Probabilistic causality Two-week summer school Central European University Budapest, Hungary July 21-August 1, 2008

tripastroturfAI and Robotics

Nov 7, 2013 (4 years and 6 days ago)

99 views


1

Probabilistic causality

Two
-
week summer school

Central European University

Budapest, Hungary

July
21
-
August 1, 2008


1. Syllabus


a) Statement of the purpose of the course



The aim of the summer school is to teach and discuss current results and recent t
rends in
probabilistic causation. Probabilistic causality emerged during the second half of the 20
th

century as a truly interdisciplinary field, involving concepts and methods of philosophy
(metaphysics and philosophy of science), classical and non
-
classi
cal probability theory and
the special sciences, especially physics and economics. A recent outgrowth of the theory is
Bayes nets, investigated not only in philosophy of science but also in computer science and
utilized in causal modeling. After a review o
f the basic notions and classical results on
probabilistic causation the course focuses on discussing problems that are open and debated
in the literature at this time. The course intends to bring together advanced graduate students
and young researchers
from different disciplines (philosophy, physics, economics and
computer science) and provides an opportunity for cross
-
disciplinary discussion. Such
discussions will be facilitated by organizing sessions of short presentations by participants; in
the short

talks participants can formulate their research topics and solicit comments by
faculty and other participants during the summer school. Faculty of the summer school have
taught different aspects of probabilistic causality in regular courses at LSE, ELTE,
and CEU,
and the summer school is based on a combination of these different courses.


b) Pre
-
requisites for the course


Participants are assumed to be familiar with the basic philosophical literature on classical
analysis of causation and are expected to
possess basic knowledge of classical probability
theory.


c) Brief overview of the course


Probabilistic theories of causation have emerged during the second half of the 20
th

century
with the development of mathematical probability theory and with the g
reat success of
probabilistic methods in both the exact and social sciences. One can discern two,
complementary trends in this development: motivated by the sciences and relying on their
concepts and techniques, abstract, philosophical theories of probabil
istic causation were
worked out, enriching analytic metaphysics by creating new approaches to the classical
problem of causation. Examples of such theories include H. Reichenbach’s notion of
common cause to explain probabilistic correlations and D. Lewis’
theory of counterfactual
probabilistic causation. In turn, these philosophically elaborated and technically sharpened
new concepts and tools have found their way back to the sciences: interesting new questions
about causation in the particular sciences hav
e been raised and new developments in special
sciences were triggered. Examples of this latter include the problem of whether quantum
correlations can have causal explanations in terms of Reichenbachian common causes, and
the theory of causal (Bayes) nets,

which are now popular also in computer science. This
mutual fertilization of philosophy and sciences is very characteristic of probabilistic causality

2

and makes probabilistic causation a truly interdisciplinary field. The course reviews the
recent results

in the theory of probabilistic causation, putting the emphasis on the open
problems and on the currently debated issues.


The course is divided into six major sections:


I.

Introductory lectures
. A general review of the current status of probabilistic
caus
ation is given, and, since notions of probability theory will be extensively
used in the subsequent lectures and discussions, one lecture will review briefly the
relevant concepts of both classical
and

non
-
classical (quantum) probability theory.

II.

The Common

Cause Principle.
In this block

Reichenbach’s classical notion

of
common cause and the related Common Cause Principle is recalled and analyzed.
The problem of causal (in)completeness and common cause completability of
classical and quantum probability spac
es is defined, and results on common cause
(in)completeness and common cause completability are presented and analyzed.
Generalizations of the notion of common cause to common cause s
ystems

will be
given and, after proving existence theorems about Reichenb
achian Common
Cause systems, properties of these common cause systems will be investigated.
Causal nets and the causal Markov condition used in Bayes nets are
generalizations of the Common Cause Principle. The basic definitions of and the
recent debates ab
out the causal Markov condition will be reviewed and discussed.

III.

