• Corpus ID: 203951375

Estimating Density Models with Complex Truncation Boundaries

  title={Estimating Density Models with Complex Truncation Boundaries},
  author={Song Liu and Takafumi Kanamori},
Truncated densities are probability density functions defined on truncated input domains. These densities share the same parametric form with their non-truncated counterparts up to a normalization term. However, normalization terms usually cannot be obtained in closed form for these distributions, due to complicated truncation domains. Score Matching is a powerful tool for fitting parameters in unnormalized models. However, it cannot be straightforwardly applied here as boundary conditions used… 
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Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable
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Generalised Kernel Stein Discrepancy(GKSD): A Unifying Approach for Non-parametric Goodness-of-fit Testing
  • Wenkai Xu
  • Mathematics
  • 2021
Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing
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Some extensions of score matching
  • A. Hyvärinen
  • Mathematics, Computer Science
    Comput. Stat. Data Anal.
  • 2007
It is shown how to estimate non-normalized models defined in the non-negative real domain, i.e. R"+^n", and it is shown that the score matching estimator can be obtained in closed form for some exponential families.
Estimation of Non-Normalized Statistical Models by Score Matching
  • A. Hyvärinen
  • Computer Science, Mathematics
    J. Mach. Learn. Res.
  • 2005
While the estimation of the gradient of log-density function is, in principle, a very difficult non-parametric problem, it is proved a surprising result that gives a simple formula that simplifies to a sample average of a sum of some derivatives of the log- density given by the model.
Generalized Score Matching for Non-Negative Data
This paper gives a generalized form of score matching for non-negative data that improves estimation efficiency and addresses an overlooked inexistence problem by generalizing the regularized score matching method of Lin et al. (2016) and improving its theoretical guarantees fornon-negative Gaussian graphical models.
Graphical Models for Non-Negative Data Using Generalized Score Matching
This paper gives a generalized form of score matching for non-negative data that improves estimation efficiency and generalizes the regularized score matching method of Lin et al. (2016) fornon-negative Gaussian graphical models, with improved theoretical guarantees.
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In some applications with astronomical and survival data, doubly truncated data are sometimes encountered. In this work we introduce kernel-type density estimation for a random variable which is
Minimum Stein Discrepancy Estimators
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A Kernel Test of Goodness of Fit
A nonparametric statistical test for goodness-of-fit is proposed: given a set of samples, the test determines how likely it is that these were generated from a target density function, taking the form of a V-statistic in terms of the log gradients of the target density and the kernel.
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One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score
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The Dirichlet distribution and its compound variant, the Dirichlet-multinomial, are two of the most basic models for proportional data, such as the mix of vocabulary words in a text document. Yet the
Interpretation and Generalization of Score Matching
  • Siwei Lyu
  • Computer Science, Mathematics
  • 2009
This paper provides a formal link between maximum likelihood and score matching and develops a generalization of score matching, which shows that score matching finds model parameters that are more robust with noisy training data.