contribution is a novel notion in data provenance which we call related inputs, a relation of mutual relevance or "cognacy" which arises between inputs when they contribute to common features of the output. Queries of this form allow readers to ask questions like "What outputs use this data element, and what other data elements are used along with it?". We show how Jonsson and Tarski's concept of conjugate operators on Boolean algebras appropriately characterises the notion of cognacy in a dependence graph, and give a procedure for computing related inputs over such a graph.

Cognacy Queries over Dependence Graphs for Transparent Visualisations

TL;DR

A new program analysis framework which supports interactive exploration of fine-grained I/O relationships directly through computed outputs, making use of dynamic dependence graphs, and shows how Jonsson and Tarski's concept of conjugate operators on Boolean algebras appropriately characterises the notion of cognacy in a dependence graph.

Abstract

Charts, figures, and text derived from data play an important role in decision making, from data-driven policy development to day-to-day choices informed by online articles. Making sense of, or fact-checking, outputs means understanding how they relate to the underlying data. Even for domain experts with access to the source code and data sets, this poses a significant challenge. In this paper we introduce a new program analysis framework which supports interactive exploration of fine-grained I/O relationships directly through computed outputs, making use of dynamic dependence graphs. Our main contribution is a novel notion in data provenance which we call related inputs, a relation of mutual relevance or "cognacy" which arises between inputs when they contribute to common features of the output. Queries of this form allow readers to ask questions like "What outputs use this data element, and what other data elements are used along with it?". We show how Jonsson and Tarski's concept of conjugate operators on Boolean algebras appropriately characterises the notion of cognacy in a dependence graph, and give a procedure for computing related inputs over such a graph.
Paper Structure (51 sections, 16 theorems, 23 equations, 19 figures)

This paper contains 51 sections, 16 theorems, 23 equations, 19 figures.

Table of Contents

  1. Introduction: Towards Transparent Research Outputs
  2. Data transparency as PL infrastructure
  3. Contributions and roadmap
  4. Overview: Fine-Grained Interactive Provenance
  5. 1. Fine-grained linking of the data to the view.
  6. 2. Linked inputs.
  7. 3. Fine-grained linking of the view to the data.
  8. 4. Linked outputs.
  9. A Core Calculus for Transparent Outputs
  10. Some notation.
  11. Syntax
  12. Terms
  13. Foreign functions
  14. Continuations and eliminators
  15. Addresses, values and environments
  16. ...and 36 more sections

Key Result

lemma thmcounterlemma

$\hbox{o}rigin=c]{180}{$▿$}_{R}$ and $\triangledown_{R}$ are conjugate.

Figures (19)

  • Figure 1: A hand-crafted transparent visualisation due to bremer15
  • Figure 2: Data transparency: demanded by ($\hbox{o}rigin=c]{180}{$▿$}$) and demands ($\triangledown$) operators link inputs that share common output dependencies.
  • Figure 3: Moving average source code
  • Figure 4: Data transparency: demands ($\triangledown$) and demanded by ($\hbox{o}rigin=c]{180}{$▿$}$) operators link outputs that share common input dependencies.
  • Figure 5: Non-renewable energy source code
  • ...and 14 more figures

Theorems & Definitions (48)

  • definition thmcounterdefinition: In-star notation
  • definition thmcounterdefinition: Boolean algebra
  • definition thmcounterdefinition: Image and Preimage Functions for a Relation
  • definition thmcounterdefinition: Conjugate Functions
  • lemma thmcounterlemma
  • definition thmcounterdefinition: Galois connection
  • proposition thmcounterproposition
  • definition thmcounterdefinition: De Morgan Dual
  • definition thmcounterdefinition: Dual Image and Preimage Functions for a Relation
  • lemma thmcounterlemma: Duality of image and preimage functions
  • ...and 38 more