Probabilistic causality in economics.

There is a long tradition of concepts of causality in economics, particularly in the
sub
-
discipline of econometrics, which aims to identify causal rela
tions from non
-
experimental economic data. In this part of the course, the main approaches to
causality in econometrics will be presented, critically compared and contrasted to
each other. In particular, Granger causality (where causal order is based on

time
order) and structural approach (where causal order is based on invariance
-
to
-
interventions) will be presented. These two key approaches represent the two
dominant strands of causality in econometrics, and both have affinities with
philosophical trea
tments of probabilistic causality. Granger causality is close to
Suppes’ probabilistic causality, while the structural approach, relates closely to
work on causality by Cartwright, Woodward and others. This course will be
concluded by analysis of how meth
ods of causal inference work in econometrics
for both kinds of causality presented above.




IV.

Causal explanations in physics.

EPR correlations predicted by quantum
mechanics (and observed in Nature) are a special challenge for the Common
Cause Principle bec
ause to explain these correlations in terms of common causes,
the common causes need to satisfy additional locality conditions that express the
no
-
action
-
at
-
a
-
distance principle of relativistic physics. The lectures in this section
review the possible form
ulations of the locality conditions and the new No
-
go
theorems that have been recently obtained, which indicate that EPR correlations
cannot be explained by local Reichenbachian common causes. Local (relativistic)
quantum field theory also predicts correl
ations between causally disjoint
(spacelike) entities; hence the status of the Common Cause Principle arises in
quantum field theory as well, this (largely) open problem will be analyzed.



3

V.

Learning Causal Influences Using Bayesian Networks

Bayesian net
works are
graphical structures for representing the probabilistic relationships among a large
number of variables and doing probabilistic inference with those variables. The
1990's saw the emergence of excellent algorithms for learning Bayesian networks
fr
om passive data. By making certain assumptions about the probabilistic causal
relationships among the observed variables, we can learn something about causal
influences in Bayesian networks learning algorithms. This course will discuss
both the constraint
-
based and Bayesian approaches to learning these causal
influences. Furthermore, the course will discuss the identification of causal effects
using a causal graph.


VI.

Presentation by participants
. In this section, planned to take place at the end of
the cour
se, participants will give short (20 min.) presentations of their research
topic, which will be commented on by faculty and participants of the summer
school.


d) Bibliography and Reader




Background reading

Literature used by faculty in designing the cou
rse is listed below




Reader

A Reader containing a selection of the most important papers the
lectures and seminars rely on will be created and made available
for participants at the
e
-
Learning page

link


Background reading:


G.E.M Anscombe (1993) “Caus
ality and Determination” in E. Sosa


M. Tooley (eds.)
Causation

(Oxford University Press, 1993) 88
-
104.


N. Cartwright (2007):
Hunting Causes and Using Them: Approaches in Philosophy and
Economics
(Cambridge University Press, 2007)


N. Cartwright (2006):

“From metaphysics to method: Comments on manipulability and the
causal Markov condition”

British Journal for the Philosophy of Science

57

(2006) 197
-
218


N. Cartwright (2000): “Measuring Causes: Invariance, Modularity and the Causal Markov
Condition”,
Me
asurement in Physics and Economics,

Discussion Paper Series Monograph
DP MEAS 9/00, London: Centre for Philosophy of Natural and Social Science, 2000


N. Cartwright (2001): “What is wrong with Bayes nets?”
The Monist

(2001) 242
-
264


N. Cartwright (1999):
T
he Dappled World
, Cambridge: Cambridge University Press. (Esp.
Ch. 5, 'Causal Diversity, Causal Stability')


N. Cartwright (1993): "Causality and realism in the EPR experiment"
Erkenntnis

38
(1993)
269
-
190



4

N. Cartwright (1989):
Nature’s Capacities and the
ir Measurement

(Oxford, Claredon Press,
1989)


