Centrality Estimators for Probability Density Functions
In this report, we explore the data selection leading to a family of estimators maximizing a centrality. The family allows a nice properties leading to accurate and robust probability density function fitting according to some criteria we define. We establish a link between the centrality estimator and the maximum likelihood, showing that the latter is a particular case. Therefore, a new probability interpretation of Fisher maximum likelihood is provided. We will introduce and study two specific centralities that we have named H\"older and Lehmer estimators. A numerical simulation is provided showing the effectiveness of the proposed families of estimators opening the door to development of new concepts and algorithms in machine learning, data mining, statistics, and data analysis.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Efficient Nonparametric Smoothness Estimation
Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical…
Two-sample testingCentrality measures for graphons: Accounting for uncertainty in networks
As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particu…
Binary Losses for Density Ratio Estimation
Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observa…
Density Ratio EstimationDomain AdaptationHigh-Dimensional Non-Parametric Density Estimation in Mixed Smooth Sobolev Spaces
Density estimation plays a key role in many tasks in machine learning, statistical inference, and visualization. The main bottleneck in high-dimensional density estimation is the prohibitive computational cost and the sl…
Density EstimationVocal Bursts Intensity PredictionNonparametric Estimation of Band-limited Probability Density Functions
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML…
Density Estimation