Submitted by
Assigned_Reviewer_5
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
The paper extends the existing machine of kernel
dependence tests to three way interactions. This is an interesting and
well executed piece of work that attacks an important problem for which
there are very limited tools at present. The paper is generally well
written.
Some minor comments. Explain V-structure more
explicitly on its first use. Give a pointer to V-statistics (I had
heard of U-Statistics, but not V-statistics) Equation (1) does not
make sense as written. You need to define P^* more clearly. The "where"
after (1) does not make it clear.
In the experiments, explain
sample size. Q2: Please summarize your review in 1-2
sentences
Nice extension of kernel dependence tests to three-way
interactions. Submitted by
Assigned_Reviewer_6
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
This paper provides a very interesting nonparametric
approach to test for three-variable interactions (and independence) using
embedding properties of ISPD kernels. The paper is overall well-written,
clear and exhaustive in its coverage of the underlying algebraic proofs.
With the need for efficient statistical testing tools to detect complex
interaction effects in bioinformatics, this work seems promising in its
applications. Given the stated illustrative purpose of identifying
gene interactions, it could have been nice to see experiments on
non-synthetic data and/or comparison of performances to other genomics
methods (such as based on partial correlation). Also, the possibility
raised in the concluding paragraph that the test could be extended to more
than 3 variables seems to be somewhat contradicted by the point raised in
section 4.3. Finally, it would be of great interest to see how the method
behaves in large-dimensional spaces. Minor issue: There is no
reference to Figure 3 in the main text Q2: Please
summarize your review in 1-2 sentences
A solid and novel statistical approach, with promising
applications. Would benefit from more exhaustive performance comparison to
other state-of-the-art methods for interaction
testing Submitted by
Assigned_Reviewer_7
Q1: Comments to author(s).
First provide a summary of the paper, and then address the following
criteria: Quality, clarity, originality and significance. (For detailed
reviewing guidelines, see
http://nips.cc/PaperInformation/ReviewerInstructions)
This paper addresses a problem of building hypothesis
tests based on kernel methods for identifying three variable interactions.
This work extends HSIC (Hilbert Schmidt Independence Criterion), which is
designed to detect two variable interactions based on kernel methods.
There exists several types of three variable interactions, but the one
authors try to detect one called Lancaster interaction, which is a singed
measure defined as ¥delta L = Pxyx -PxyPz - PxzPy - PyzPx - 2 PxPyPz. In
the proposed procedure, the above marginal and joint probabilities are all
embedded into kernel Hilbert space, and guaranteed to work as long as they
satisfy ISPD (Integrally Strictly Positive Definite) condition. In
simulation experiments, permutation test is employed with ¥delta L as a
test statistic to show the ability of the proposed method in identifying
three way interactions.
In the middle of the page 8, "Figure 2
plots the Type II error" should be "Figure 3". Q2: Please
summarize your review in 1-2 sentences
The paper is clearly written with appropriate
references and proofs. As is written in the manuscript, extension of this
method to detecting higher degrees of interactions, and to detecting
structured interactions is useful.
Q1:Author
rebuttal: Please respond to any concerns raised in the reviews. There are
no constraints on how you want to argue your case, except for the fact
that your text should be limited to a maximum of 6000 characters. Note
however that reviewers and area chairs are very busy and may not read long
vague rebuttals. It is in your own interest to be concise and to the
point.
We thank the reviewers for their kind assessment of
our paper. We are happy to incorporate the corrections and suggestions
made by the reviewers to improve the clarity of our presentation.
Regarding the suggestions of reviewer 2: we certainly hope our method will
find application in bioinformatics and other areas; this is a route we are
pursuing, and we have prepared downloadable software. We also take the
reviewer's point that our conclusion was at odds with our discussion of
the difficulty of measuring four-way interactions or higher, and have
revised accordingly.
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