N. Cartwright (1987): "How to tell a common cause: generalization of the conjunctive cause
criterion," in: J. H. Fetzer (ed.)
Probability and Causality

(Reidel, 1987) 181
-
188


R. Engle, D. Hendry and J. Richar
d (1983): ‘Exogeneity’,
Econometrica
, 51(2), 277
-
304.


D. Fennell (2005):
A Philosophical Analysis of Causality in Econometrics
, PhD Dissertation,
University of London.


J.H. Fetzer (ed.) (1988):
Probability and Causality

(Reidel Pub. Co., Boston, 1988)


C
. Granger, (1980) ‘Testing for Causality: A Personal Viewpoint’,
Journal of Economic
Dynamics and Control
, 2, 4, 329
-
352.


G. Graßhoff, S. Portmann and A. Wüthrich (2005): “Minimal Assumption Derivation of a
Bell
-
type Inequality”
British Journal for the Ph
ilosophy of Science

56

(2005) 663


680


B. Gyenis, M. Redei (2004): "When can statistical theories be causally closed?"
Foundations
of Physics

34

(2004) 1285
-
1303


J.
Halpern, and J. Pearl

(2005):


Causes and
E
xplanations: A
S
tructural
-
M
odel
A
pproach,


B
ritish Journal of Philosophy of Science
,

Vol. 56


C. Hitchcock (2005): “Of Humean Bondage,”
British Journal for the Philosophy of Science

54(1): 1
-
25


G. Hofer
-
Szabo (2007): Separate
-

versus common
-
common
-
cause
-
type derivations of the
Bell inequalities"
Sy
nthese

(forthcoming)


G. Hofer
-
Szabo, M. Redei (2006): "Reichenbachian Common Cause Systems of arbitrary
finite size exist"
Foundations of Physics Letters
35

(2006) 745
-
746


G. Hofer
-
Szabo, M. Redei, L. Szabo (2002): "Common
-
causes are not common common
-
causes"
Philosophy of Science
69

(2002) 623
-
636


G. Hofer
-
Szabo, M. Redei, L. Szabo (2000): "Reichenbach's Common Cause Principle:
Recent results and open problems"
Reports on Philosophy
, No. 20 (2000)


G. Hofer
-
Szabo, M. Redei, L. Szabo (1999): "On Reiche
nbach's common cause principle and
Reichenbach's notion of common cause"
The British Journal for the Philosophy of Science

50

(1999) 377
-
399


K. Hoover (2001)
Causality in Macroeconomics,

Cambridge University Press.


D. Lewis (1986): “Causation” and “Chanc
y Causation” in
Philosophical Papers Vol. II

(Oxford University Press, 1986) 159
-
172 and 175
-
184.



5

H. D. Mellor (1995): “On Raising the Chances of Effects”,
The Facts of Causation

(Routledge, 1995)


P. Menzies (1989): “Probabilistic Causation and Causal Pr
ocesses’ in
Philosophy of Science
,
LVI (1989) 642
-
63.


Neapolitan, R.E.,
Learning Bayesian Networks
, Prentice Hall, Upper Saddle River, NJ, 2003
.


R.E.
Neapolitan, and X. Jiang,

A Tutorial on Learning Causal Influences,


in Holmes, D.
and L. Jain (Eds.):
Innovations in Machine Learning
, Springer
-
Verlag, New York, 2006
.


