Perceiving the World through Statistics: ENBIS-14

Perceiving the World through Statistics:

Some Dimensional Thoughts

Michel Lutz

OCTO Technology

Rodolphe Le Riche

CNRS and Ecole des Mines de Saint-Etienne

ENBIS-14

Motivation

• Statistical analysis: positive facts or pure mental construction ?

• Our belief: standpoint over the contingency (Desrosières,

2010), knowledge creation, useful for decision-making,

based on our capacity to grasp our multidimensionnal world

• Consequence: « true », but inevitably partial and distorted descriptions of a complex world

Statistics analysis ≠ THE Truth

• Risks that can be avoided/controlled by a careful analysis:

• Spurious correlation due to hidden variables, large samples

(Granville, 2013) or compositional data (Pearson, 1897)

• Spurious regression caused by the presence of a unit root

(Granger & Newbold, 1974)

• Bertrand paradox: probabilities may be influed by

mechanisms or methods that produces the random variables

• Inevitable consequences of the analysis:

• Distortions of our infinite-dimensionnal world, which cannot be analyzed as a whole (Rucker, 1984)

• This is the scope of this presentation

Metaphor: welcome to Flatland

Proposition: when crunching data, we are travelling through hyperspaces

Knowledge D

(Tsoukas & Vladimirou, 2001 ; Alavi &

Leidner, 2001 ; Tuomi, 1999)

Proposition

knowledge creation

=

a dynamic back & forth process

between higher and lower dimensional hyperspaces

Going down through dimensions

D_real = ∞

D_data = M

Dinformation = m

D_knowledge = n

∞ > M > m > n

D

Why? Cognitive limitations

• Capacity of perception

• High dimension is not intuitive

• Interpretation is difficult

Why? Technical limitations

• Capacity to measure, store and process data are limited

• Curse of dimensionality: the higher the

dimension, the more data

Consequence: distortions

x1

x2 A

B

C

Dimension: number of variable

Event: ... is closer to ... than ... (Euclidean norm)

[Be A(x_a,y_a) and B(x_b,y_b) ; dist.(AB) = ]

• ^Data: A is farther to B than C.

• According to x1 : A is closer to B than C.

• According to x2 : A is farther to B than C.

(xb −xa)²+(yb −ya)²

Consequence: distortions

CONTRADICTION

Definition: “is contradictory a knowledge of the reality that is both A and non-A”

Partial knowledge

Going up through dimensions thanks to technical innovations

• « Big Data » architectures: more

measures, more storage, more processing capacities

• Machinery can help us to grasp more

complexity

Going up through dimensions thanks to ad hoc quantitative analysis

• Useful to overcome some contradictions…

Ex. : concatenation, SVM classification (Vapnik, 1995 ; Aizerman & al., 1964)

Going up through dimensions

• … can also bring to other contradictions…

Ex. : SVM kernel trick  several kernels can be used !

• … and cognitive limitations still exist !

Perceiving hyperspaces (> 3) is not straightforward for human and needs specific learning

The knowledge: a dynamic back & forth process between higher and lower dimensional hyperspaces

Too much

dimensions Reduction

Contradiction Knowledge

More dimensions Data

Human knowledge is dynamic, recurring and constantly surpassing

Statistics

Statistics

D

Conclusions

• Dynamic human knowledge process: towards complex thinking (Morin, 2005)

• Statistics serve human cognition: tools and methods to build reasoned and dialectic knowledge

• Debate:

• Machine (data processing) + human (intuition, interpretation) = increase human knowledge for decision-making

 How far can the limits of human intelligence be pushed by artificial intelligence?

• Could human limitations be surpassed by artificial intelligence?

Eg. Could human be excluded of the knowledge process for decision-making?

 Black box models

 Does a machine generate knowledge for itself?

References

Abbott, Flatland, Librio Littérature, 2013

Alavi & Leidner, Knowledge management and knowledge management systems: conceptual foundations and research issues, MIS quarterly, 2001

Aizerman, Braverman & Rozonoer, Theoretical foundations of the potential function method in pattern recognition learning, Automation and Remote Control, 1964

Desrosières, La politique des grands nombres – Histoire de la raison statistique, La Découverte, 2010Donoho, Aide-Mémoire. High-dimensional data analysis: the curses and blessings of

dimensionnality, Departement of Statistics, Stanford University, 2000

Granger & Newbold, Spurious Regression in Econometrics, Journal of Econometrics, 1974 Granville, The curse of big data, 2013, http://www.analyticbridge.com/profiles/blogs/the- curse-of-big-data

Morin, Introduction à la pensée complexe, Seuil, 2005

Pearson, Mathematical Contributions to the Theory of Evolution—On a Form of Spurious Correlation Which May Arise When Indices Are Used in the Measurement of Organs,

Proceedings of the Royal Society of London, 1897

Rucker, The fourth dimension – A guided tour of the higher universes, Houghton Mifflin Company, 1984

Tsoukas & Vladimirou, What is organizational knowledge, Journal of Management Studies, 2001Tuomi, Data is more than knowledge – Implications of the reversed knowledge hierarchy for knowledge management and organizational memory, Journal of Management Information Systems, 1999

Vapnik, The nature of statistical learning theory, Springer-Verlag, 1995

Thank you ENBIS-14

Michel Lutz & Rodolphe Le Riche