254 research outputs found
A maximum-mean-discrepancy goodness-of-fit test for censored data
We introduce a kernel-based goodness-of-fit test for censored data, where
observations may be missing in random time intervals: a common occurrence in
clinical trials and industrial life-testing. The test statistic is
straightforward to compute, as is the test threshold, and we establish
consistency under the null. Unlike earlier approaches such as the Log-rank
test, we make no assumptions as to how the data distribution might differ from
the null, and our test has power against a very rich class of alternatives. In
experiments, our test outperforms competing approaches for periodic and Weibull
hazard functions (where risks are time dependent), and does not show the
failure modes of tests that rely on user-defined features. Moreover, in cases
where classical tests are provably most powerful, our test performs almost as
well, while being more general
A Kernel Independence Test for Random Processes
A new non parametric approach to the problem of testing the independence of
two random process is developed. The test statistic is the Hilbert Schmidt
Independence Criterion (HSIC), which was used previously in testing
independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is
established when computed from samples drawn from random processes. It is shown
that earlier bootstrap procedures which worked in the i.i.d. case will fail for
random processes, and an alternative consistent estimate of the p-values is
proposed. Tests on artificial data and real-world Forex data indicate that the
new test procedure discovers dependence which is missed by linear approaches,
while the earlier bootstrap procedure returns an elevated number of false
positives. The code is available online:
https://github.com/kacperChwialkowski/HSIC .Comment: In Proceedings of The 31st International Conference on Machine
Learnin
A low variance consistent test of relative dependency
We describe a novel non-parametric statistical hypothesis test of relative
dependence between a source variable and two candidate target variables. Such a
test enables us to determine whether one source variable is significantly more
dependent on a first target variable or a second. Dependence is measured via
the Hilbert-Schmidt Independence Criterion (HSIC), resulting in a pair of
empirical dependence measures (source-target 1, source-target 2). We test
whether the first dependence measure is significantly larger than the second.
Modeling the covariance between these HSIC statistics leads to a provably more
powerful test than the construction of independent HSIC statistics by
sub-sampling. The resulting test is consistent and unbiased, and (being based
on U-statistics) has favorable convergence properties. The test can be computed
in quadratic time, matching the computational complexity of standard empirical
HSIC estimators. The effectiveness of the test is demonstrated on several
real-world problems: we identify language groups from a multilingual corpus,
and we prove that tumor location is more dependent on gene expression than
chromosomal imbalances. Source code is available for download at
https://github.com/wbounliphone/reldep.Comment: International Conference on Machine Learning, Jul 2015, Lille, Franc
A Kernel Test for Three-Variable Interactions
We introduce kernel nonparametric tests for Lancaster three-variable
interaction and for total independence, using embeddings of signed measures
into a reproducing kernel Hilbert space. The resulting test statistics are
straightforward to compute, and are used in powerful interaction tests, which
are consistent against all alternatives for a large family of reproducing
kernels. We show the Lancaster test to be sensitive to cases where two
independent causes individually have weak influence on a third dependent
variable, but their combined effect has a strong influence. This makes the
Lancaster test especially suited to finding structure in directed graphical
models, where it outperforms competing nonparametric tests in detecting such
V-structures
Kernel Bayes' rule
A nonparametric kernel-based method for realizing Bayes' rule is proposed,
based on representations of probabilities in reproducing kernel Hilbert spaces.
Probabilities are uniquely characterized by the mean of the canonical map to
the RKHS. The prior and conditional probabilities are expressed in terms of
RKHS functions of an empirical sample: no explicit parametric model is needed
for these quantities. The posterior is likewise an RKHS mean of a weighted
sample. The estimator for the expectation of a function of the posterior is
derived, and rates of consistency are shown. Some representative applications
of the kernel Bayes' rule are presented, including Baysian computation without
likelihood and filtering with a nonparametric state-space model.Comment: 27 pages, 5 figure
Discussion of: Brownian distance covariance
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and
Maria L. Rizzo [arXiv:1010.0297]Comment: Published in at http://dx.doi.org/10.1214/09-AOAS312E the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
MERLiN: Mixture Effect Recovery in Linear Networks
Causal inference concerns the identification of cause-effect relationships
between variables, e.g. establishing whether a stimulus affects activity in a
certain brain region. The observed variables themselves often do not constitute
meaningful causal variables, however, and linear combinations need to be
considered. In electroencephalographic studies, for example, one is not
interested in establishing cause-effect relationships between electrode signals
(the observed variables), but rather between cortical signals (the causal
variables) which can be recovered as linear combinations of electrode signals.
We introduce MERLiN (Mixture Effect Recovery in Linear Networks), a family of
causal inference algorithms that implement a novel means of constructing causal
variables from non-causal variables. We demonstrate through application to EEG
data how the basic MERLiN algorithm can be extended for application to
different (neuroimaging) data modalities. Given an observed linear mixture, the
algorithms can recover a causal variable that is a linear effect of another
given variable. That is, MERLiN allows us to recover a cortical signal that is
affected by activity in a certain brain region, while not being a direct effect
of the stimulus. The Python/Matlab implementation for all presented algorithms
is available on https://github.com/sweichwald/MERLi
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