J.
Pearl

(2000):

Causality: Models, Reasoning, and Inference
, Cambridge University Press,
Cambridge, UK (esp. pp. 65
-
85, 173
-
176)


P. Tetlock and A. Belkin (1996):
Counterfactual Thought Ex
periments in World Politics
,
Princeton: Princeton University Press. (esp. Ch. 1, 'Counterfactual Thought Experiments in
World Politics: Logical, Methodological, and Psychological Perspectives')


T. Placek (ed.) (2000)
, Reports on Philosophy
, Special Issue
on the Common Cause
Principle, No. 20 (2000)


M. Redei (2002): "Reichenbach's Common Cause Principle and quantum correlations" in
Modality, Probability and Bell's Theorems
, NATO Science Series, II. Vol. 64. T. Placek and
J. Butterfield (eds.), (Kluwer Ac
ademic Publishers, Dordrecht, Boston, London, 2002) 259
-
270


M. Redei, S.J. Summers (2007): "Quantum probability theory"
Studies in the History and
Philosophy of Modern Physics

(forthcoming in June 2007)


H. Reichenbach (1956):
The Direction of Time

(Univ
ersity of California Press, Los Angeles,
1956)


W.C. Salmon (1984):
Scientific Explanation and the Causal Structure of the World

(Princeton University Press, Princeton, 1984)


H. Simon, (1953) ‘Causal Ordering and Identifiability’ reprinted in Herbert Sim
on,
Models of
Man
, New York: John Wiley and Sons.


P.C.
Spirtes, C. Glymour and R. Scheines

(2000):

Causation, Prediction, and Search
,
Springer
-
Verlag, New York, 1993; 2nd ed.: MIT Press, Cambridge, Massachusetts


E. Sober (2001): “Venetian sea levels, Bri
tish bread prices, and the principle of common
cause”
The British Journal for the Philosophy of Science
52

331
-
346


L. E. Szabo (2007): “The Einstein
--
Podolsky
--
Rosen Argument and the Bell Inequalities”
(To be published in the
Internet Encyclopedia of Phil
osophy
)


L.E. Szabo (2000): “On an attempt to resolve the EPR
-
Bell paradox via Reichenbachian
concept of common cause
” International Journal of Theoretical Physics

39

(2000) 911



6

J.
Tian and J. Pearl

(2002):

“Gen
eral Identification Condition for Causal Ef
fects
,”

In
Proceedings of the Eighteenth Conference on Artificial Intelligence
, AAAI/The MIT Press:
Menlo Park, August



B. C. Van Fraassen (1982): "Rational Belief and Common Cause Principle," in: R.
McLaughlin (ed.),
What? Where? When? Why?,

Reidel, 193
-
209.


B.C. Van Fraassen (1989). "The charybdis of realism: epistemological implications of Bell's
inequality," in: J. T. Cushing and E. McMullin (eds.),
Philosophical Consequences of
Quantum Theory

(University of Notre Dame Press, Ind., 1989) 97
-
113.


M. W
eber (2001 [1905]): "Objective Possibility and Adequate Causation in Historical
Explanation", in Michael Martin and Lee McIntyre (eds),
Readings in the Philosophy of
Social Science
, Cambridge (MA): MIT Press


J. Williamson (2006): “Causal pluralism versus
epistemic causality,”
Philosophica

77(1): 69
-
96



































7

2.
Course schedule
:


Day 1. Monday, July 21, 2008



Introductory lectures (3 lectures + 2 seminar discussions)


Day 1


Title/topic

Lecturer

Lecture 1

50 min


Seminar 1

50 m
in

Pluralism in the Philosophy of Causation




Literature: Williamson (2006), additional: Hitchcock (2005)

Reiss

Lecture 2

50 min



Seminar 2

50 min

Causation and Probability


Traditional accounts of causation were deterministic in the sense that
undeterm
ined events (provided that any such event exists) were taken
to be uncaused. Almost all of the contemporary theories of causation
admit, however, the possibility of probabilistic causation. The lecture
and the seminar will address the following questions.
1. What are our
conceptual reasons for introducing the notion of probabilistic
causation? 2. How can some of the extant theories of causation
accommodate the idea of probabilistic causation?


Literature: Mellor (1995), Menzies (1989)


Huoranszki

Lecture 3


50 min

Basic notions of classical and non
-
commutative probability
theory


Classical probability theory in measure theoretic form: Boolean
algebras, classical probability measures, random variables, conditional
probability, independence, correlations. Non
-
classical probability
theory as non
-
commutative measure theory: Hilbert lattices and von
Neumann lattices, quantum states as probability measures, operators as
random variables. Types of classical and non
-
classical probability
spaces.


