Managing large-scale scientific hypotheses as uncertain and probabilistic data

1.9 MB·English

by  Bernardo Gonçalves

National Laboratory for Scientific Computing
Graduate Program in Computational Modeling
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PETROPOLIS, RJ - BRASIL
FEBRUARY - 2015
MANAGING LARGE-SCALE SCIENTIFIC HYPOTHESES AS
UNCERTAIN AND PROBABILISTIC DATA
Bernardo Gon¸calves
THESIS SUBMITTED TO THE EXAMINING COMMITTEE IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOC-
TOR OF SCIENCES IN COMPUTATIONAL MODELING.
Approved by:
Prof. Fabio Porto, D.Sc.
(Chair)
Prof. Pedro L. Dias, Ph.D.
Prof. Marco A. Casanova, Ph.D.
Prof. Ana Carolina Salgado, D.Sc.
´
PETROPOLIS, RJ - BRASIL
FEBRUARY - 2015
© 2015, Bernardo Nunes Gon¸calves.
All rights reserved.
Gon¸calves, Bernardo
G635m Managing large-scale scientific hypotheses as uncertain and probabilis-
tic data / Bernardo Gon¸calves. Petropo´lis, RJ. : National Laboratory for
Scientific Computing, 2015.
xvii, 128p. : il.; 29 cm
Orientador: Fabio Porto
Thesis(D.Sc.)–National Laboratory for Scientific Computing, 2015.
1. Hypothesis management. 2. Predictive analytics. 3. Uncertain and
probabilistic data. 4. Causal reasoning. 5. Probabilistic database design. I.
Porto, Fabio. II. LNCC/MCT. III. T´ıtulo.
CDD – 629.8
Dedicatory
To my parents Tania and Francisco,
and to my special love, Marcelle,
for being an island of certainty in an
uncertain world.
Acknowledgments
This thesis work has been supported by LNCC (Graduate Program in Com-
putational Modeling), CNPq (grant 141838/2011-6), FAPERJ (grant ‘Nota 10’
E-26/100.286/2013) and IBM (Ph.D. Fellowship 2013/2014).
I would like to express my gratitude to my advisor Fabio Porto for the gift
of the challenging topic of this thesis, so special to me. I am grateful to him
for being an inspiring advisor, and for nicely influencing me towards database
research. I also thank my thesis committee for their attention and time devoted in
the assessment of my work. I am indebted to Ana Maria Moura for her generous
advice and support throughout my Ph.D. research, and to Frederico C. Silva and
Adolfo Simo˜es for their support to my research project at DEXL/LNCC.
I would like to thank very much all researchers at LNCC who give lectures in
thegraduateprogram, speciallyProf. Jos´eKaramFilhoforteachingmegenerously
about the roots of mathematical modeling. They have contributed significantly to
my education as a cross-disciplinary thinker and the shaping of my scientific and
mathematical skills. I thank my Ph.D. colleagues and friends at LNCC, specially
Eduardo Lima, Ramon Costa, Klaus Wehmuth, Raquel Lopes, Karine Guimar˜aes
and Diego Paredes for their companionship and joy shared in the pursuit of their
Ph.D. theses. I would also like to gratefully recall my earlier professors at UFES,
Jos´e Gon¸calves, Giancarlo Guizzardi, Rosane Caruso and Berilhes Garcia for shap-
ing the most essential building blocks in my education.
Finally, I would like to thank my family for their support: my father Fran-
cisco, my example of simplicity and goodness; my mother, Tania, for her tenacity
and true love; Leo and Sche, my dear brother and sister, true union for life; my
grandmothers Zeca, Orizontina and Rosita for their love and prayers. I thank also
Marcel and Maris for the greatest gift, their daughter and my near future wife,
Marcelle – the best partner one could ever hope for.
“Originally, there was just experimental science, and
then there was theoretical science, with Kepler’s
Laws, Newton’sLawsofMotion, Maxwell’sequations,
and so on. Then, for many problems, the theoreti-
cal models grew too complicated to solve analytically,
and people had to start simulating. These simulations
have carried us through much of the last half of the
last century. At this point, these simulations are gen-
erating a whole lot of data, along with a huge increase
in data from the experimental sciences.”
— Jim Gray, 2007
Abstract of Thesis presented to LNCC/MCT in partial fulfillment of the require-
ments for the degree of Doctor of Sciences (D.Sc.)
MANAGING LARGE-SCALE SCIENTIFIC HYPOTHESES AS
UNCERTAIN AND PROBABILISTIC DATA
Bernardo Gonc¸alves
February - 2015
Advisor: Fabio Porto, D.Sc.
In view of the paradigm shift that makes science ever more data-driven, in this
thesis we propose a synthesis method for encoding and managing large-scale de-
terministic scientific hypotheses as uncertain and probabilistic data.
In the form of mathematical equations, hypotheses symmetrically relate as-
pectsofthestudiedphenomena. Forcomputingpredictions,however,deterministic
hypotheses can be abstracted as functions. We build upon Simon’s notion of struc-
turalequationsinordertoefficientlyextractthe(so-called)causalorderingbetween
variables, implicit in a hypothesis structure (set of mathematical equations).
Weshowhowtoprocessthehypothesispredictivestructureeffectivelythrough
original algorithms for encoding it into a set of functional dependencies (fd’s) and
then performing causal reasoning in terms of acyclic pseudo-transitive reasoning
