The end of geographic theory ? Prospects for model discovery in the geographic domain Mark Gahegan Centre 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.

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 Discovery 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 Discovery Given: – 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,

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 Evaluation: EXPLAINING, TESTING, GENERALIZING Presentation: COMMUNICATING, CONSENSUS- BUILDING Presentation: COMMUNICATING, CONSENSUS- BUILDING Synthesis: LEARNING, CATEGORIZING Data Map Explanation confidence Results Theory Category, relation Model Concept Hypothesis 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 and 5.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