Qualifying exam for Peter Gorniak
100 points total
Try to answer all the questions, but you do not need to answer them
all correctly to pass. I think the threshold for passing will be
approximately 70 points (our of 100) correct, but that may change
after I see your answers. Unfortunately, since this exam is only for
one person, I cannot draw on previous experience to give you a firm
threshold for passing. Use the point specifications more as a guide
for how much time to spend on each question.
1. Pearl and Spirtes et al. describe similar approaches to learning
the structure of a causal Bayes net from purely observational data,
based on the conditional independence relations found in the observed
data. To what extent and under what circumstances can these
approaches infer causal structure in the presence of hidden
(unobserved) causes? To what extent and under what circumstances can
these approaches infer the existence and connection patterns of hidden
causes? Give an answer that is as formally precise as possible, in
terms of the inductive compentence of the algorithms, without
necessarily going into the details of the search procedures used.
Concrete examples will help. [20 points]
2. How does the performance of the causal learning algorithms
advocated by Pearl and Spirtes et al. depend on the amount of data
available, both in theory and in practice? The algorithms should give
identical answers in the limit of infinite data, but will they perform
differently with finite data sets? If so, how? [10 points]
3. Gopnik and colleagues propose that the algorithms for learning
causal structure based on conditional independence patterns proposed
by Pearl and Spirtes et al. provide a rational framework for
understanding how people learn successfully about the causal structure
of their world. Critically evaluate this claim. What assumptions are
necessary to bring the algorithms of Pearl and Spirtes et al. to bear
on the experiments of Gopnik et al. and Steyvers et al., and to what
extent are those assumptions cognitively or computationally
well-motivated? What are the advantages and disadvantages of the
alternative Bayesian approach to inferring causal structure advocated
by Tenenbaum and colleagues? What aspects of human causal inference
are not well captured by the Bayesian approach? [20 points]
4. What is the relation between Cheng's Power PC theory and algorithms
for learning causal Bayes nets? In particular, consider two aspects
of causal Bayes nets: maximum likelihood parameter estimation and
Pearl's (2000) notion of the probability of a sufficient or necessary
cause. What (if anything) can we gain by reformulating the Power PC
theory of human causal judgment in terms of Bayes net learning and
inference? [10 points]
5. (a) How would a proponent of Johnson-Laird's mental models paradigm
interpret the results in Krynski and Tenenbaum? Could the mental
models paradigm offer new insights into their results? (b) Pearl
(2000) discusses the proper relation between causal knowledge and
probabilistic knowledge in building an intelligent reasoner. How
might Pearl's arguments relate to and inform the discussion in Krynski
and Tenenbaum? [10 points]
6. Compare and contrast the mental models approach to deductive
reasoning (a la Johnson-Laird) with the Bayesian approach to inductive
reasoning (a la Kemp and Tenenbaum). Are these approaches more
competitive or more complementary? Could there be a productive hybrid
of these approaches, combining probabilistic inference with the
representational format of mental models? What would this hybrid
offer over the basic mental models paradigm? [15 points]
7. Compare qualitative approaches to physical and spatiotemporal
reasoning (Kuipers, Johnson-Laird) with Pearl's (2000) approach to
causal reasoning. Most work in qualitative physics was done before
the recent wave of formal approaches to causality led by Pearl. What
would be the most important ways to reconceptualize qualitative
physics in light of the tools introduced by Pearl? Are there
important aspects of qualitative physics or intuitive physical
understanding that Pearl's approach is incapable of capturing or
addressing? If so, what would be needed to integrate causal Bayes nets
into a more complete framework for modeling intuitive physical
understanding? [15 points]