over fd’s. Such reasoning reveals important causal dependencies implicit in the hy-
pothesispredictivedataandguideoursynthesisofaprobabilisticdatabase. Likein
the field of graphical models in AI, such a probabilistic database should be normal-
ized so that the uncertainty arisen from competing hypotheses is decomposed into
factors and propagated properly onto predictive data by recovering its joint prob-
ability distribution through a lossless join. That is motivated as a design-theoretic
principle for data-driven hypothesis management and predictive analytics.
The method is applicable to both quantitative and qualitative deterministic
hypotheses and demonstrated in realistic use cases from computational science.
ResumodaTeseapresentadaaoLNCC/MCTcomopartedosrequisitosnecessa´rios
para a obten¸c˜ao do grau de Doutor em Ciˆencias (D.Sc.)
GEREˆNCIA DE HIPO´TESES CIENT´IFICAS DE LARGA-ESCALA
COMO DADOS INCERTOS E PROBABIL´ISTICOS
Bernardo Gonc¸alves
Fevereiro, 2015
Orientador: Fabio Porto, D.Sc.
Tendo em vista a mudan¸ca de paradigma que faz da ciˆencia cada vez mais guiada
pordados, nestatesepropomosumm´etodoparacodifica¸ca˜oegerˆenciadehip´oteses
cient´ıficas determin´ısticas de larga escala como dados incertos e probabil´ısticos.
Na forma de equa¸co˜es matema´ticas, hipo´teses relacionam simetricamente as-
pectos do fenoˆmeno de estudo. Para computa¸ca˜o de predic¸˜oes, no entanto, hipo´te-
ses determin´ısticas podem ser abstra´ıdas como fun¸co˜es. Levamos adiante a noc¸˜ao
de Simon de equa¸co˜es estruturais para extrair de forma eficiente a ent˜ao chamada
ordena¸c˜ao causal impl´ıcita na estrutura de uma hipo´tese.
Mostramos como processar a estrutura preditiva de uma hip´otese atrav´es de
algoritmos originais para sua codifica¸ca˜o como um conjunto de dependˆencias fun-
cionais (df’s) e ent˜ao realizamos inferˆencia causal em termos de racioc´ınio ac´ıclico
pseudo-transitivo sobre df’s. Tal racioc´ınio revela importantes dependˆencias cau-
sais impl´ıcitas nos dados preditivos da hip´otese, que conduzem nossa s´ıntese do
banco de dados probabil´ıstico. Como na a´rea de modelos gra´ficos (IA), o banco de
dados probabil´ıstico deve ser normalizado de tal forma que a incerteza oriunda de
hipo´teses alternativas seja decomposta em fatores e propagada propriamente re-
cuperando sua distribui¸ca˜o de probabilidade conjunta via jun¸ca˜o ‘lossless.’ Isso ´e
motivadocomoumprinc´ıpiote´oricodeprojetoparagerˆenciaeana´lisedehip´oteses.
O m´etodo proposto ´e aplica´vel a hipo´teses determin´ısticas quantitativas e
qualitativas e ´e demonstrado em casos real´ısticos de ciˆencia computacional.
Table of Contents
1 Introduction 1
1.1 Problem Space and Specific Goals . . . . . . . . . . . . . . . . . . . 4
1.2 Thesis Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Vision: Hypotheses as Data 15
2.1 Running Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Hypothesis Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Reasoning over FD’s . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Uncertainty Introduction . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Predictive Analytics . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7 Summary: Key Points . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Hypothesis Encoding 32
3.1 Preliminaries: Structural Equations . . . . . . . . . . . . . . . . . . 32
3.2 The Problem of Causal Ordering . . . . . . . . . . . . . . . . . . . 36
3.3 Total Causal Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4 The Encoding Scheme . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.6 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.7 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 Causal Reasoning over FD’s 49
4.1 Preliminaries: Armstrong’s Inference Rules . . . . . . . . . . . . . . 49
TABLEOFCONTENTS x
4.2 Acyclic Pseudo-Transitive Reasoning . . . . . . . . . . . . . . . . . 50
4.3 Equivalence with Causal Ordering . . . . . . . . . . . . . . . . . . . 55
4.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.6 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Probabilistic Database Synthesis 61
5.1 Preliminaries: U-Relations and Probabilistic WSA . . . . . . . . . . 61
5.2 Running Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3 U-Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.4 U-Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.5 Design-Theoretic Properties . . . . . . . . . . . . . . . . . . . . . . 73
5.6 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.7 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6 Applicability 79
6.1 The Physiome Project as a Testbed . . . . . . . . . . . . . . . . . . 79
6.2 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3 System Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7 Conclusions 102
7.1 Revisiting the Research Questions . . . . . . . . . . . . . . . . . . . 102
7.2 Significance and Limitations . . . . . . . . . . . . . . . . . . . . . . 105
7.3 Open Problems and Future Work . . . . . . . . . . . . . . . . . . . 106
7.4 Final Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 107