On the statistical properties of least-square estimators of layered neural networks

2004 ◽  
Vol 35 (12) ◽  
pp. 1-9
Author(s):  
Masashi Kitahara ◽  
Taichi Hayasaka ◽  
Naohiro Toda ◽  
Shiro Usui
Keyword(s):  
Neural Networks ◽  
Statistical Properties ◽  
Least Square ◽  
Least Square Estimators

scholarly journals Impacts of multicollinearity on CAPT modalities: An heterogeneous machine learning framework for computer-assisted French phoneme pronunciation training

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0257901
Author(s):  
Yanjing Bi ◽  
Chao Li ◽  
Yannick Benezeth ◽  
Fan Yang
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Support Vector Machines ◽  
Partial Least Square ◽  
Least Square ◽  
Support Vector ◽  
Computer Assisted ◽  
Long Distance ◽  
Relationship Analysis ◽  
Vector Machines

Phoneme pronunciations are usually considered as basic skills for learning a foreign language. Practicing the pronunciations in a computer-assisted way is helpful in a self-directed or long-distance learning environment. Recent researches indicate that machine learning is a promising method to build high-performance computer-assisted pronunciation training modalities. Many data-driven classifying models, such as support vector machines, back-propagation networks, deep neural networks and convolutional neural networks, are increasingly widely used for it. Yet, the acoustic waveforms of phoneme are essentially modulated from the base vibrations of vocal cords, and this fact somehow makes the predictors collinear, distorting the classifying models. A commonly-used solution to address this issue is to suppressing the collinearity of predictors via partial least square regressing algorithm. It allows to obtain high-quality predictor weighting results via predictor relationship analysis. However, as a linear regressor, the classifiers of this type possess very simple topology structures, constraining the universality of the regressors. For this issue, this paper presents an heterogeneous phoneme recognition framework which can further benefit the phoneme pronunciation diagnostic tasks by combining the partial least square with support vector machines. A French phoneme data set containing 4830 samples is established for the evaluation experiments. The experiments of this paper demonstrates that the new method improves the accuracy performance of the phoneme classifiers by 0.21 − 8.47% comparing to state-of-the-arts with different data training data density.

A Cooperative Recurrent Neural Network for Solving L1 Estimation Problems with General Linear Constraints

2008 ◽  
Vol 20 (3) ◽  
pp. 844-872 ◽  
Author(s):  
Youshen Xia ◽  
Mohamed S. Kamel
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Network ◽  
Parallel Implementation ◽  
Linear Constraints ◽  
Estimation Problem ◽  
Least Square ◽  
General Linear ◽  
Attractive Alternative ◽  
Estimation Problems

The constrained L1 estimation is an attractive alternative to both the unconstrained L1 estimation and the least square estimation. In this letter, we propose a cooperative recurrent neural network (CRNN) for solving L1 estimation problems with general linear constraints. The proposed CRNN model combines four individual neural network models automatically and is suitable for parallel implementation. As a special case, the proposed CRNN includes two existing neural networks for solving unconstrained and constrained L1 estimation problems, respectively. Unlike existing neural networks, with penalty parameters, for solving the constrained L1 estimation problem, the proposed CRNN is guaranteed to converge globally to the exact optimal solution without any additional condition. Compared with conventional numerical algorithms, the proposed CRNN has a low computational complexity and can deal with the L1 estimation problem with degeneracy. Several applied examples show that the proposed CRNN can obtain more accurate estimates than several existing algorithms.

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