The end of geographic theory?

Prospects for model discovery in the geographic domain

Mark GaheganCentre for eResearch & Dept. Computer Science

University of Auckland, New Zealand

The holy grail of analytics

Analytical models that can explain their own reasoning

– David Harvey– Peter Gould– Stan Openshaw

Computational Model Discovery (or Discovery Informatics)

Recap: there are two kinds of analytical models…

- Predictive models

- Descriptive models

In what way is this new?

Data mining & knowledge discovery– Does not emphasize model comprehensibility– Does not take advantage of prior knowledge– Produces predictive models that do not connect to

existing knowledge

Computational Model Discovery– Focus on interpretability of models by humans– Interested in explanations by connecting

observations to theory

Explanation in Geography (Harvey 1969)

Examines the stages of geographic investigation and how together they support explanation, via:- methodological frameworks: the nature of investigation and - philosophy: the nature of the science process and its various conceptual artifacts (includes ontology), - which determine representation: how we abstract and represent the world and - analysis: how we model and analyze the world - through to explanation: which uses theory to describe what our analysis reveals.

Theory

Domain model

Scientific process model

Inductive learning of models based on processes

• A process is a collection of related functions– Differential or algebraic form– Can be a single equation

• Can have unobserved variables• Specifies a causal relationship between one or

more input and output variables

Computational Model DiscoveryPredator prey ecosystem

Concentration

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

Tim e (days)

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6

A u r - O b sN a s - O B S

Prey

Predator

Example Process Model (from SC-IPM, Bridewell, 2008)

Prey growth

Predation

Predator loss

Algebraic process to calculate grazing rate

Bridewell et al, 2008

Inducing Process Models Summary

• Input– Time-series data– Domain knowledge– Processes and constraints

• Structure search– Combine processes together using constraints and an

evaluation strategy to limit the search• Parameter search

– For a given structure, fit parameters and evaluate• Output

– List of models ranked by score

Computational Model DiscoveryGiven:– a methodology for the research and– a meta-model for the process of the research and– a set of representational forms for the observations (data)– observations for a set of variables;– a set of categories (entities) that the model may include;– a set of generic processes that specify relations among

entities;– a set of constraints that indicate plausible relations among

processes and entities;Find: – a specific process model and associated parameterization that

not only predicts the observed values but also explains them

EVE, a bench robot for drug discovery?

Qi et al, 2010, Journal of Integrative Bioinformatics, 7(3):126, 2010 http://journal.imbio.de

GOES early fire detection system

Koltunov et al, 2012

So, how close are we, in GIScience, to discovering process models?

Example domain model: OneGeology

Example library of analytical functions (PySAL)

One possible process for scientific investigation

Exploration: EXPLORING,

DISCOVERING

Analysis: GENERALIZING

, MODELING

Evaluation:EXPLAINING,

TESTING,GENERALIZING

Presentation: COMMUNICATING,

CONSENSUS-BUILDING

Synthesis: LEARNING,

CATEGORIZING

Data

Map

Explanation confidence

Results

Theory

Category, relation

Model

ConceptHypothesis

Gahegan, 2005

CyberGIS Grand Challenge

Create a ‘Geographical Process Model Discovery System’ that integrates:

– a science model– a domain (data) model– analysis software– data– (constraints)

Are there limits to what we can learn from data?

• Yes, but our learned models may still be useful• Yes, the model is—at best—as good as the

data– But this still might be better than current theory

• Yes, but as data becomes ubiquitous, then these limits will retreat

End

CyberGIS Workflow: 5 simple (and also very complicated) steps

1. Discover and gain access to, and – to some extent – understand (e.g. the semantics, the provenance, the limitations of) each dataset we intend to use.

2. Harmonize these datasets into a consistent form (data model), for example by re-projecting, converting from raster to vector and harmonizing the semantics. (Data Model Integration)

3. Analyze the datasets via an analytical workflow of some kind. (Software Integration)

4. Validate the accuracy and suitability of the results and5. Publish the results back into the Infrastructure. The results

are of little value unless they maintain connections to the above steps.

Learn a predictive model, even when entire steps/states are missing?Bayesian belief network learning

An example inferred model from GIScience

The consumer wants fit-for-purpose data, but the task and domain semantics are not given (latent variables).

Gahegan & Adams, 2014

The education of the GIScientist?

• Better data custodian skills• Better scientific computing skills—but you

have to bring the geographic understanding too

• Deeper awareness of the processes /philosophy of our science

• A greater respect for data…• An outward gaze…

Data

Concept

Results

Theory

Explanation confidence

Exploration: EXPLORING,

DISCOVERING

Analysis: GENERALIZING,

MODELING

Evaluation:EXPLAINING,

TESTING,GENERALIZING

Presentation: COMMUNICATING

, CONSENSUS-BUILDING

Synthesis: LEARNING,

CATEGORIZING Category, relation

Map

Model

Hypothesis

Scatterplot, grand tour, projection pursuit, parallel coordinate plot, iconographic displays

Self organizing map, k-means, clustering, geographical analysis machine, data mining, concept learning.

Interactive visual classification, parallel coordinate plot, separability plots, graphs of relationships

machine learning, maximum. likelihood, decision trees, regression & correlation analysis

Scene composition, information fusion, visual overlay

Statistical modeling,

Uncertainty visualization

Statistical testing, M-C simulation

Maps, navigable worlds, charts, immersive visualizations

Databases, Digital libraries, clearinghouses

…with types of inference and examples of visual and computational methods

The First Paradigm:Experiment/Measurement

The Second Paradigm:Analytical Theory

The Third Paradigm:Numerical Simulations

The Fourth Paradigm:Data-Driven Science?Data fusion + data mining + synthesis/learning + explanation

The Evolving Paths to Knowledge

George Djorgovski, Caltech)

Building Explanatory Models from Time-Series Data

• Process models are a natural choice• Many ways to define process• Processes are casual relations between one or

more input and output variables• Processes represent knowledge in notation

familiar to scientists– Helpful for explanation