19,991 research outputs found
Consistency of Causal Inference under the Additive Noise Model
We analyze a family of methods for statistical causal inference from sample
under the so-called Additive Noise Model. While most work on the subject has
concentrated on establishing the soundness of the Additive Noise Model, the
statistical consistency of the resulting inference methods has received little
attention. We derive general conditions under which the given family of
inference methods consistently infers the causal direction in a nonparametric
setting
On the Decreasing Power of Kernel and Distance based Nonparametric Hypothesis Tests in High Dimensions
This paper is about two related decision theoretic problems, nonparametric
two-sample testing and independence testing. There is a belief that two
recently proposed solutions, based on kernels and distances between pairs of
points, behave well in high-dimensional settings. We identify different sources
of misconception that give rise to the above belief. Specifically, we
differentiate the hardness of estimation of test statistics from the hardness
of testing whether these statistics are zero or not, and explicitly discuss a
notion of "fair" alternative hypotheses for these problems as dimension
increases. We then demonstrate that the power of these tests actually drops
polynomially with increasing dimension against fair alternatives. We end with
some theoretical insights and shed light on the \textit{median heuristic} for
kernel bandwidth selection. Our work advances the current understanding of the
power of modern nonparametric hypothesis tests in high dimensions.Comment: 19 pages, 9 figures, published in AAAI-15: The 29th AAAI Conference
on Artificial Intelligence (with author order reversed from ArXiv
A stochastic process approach to false discovery control
This paper extends the theory of false discovery rates (FDR) pioneered by
Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300].
We develop a framework in which the False Discovery Proportion (FDP)--the
number of false rejections divided by the number of rejections--is treated as a
stochastic process. After obtaining the limiting distribution of the process,
we demonstrate the validity of a class of procedures for controlling the False
Discovery Rate (the expected FDP). We construct a confidence envelope for the
whole FDP process. From these envelopes we derive confidence thresholds, for
controlling the quantiles of the distribution of the FDP as well as controlling
the number of false discoveries. We also investigate methods for estimating the
p-value distribution
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