Nonparametric Density Estimation from Markov Chains
This provides a potentially improved foundation for density-based algorithms in machine learning, though it appears incremental as a generalization of KDE.
The authors tackled the problem of nonparametric density estimation by introducing a new estimator based on Markov Chains that generalizes Kernel Density Estimation (KDE). They proved its consistency and found it typically outperforms KDE in large sample size and high dimensionality scenarios, with promising results when applied to outlier detection on realistic datasets.
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 outlier detector, showing very promising results when applied to some realistic datasets.