Literature: Redei
and Summers, 2007

Redei











Day 2. Tuesday, July 22, 2008


The Common Cause Principle

I. (2 lectures + 2 seminar discussions)


Day 2


Title/topic

Lecturer


8

Lecture 1

50 min


Seminar 1

50 min

Reichenbach’s notion of common cause and the Common
Caus
e Principle


In the history of probabilistic causation Reichenbach's definition of the
common cause was one of the first technically explicit formulations of
a causal concept. The definition is a combination of statistical
relevance conditions relating the

cause to its two effects and of the so
called screening
-
off property. Reichenbach's definition has become
central in the philosophy of causation and in particular in the
interpretation of the Common Cause Principle: no correlation without
causation. In th
e Lecture Reichenbach's definition of the common
cause will be recalled, some elementary examples for correlations and
common causes will be presented, and various interpretations of the
Reichenbachian Common Cause Principle will be distinguished and
discu
ssed.


Literature: Sober, 2001;

Hofer
-
Szabo, Redei and Szabo, 2000;
additional: Reichenbach, 1956;
Van Fraassen, 1982; Cartwright, 1987

Hofer

Lecture 2

50 min


Seminar 2

50 min

Common cause completability and causal completeness of
probability theories


A probabilistic theory is common cause completable with respect of a
correlation if it can be extended in such a way that the extension
contains a common cause of the correlation. Proof of common cause
completability of classical and quantum probability
spaces. The
implications of common cause completability for the problem of
falsifiability of the Common Cause Principle. A probability space is
causally complete if it contains a common cause of every correlation
between causally independent events. Exampl
es of causally complete
and incomplete probabilistic theories.


Literature:
Hofer
-
Szabo, Redei and Szabo, 1999; Gyenis and Redei,
2004

Redei


Day 3. Wednesday, July 23, 2008


The Common Cause Principle

II. (3 lectures + 1 seminar discussion)


Day 3


Titl
e/topic

Lecturer

Lecture 1

50 min


Seminar 1

50 min

Reichenbachian common cause systems


The Reichenbachian common cause system is a natural generalization
of Reichenbach's original definition of the common cause to the case
when more than one single fact
or contribute to the correlation: The
Reichenbachian common cause system of a correlation is a partition
such that every element of the partition screens off the correlation and
any two elements in the partition behave like a Reichenbachian
common cause an
d its complement. It is shown that given any finite
size and any correlation in a classical probability measure space, the
space can be extended in such way that there exists a Reichenbachian
common cause system of the given size in the extension. It will
also be
shown that every chain in the partially ordered set of all partitions of
an algebra contains only one Reichenbachian common cause system
for a given correlation.


Literature: Hofer
-
Szabo and Redei, 2006;


Hofer


9

Lecture 2

50 min


Lecture 3

50 min


Some Comments on Recent Work on the Causal Markov
Condition


Counterfactuals, Thought Experiments and Singular
Causal Inference in History


Literature
:
Sober (2001), additional: Cartwright (1999)

Literature: Weber (2001), additional: Tetlock
-
Belkin (1996)

Reiss





Day 4. Thursday, July 24, 2008


Probabilistic causation in economics (2 lectures + 2 seminars)


Day 4


Title/topic

Lecturer

Lecture 1

50 min


Lecture 2

50 min

Introduction to Causality in Econometrics


To understand causality in economics re
quires a basic understanding of
econometrics. These two lectures will present some simple
econometric models, to show how the statistical inference in
econometrics takes place. Given this, the lecture will introduce the
two key approaches to causality in

econometrics, Granger causality
and the structural approach. These will be related briefly to some
counterparts in the philosophical literature. Important aspects will be
emphasized, such as the strong counterfactual assumptions of the
econometric appro
ach.

