Multivariate data-driven k-NN function estimation

k-NN Estimation of Directed Information

This report studies data-driven estimation of the directed information (DI) measure between twoem discrete-time and continuous-amplitude random process, based on the k-nearest-neighbors (k-NN) estimation framework. Detailed derivations of two k-NN estimators are provided. The two estimators differ in the metric based on which the nearest-neighbors are found. To facilitate the estimation of the ...

k-NN Estimation of Directed Information

Detection and estimation of causality relationships between two random processes is a fundamental problem in many natural and social sciences [1]. This task is in particular challenging as in many real-life scenarios one does not have a good underlying statistical model for the considered process, e.g., in the fields of neuroscience, financial markets, meteorology, etc. For such scenarios it is...

K-NN Classifier for Relationally Encrypted Data

With internet expanding in every aspect of businesses infrastructure, it becomes more and more important to make these businesses infrastructures safe and secure to the numerous attacks perpetrated on them conspicuously when it comes to denial of service (DoS) attack. IP is an internet protocol each and every system having a unique address to use this address to communicate to the internet. The...

K1D: Multivariate Ripley’s K-function for one-dimensional data

Optimal rates for k-NN density and mode estimation

We present two related contributions of independent interest: (1) high-probability finite sample rates for k-NN density estimation, and (2) practical mode estimators – based on k-NN – which attain minimax-optimal rates under surprisingly general distributional conditions.