• Corpus ID: 221557210

Nonparametric Density Estimation from Markov Chains

@article{Simone2020NonparametricDE,
  title={Nonparametric Density Estimation from Markov Chains},
  author={Andrea De Simone and Alessandro Morandini},
  journal={ArXiv},
  year={2020},
  volume={abs/2009.03937}
}
We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used straightforwardly as a foundation in all density-based algorithms. We prove the consistency of our estimator and we find it typically outperforms KDE in situations of large sample size and high dimensionality. We also employ our density estimator to build a local… 
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37 References

Statistical outlier detection using direct density ratio estimation

A new statistical approach to the problem of inlier-based outlier detection, i.e., finding outliers in the test set based on the training set consisting only of inliers, using the ratio of training and test data densities as an outlier score is proposed.

Outlier Detection with Kernel Density Functions

A novel unsupervised algorithm for outlier detection with a solid statistical foundation is proposed, modifying a nonparametric density estimate with a variable kernel to yield a robust local density estimation.

A Local Density-Based Approach for Local Outlier Detection

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LOF: identifying density-based local outliers

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Density-based Clustering

  • M. Ester
  • Computer Science, Business
    Encyclopedia of Database Systems
  • 2009
The clustering methods like K-means or Expectation-Maximization are suitable for finding ellipsoid-shaped clusters, but for non-convex clusters, these methods have trouble finding the true clusters, since two points from different clusters may be closer than two points in the same cluster.