F i n a l l y, s o m e o f t h e d i f f e r e n t w a y s
e c o n o m e t r i c m e t h o d s c a n b e u s e d t o f i n d o u t a b o u t c a u s e s w i l l b e s e t
o u t.


R e q u i r e d r e a d i n g: C h a p 7, H o o v e r 2 0 0 1

F e n n e l l

L e c t u r e 3

5 0 m i n



S e m i n a r 1

5 0 m i n

C a u s a l I n f e r e n c e a n d I s s u e s i n E c o n o m e t r i c s


H o w d o c o n c
e p t s o f c a u s a l i t y r e l a t e t o t h e m e t h o d s o f i n f e r e n c e u s e d i n
e c o n o m e t r i c s? I n t h i s l e c t u r e, t h r e e k e y p r o b l e m s w i l l b e p r e s e n t e d:
t h e p r o b l e m o f e x o g e n e i t y, t h e u s e o f i n s t r u m e n t a l v a r i a b l e s a n d t h e
p r o b l e m o f i d e n t i f i c a t i o n. T h e l e c t u r e w i l l e m p h a s i z e h
o w b r i n g i n g a
p h i l o s o p h i c a l p e r s p e c t i v e t o e c o n o m e t r i c m e t h o d s h e l p s t o s h o w i t s
s t r e n g t h s a n d l i m i t s, w h i l e c o n v e r s e l y, e c o n o m e t r i c m e t h o d s s h o w h o w
p r o b a b i l i s t i c c a u s a l i t y c a n b e p u t i n t o p r a c t i c e i n d i f f i c u l t
c i r c u m s t a n c e s.


T h e s e m i n a r w i l l b e u s e d t o
g o o v e r t h e c o n c e p t s a n d i s s u e s d i s c u s s e d
i n t h e l e c t u r e s, a n d c r i t i c a l l y d i s c u s s t h e H o o v e r 2 0 0 1 r e a d i n g.


R e q u i r e d r e a d i n g: C h a p 7, H o o v e r 2 0 0 1.

F e n n e l l


10



Day 5. Friday, July 25, 2008


Presentations by participants


Presentations are scheduled to tak
e place in one
-
hour sessions, one session accommodating 2
presentations, on the following model of the schedule of the first session of the day:


Day 5.

Time

Title of presentation

Speaker

9.00
-
9.20

9.20
-
9.30 discussion



9.30
-
9.50

9.50
-
10.00 discussion




3 such sessions (altogether 6 presentations) are planned for Day 9. of the summer school.


Saturday, Sunday, July 26 and 27


Free time


Day 6. Monday, July 28, 2008


Causal explanation of correlations in physics II. (3 lectures + 2 seminar discussio
ns)


Day 6.


Title/topic

Lecturer

Lecture 1

50 min


Lecture 2

50 min


Seminar 1

50 min

EPR correlations and the Common Cause Principle


EPR experiments, the Reality Criterion and the original EPR argument.
To complicate matter: non
-
Kolmogorovity of quant
um probability,
locality, non
-
conspiracy. What would it mean to explain EPR
correlations in terms of common causes? Bell’s inequalities. Further
discussions: Are "quantum probabilities" probabilities? What do we
actually observe in an EPR correlation exper
iment? What does locality
actually mean?


Literature: Szabo, 2007

Szabo

Lecture 3

50 min


Seminar 2

Recent No
-
go theorems on local Reichenbachian common
cause explanations of EPR correlations


Standard derivations of the Bell’s inequalities assume, beside
s locality
and no
-
conspiray, a
common

common cause system that is a common
screener
-
off for all correlations featuring in Bell’s inequalities.
However, replacing the strong assumption of a
common

common cause
system for the correlations by the weaker assum
ption of
separate

common cause systems (= a set of separate screener
-
offs explaining the
correlations separately) some Bell
-
like inequalities can still be derived.
The violation of these Bell
-
like inequalities entails the non
-
existence of
a local, non
-
cons
piratorial, separate
-
common
-
cause
-
model of both
perfect and imperfect EPR correlations.


