Online Variable Kernel Estimator

2017 ◽  
Vol 8 (1) ◽  
pp. 58-92
Author(s):  
Yissam Lakhdar ◽  
El Hassan Sbai
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Maximum Entropy Principle ◽  
Kernel Estimation ◽  
Simulated Data ◽  
Kernel Estimator ◽  
Variable Kernel ◽  
Entropy Principle ◽  
And Performance

In this work, the authors propose a novel method called online variable kernel estimation of the probability density function (pdf). This new online estimator combines the characteristics and properties of two estimators namely nearest neighbors estimator and the Parzen-Rosenblatt estimator. Their approach allows a compact online adaptation of the estimated probability density function from the new arrival data. The performance of the online variable kernel estimator (OVKE) depends on the choice of the bandwidth. The authors present in this article a new technique for determining the optimal smoothing parameter of OVKE based on the maximum entropy principle (MEP). The robustness and performance of the proposed approach are demonstrated by examples of online estimation of real and simulated data distributions.

Notes on Bell-Sejnowski PDF-Matching Neuron

2002 ◽  
Vol 14 (12) ◽  
pp. 2847-2855 ◽  
Author(s):  
Simone Fiori
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Single Unit ◽  
Neuron Model ◽  
Maximum Entropy Principle ◽  
Entropy Principle ◽  
Single Input ◽  
Pdf Matching

This article investigates the behavior of a single-input, single-unit neuron model of the Bell-Sejnowski class, which learn through the maximum-entropy principle, in order to understand its probability density function matching ability.

Some Results on the Random Wear Coefficient of the Archard Model

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Fabio Antonio Dorini ◽  
Rubens Sampaio
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Maximum Entropy Principle ◽  
Linear Wear ◽  
Wear Depth ◽  
Wear Coefficient ◽  
Wear Process ◽  
Entropy Principle ◽  
Wear Law

The most used model for predicting wear is the linear wear law proposed by Archard. A common generalization of Archard’s wear law is based on the assumption that the wear rate at any point on the contact surface is proportional to the local contact pressure and the relative sliding velocity. This work focuses on a stochastic modeling of the wear process to take into account the experimental uncertainties in the identification process of the contact-state dependent wear coefficient. The description of the dispersion of the wear coefficient is described by a probability density function, which is performed using the maximum entropy principle using only the information available. Closed-form results for the probability density function of the wear depth for several situations that commonly occur in practice are provided.

scholarly journals Numerical Algorithms for Estimating Probability Density Function Based on the Maximum Entropy Principle and Fup Basis Functions

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1559
Author(s):  
Nives Brajčić Kurbaša ◽  
Blaž Gotovac ◽  
Vedrana Kozulić ◽  
Hrvoje Gotovac
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Moment Problem ◽  
Statistical Power ◽  
Maximum Entropy Principle ◽  
Basis Functions ◽  
Approximation Properties ◽  
Hybrid Strategy

Estimation of the probability density function from the statistical power moments presents a challenging nonlinear numerical problem posed by unbalanced nonlinearities, numerical instability and a lack of convergence, especially for larger numbers of moments. Despite many numerical improvements over the past two decades, the classical moment problem of maximum entropy (MaxEnt) is still a very demanding numerical and statistical task. Among others, it was presented how Fup basis functions with compact support can significantly improve the convergence properties of the mentioned nonlinear algorithm, but still, there is a lot of obstacles to an efficient pdf solution in different applied examples. Therefore, besides the mentioned classical nonlinear Algorithm 1, in this paper, we present a linear approximation of the MaxEnt moment problem as Algorithm 2 using exponential Fup basis functions. Algorithm 2 solves the linear problem, satisfying only the proposed moments, using an optimal exponential tension parameter that maximizes Shannon entropy. Algorithm 2 is very efficient for larger numbers of moments and especially for skewed pdfs. Since both Algorithms have pros and cons, a hybrid strategy is proposed to combine their best approximation properties.

scholarly journals Ensemble age inversions for large spectroscopic surveys

2019 ◽  
Vol 629 ◽  
pp. A127
Author(s):  
Alexey Mints ◽  
Saskia Hekker ◽  
Ivan Minchev
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Age Distribution ◽  
Simulated Data ◽  
Probability Density Functions ◽  
Inversion Method ◽  
Weighted Sum ◽  
Stellar Ages ◽  
The Galaxy

Context. Galactic astrophysics is now in the process of building a multi-dimensional map of the Galaxy. For such a map, stellar ages are an essential ingredient. Ages are measured only indirectly however, by comparing observational data with models. It is often difficult to provide a single age value for a given star, as several non-overlapping solutions are possible. Aims. We aim at recovering the underlying log(age) distribution from the measured log(age) probability density function for an arbitrary set of stars. Methods. We build an age inversion method, namely we represent the measured log(age) probability density function as a weighted sum of probability density functions of mono-age populations. Weights in that sum give the underlying log(age) distribution. Mono-age populations are simulated so that the distribution of stars on the log g-[Fe/H] plane is close to that of the observed sample. Results. We tested the age inversion method on simulated data, demonstrating that it is capable of properly recovering the true log(age) distribution for a large (N > 103) sample of stars. The method was further applied to large public spectroscopic surveys. For RAVE-on, LAMOST and APOGEE we also applied age inversion to mono-metallicity samples, successfully recovering age–metallicity trends present in higher-precision APOGEE data and chemical evolution models. Conclusions. We conclude that applying an age inversion method as presented in this work is necessary to recover the underlying age distribution of a large (N > 103) set of stars. These age distributions can be used to explore age–metallicity relations, for instance.

Operational Performance Measures of American Roundabouts

1997 ◽  
Vol 1572 (1) ◽  
pp. 68-75 ◽  
Author(s):  
Aimee Flannery ◽  
Tapan Datta
Keyword(s):  
United States ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
The United States ◽  
Performance Level ◽  
Operational Performance ◽  
Gap Acceptance ◽  
And Performance ◽  
Better Than

The introduction of a new form of at-grade intersection control in the United States, termed a roundabout, has left many researchers and practitioners puzzled about their performance level. Many researchers and practitioners have looked to foreign design and operational manuals for guidance. Although the methods contained in these manuals have been implemented in their respective countries, no one is certain how they will transfer to conditions in the United States. Considering that driver characteristics are a major contributor to operational performance, these methods may not accurately depict the performance level of roundabouts with American drivers. Driver characteristics, in relation to operational performance, of four single-lane roundabouts located in the United States are described. The same driver characteristics are compared with findings in Australia under similar conditions; in addition, the probability density function for gap acceptance is derived. American drivers do not always react the same as Australian drivers under similar conditions. However, use of the Australian methods is, in most cases, more conservative and therefore should not overpredict the capacity and performance of roundabouts in the United States. The probability density function for gap acceptance at roundabouts was similar in shape and slope to that of two-way stop control. However, comparison of the gap-acceptance values of right-turning vehicles at two-way stop control with those at a roundabout indicates that drivers at roundabouts accept smaller gaps in the traffic stream on entry. This leads to the conclusion that roundabouts should perform better than two-way or all-way stop-controlled intersections under most conditions. The question remains: When do roundabouts function better than traffic signals?

Kernel estimation for a superpopulation probability density function under informative selection

METRON ◽  
2017 ◽  
Vol 75 (3) ◽  
pp. 301-318 ◽  
Author(s):  
Daniel Bonnéry ◽  
F. Jay Breidt ◽  
François Coquet
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Kernel Estimation
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