Parzen neural networks: Fundamentals, properties, and an application to forensic anthropology

Trentin, Edmondo; Lusnig, Luca; Cavalli, Fábio

doi:10.1016/j.neunet.2017.10.002

Cited by 21 publications

(31 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This Section shows that for any nonpaltry pdf p(•) over X [11] and any ∈ R + a SC-NN-4pdf exists which computes ϕ ( ) (•) such that the corresponding density estimatep ( )…”

Section: Modeling Capabilitiesmentioning

confidence: 99%

“…Finally, the task of estimating conditional probability distributions is fundamental to the broad area of probabilistic graphical models [9,10]. Statistical parametric and non-parametric techniques are available to practitioners [1], but they suffer from several significant shortcomings [11]. In fact, parametric techniques require a strong assumption on the form of the probability density function (pdf) at hand, while non-parametric approaches are memory-based (i.e., prone to overfitting), overly complex in time and space, and unreliable over small data samples.…”

Section: Introductionmentioning

confidence: 99%

“…Traditional ANN-based attempts to tackle the pdf estimation problem could not overcome some major shortcomings [11]. First of all, when applied to pdf estimation, the so-called "probabilistic neural network" [15] reduces to a neural version of the Parzen window estimator [1], with a hidden neuron per each Parzen kernel, such that it inherits the aforementioned drawbacks of statistical non-parametric techniques.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic Convergence of Soft-Constrained Neural Networks for Density Estimation

Trentin

2020

Mathematics

Self Cite

View full text Add to dashboard Cite

A soft-constrained neural network for density estimation (SC-NN-4pdf) has recently been introduced to tackle the issues arising from the application of neural networks to density estimation problems (in particular, the satisfaction of the second Kolmogorov axiom). Although the SC-NN-4pdf has been shown to outperform parametric and non-parametric approaches (from both the machine learning and the statistics areas) over a variety of univariate and multivariate density estimation tasks, no clear rationale behind its performance has been put forward so far. Neither has there been any analysis of the fundamental theoretical properties of the SC-NN-4pdf. This paper narrows the gaps, delivering a formal statement of the class of density functions that can be modeled to any degree of precision by SC-NN-4pdfs, as well as a proof of asymptotic convergence in probability of the SC-NN-4pdf training algorithm under mild conditions for a popular class of neural architectures. These properties of the SC-NN-4pdf lay the groundwork for understanding the strong estimation capabilities that SC-NN-4pdfs have only exhibited empirically so far.

show abstract

“…This Section shows that for any nonpaltry pdf p(•) over X [11] and any ∈ R + a SC-NN-4pdf exists which computes ϕ ( ) (•) such that the corresponding density estimatep ( )…”

Section: Modeling Capabilitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic Convergence of Soft-Constrained Neural Networks for Density Estimation

Trentin

2020

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…28 Nonparametric models are the method for solving optimization problems without objective function or constraint function. [31][32][33][34] However, nonparametric models are used to fall into nonconvex optimization and local minimum. It provides a scientific calculation method so it has important practical value.…”

Section: Nonparameter Modelsmentioning

confidence: 99%

Big data‐driven machine learning‐enabled traffic flow prediction

Kong

Jiang

et al. 2018

Trans Emerging Tel Tech

View full text Add to dashboard Cite

Real‐time effective traffic flow big data prediction network has important application significance. Over the past few years, traffic flow data have been exploding and we have entered the big data era. The key challenge of traffic flow prediction network is how to construct an adaptive model relying on historical data. Existing big data‐driven traffic flow prediction networking approaches mainly use shallow learning, and there are unsatisfying for many realistic applications, which inspire us to rethink the traffic flow big data prediction problem with deep learning. In this paper, we propose a novel prediction approach based on machine learning. In addition to the minimum prediction error as the goal, we present the long short‐term memory model, which is a typical machine learning algorithm with deep learning network. This method is applied into the real‐world traffic big data from performance measurement system. Experimental results show that the proposed machine learning algorithm has more applicability and higher performance, compared with shallow machine learning prediction network.

show abstract

“…In the extended version to his ANNPR2016 paper [24], titled Soft-constrained Neural Networks for Nonparametric Density Estimation, Edmondo Trentin introduces a robust non-parametric connectionist technique for the estimation of probability density functions. The approach relates loosely to [26,27] but accounts for the issue of having a feed-forward neural network to respect Kolmogorov's axioms of probability. The experiments (involving univariate and multivariate data drawn from complex distributions) show a statistically significant improvement over the established techniques.…”

Section: The Si: Organization and List Of Papersmentioning

confidence: 99%

Off the Mainstream: Advances in Neural Networks and Machine Learning for Pattern Recognition

Trentin

Schwenker

Gayar

et al. 2018

Neural Process Lett

Self Cite

View full text Add to dashboard Cite

Parzen neural networks: Fundamentals, properties, and an application to forensic anthropology

Cited by 21 publications

References 32 publications

Asymptotic Convergence of Soft-Constrained Neural Networks for Density Estimation

Asymptotic Convergence of Soft-Constrained Neural Networks for Density Estimation

Big data‐driven machine learning‐enabled traffic flow prediction

Off the Mainstream: Advances in Neural Networks and Machine Learning for Pattern Recognition

Contact Info

Product

Resources

About