Literature:
Szabo, 2000; Grasshoff, Portman and Wüthrich, 2005;
Hofer
-
Szabo, 2007

Hofer


11


Day 7. Tuesday, July 29, 2008



Causal explanation of correlations in physic
s II. (3 lectures + 1 seminar discussion)


Day 7.


Title/topic

Lecturer

Lecture 1

50 min


Lecture 2

50 min

Spacelike correlations in local relativistic quantum field
theory


The idea of a local quantum physics: associating explicitly physical
observable
s with definite spatiotemporal locations. Locality and local
observables in local relativistic quantum field theory. The notion of
maximal Bell correlation between observables localized in spacelike
separated local spacetime regions. Propositions character
izing maximal
and non
-
maximal violations of Bell’s inequality for observables
pertaining to typical tangent and strictly spacelike separated regions.
The difference between violations of Bell’s inequality in ordinary and
relativistic quantum theory.


Lite
rature: Redei and Summers, 2002

Redei

Lecture 3

50 min


Seminar

50 min

The status of Reichenbach’s Common Cause Principle in
quantum field theory


The notion of a local Reichenbachian common cause in relativistic
quantum field theory and the open problem
of the status of the
Common Cause Principle: Can spacelike correlations be explained by
a common cause localized in the common causal past of the correlated
observables? A Reichanbchian common cause in quantum field theory
is called weakly localized if it
is in the union of the causal pasts of the
correlated observables. Proof of existence of weakly localized common
causes of spacelike correlations. Is the problem of status of the
Common Cause Principle decidable by the axioms of local quantum
field theory?


Literature:

Redei and Summers, 2002

Redei


Day 8. Wednesday, July 30, 2008


Learning Causal Influences Using Bayesian Networks (2 lectures +2 seminar
discussions)


Day 8.


Title/topic

Lecturer

Lecture 1

1.5 hours



Seminar

.5 hours


Lecture 2

1.5 hou
rs


Learning Causes Using Manipulation.

Causal Graphs.

Causal Markov Assumption.

Causal Faithfulness Assumption.

Constraint
-
Based Causal Learning Assuming Faithfulness.




Causal Embedded Faithfulness Assumption.

Constraint
-
Based Learning

Assuming Embedded Faithfulness.

Causal Embedded Faithfulness Assumption with Selection Bias.

Constraint
-
Based Learning Assuming Embedded Faithfulness with
Neapolitan


12


Seminar

.5 hours

Selection Bias.




Literature:
Neapolitan
, 2003;
Spirtes, Glymour, and Scheines,

2000



Day 9. Thursday, July 31, 2008


Learning Causal Influences Using Bayesian Networks II. (2 lectures +2 seminar
discussions)


Day 9.


Title/topic

Lecturer

Lecture 3

1.5 hours


Seminar

.5 hours


Lecture 4

1.5 hours


Seminar

.5 hours

Bayesian Method for Caus
al Learning.

Causal Learning from Data on Two Variables.






Identifying Causal Influences Using a Causal Graph.






Literature:
Halpern

and Pearl
, 2005;
Neapolitan,
2003;
Pearl, 2000
;
Tian and Pearl
, 2002.


Neapolitan



Day 10. Friday, August 1, 2008


Presentations by participants


Presentations are scheduled to take place in one
-
hour sessions, one session accommodating 2
presentations, on the following model of the schedule of the first session of the day:


Day 10.

Time

Title of presentation

Speake
r

9.00
-
9.20

9.20
-
9.30 discussion



9.30
-
9.50

9.50
-
10.00 discussion




3 such sessions (altogether 6 presentations) are planned for Day 10. of the summer school.