Open AccessProceedings Article
A kernelized stein discrepancy for goodness-of-fit tests
Qiang Liu,Jason D. Lee,Michael I. Jordan +2 more
- pp 276-284
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TLDR
A new discrepancy statistic for measuring differences between two probability distributions is derived based on combining Stein's identity with the reproducing kernel Hilbert space theory and a new class of powerful goodness-of-fit tests are derived that are widely applicable for complex and high dimensional distributions.Abstract:
We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic model fits a set of observations, and derive a new class of powerful goodness-of-fit tests that are widely applicable for complex and high dimensional distributions, even for those with computationally intractable normalization constants. Both theoretical and empirical properties of our methods are studied thoroughly.read more
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References
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TL;DR: In this article, an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data is described.
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Probabilistic graphical models : principles and techniques
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TL;DR: The framework of probabilistic graphical models, presented in this book, provides a general approach for causal reasoning and decision making under uncertainty, allowing interpretable models to be constructed and then manipulated by reasoning algorithms.
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Testing statistical hypotheses
TL;DR: The general decision problem, the Probability Background, Uniformly Most Powerful Tests, Unbiasedness, Theory and First Applications, and UNbiasedness: Applications to Normal Distributions, Invariance, Linear Hypotheses as discussed by the authors.
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A kernel two-sample test
TL;DR: This work proposes a framework for analyzing and comparing distributions, which is used to construct statistical tests to determine if two samples are drawn from different distributions, and presents two distribution free tests based on large deviation bounds for the maximum mean discrepancy (MMD).
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A Class of Statistics with Asymptotically Normal Distribution
TL;DR: In this article, the authors considered the problem of estimating a U-statistic of the population characteristic of a regular functional function, where the sum ∑″ is extended over all permutations (α 1, α m ) of different integers, 1 α≤ (αi≤ n, n).