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In this example, HSIC, a kernel-based test for independence is used to detect | ||
dependence of a mixture of Gaussians and a rotated version of the same data. | ||
The HSIC statistic is computed and available methods for computing a threshold | ||
of the null distribution are used. In addition, p-values of the test are | ||
computed. Note that these methods require more iterations than used here. A | ||
Gaussian kernel is selected via the median heuristic. | ||
See tutorial and Class documentation for more details. |
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examples/descriptions/modular/statistics_linear_time_mmd.txt
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In this example, the linear time MMD statistic for kernel-based two-sample | ||
testing is illustrated. It is a streaming based statistic for large amounts | ||
of data. The used dataset is a bunch of standard Gaussian vectors where the | ||
first dimensions differs in both distributions p and q. The test statistic | ||
is computed and available methods for computing a threshold of the null | ||
distribution are used. In addition, p-values for the test are computed. | ||
Note that these methods require more iterations/samples that used here. A | ||
Gaussian is selected via the median heuristic. There are more clever | ||
kernel selection methods available. | ||
See tutorial and Class documentation for more details. |
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examples/descriptions/modular/statistics_mmd_kernel_selection.txt
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In this example, kernel selection methods for MMD based statistics are | ||
illustrated. A difficult synthetic dataset is used to illustrate their | ||
performance in two-sample testing. All kernel selection methods for MMD | ||
work via creating a combined kernel with all desired baseline kernels. | ||
The example demonstrates how to perform kernel selection and use it | ||
for two-sample testing. Methods for both single and combined kernels | ||
are demonstrated. In addition, type I and II error estimates | ||
are computed. As usual, there are more iterations/samples required in | ||
practice. | ||
See tutorial and Class documentation for more details. |
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examples/descriptions/modular/statistics_quadratic_time_mmd.txt
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In this example, the quadratic time MMD statistic for kernel-based two-sample | ||
testing is illustrated. It is a statistic for smaller amounts of data where | ||
one is interested to compute the best possible test. The used dataset is a | ||
bunch of standard Gaussian vectors where the first dimensions differs in both | ||
distributions p and q. The test statistic is computed and available methods | ||
for computing a threshold of the null distribution are used. In addition, | ||
p-values for the test are computed. Note that these methods require more | ||
iterations/samples that used here. A Gaussian is with a fixed kernel size is | ||
used. There are more clever kernel selection methods available. | ||
See tutorial and Class documentation for more details. |
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