LEAST SQUARE REGRESSION WITH COEFFICIENT REGULARIZATION BY GRADIENT DESCENT

2012 ◽  
Vol 10 (01) ◽  
pp. 1250005 ◽  
Author(s):  
JUAN HUANG ◽  
HONG CHEN ◽  
LUOQING LI
Keyword(s):  
Integral Operator ◽  
Explicit Expression ◽  
Gradient Descent ◽  
Stochastic Gradient ◽  
Least Square ◽  
Stochastic Gradient Descent ◽  
Least Square Regression ◽  
Learning Rates ◽  
Gradient Descent Algorithm ◽  
Regularization Parameters

We propose a stochastic gradient descent algorithm for the least square regression with coefficient regularization. An explicit expression of the solution via sampling operator and empirical integral operator is derived. Learning rates are given in terms of the suitable choices of the step sizes and regularization parameters.

Soft-Sign Stochastic Gradient Descent Algorithm for Wireless Federated Learning

2021 ◽  
Author(s):  
Seunghoon Lee ◽  
Chanho Park ◽  
Songnam Hong ◽  
Yonina C. Eldar ◽  
Namyoon Lee
Keyword(s):  
Gradient Descent ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Descent Algorithm ◽  
Gradient Descent Algorithm

scholarly journals Optical Recognition of Handwritten Logic Formulas Using Neural Networks

Electronics ◽  
2021 ◽  
Vol 10 (22) ◽  
pp. 2761
Author(s):  
Vaios Ampelakiotis ◽  
Isidoros Perikos ◽  
Ioannis Hatzilygeroudis ◽  
George Tsihrintzis
Keyword(s):  
Neural Networks ◽  
Character Recognition ◽  
Gradient Descent ◽  
Feedforward Neural Networks ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Training Algorithms ◽  
Gradient Descent Algorithm ◽  
Two Stages ◽  
And Training

In this paper, we present a handwritten character recognition (HCR) system that aims to recognize first-order logic handwritten formulas and create editable text files of the recognized formulas. Dense feedforward neural networks (NNs) are utilized, and their performance is examined under various training conditions and methods. More specifically, after three training algorithms (backpropagation, resilient propagation and stochastic gradient descent) had been tested, we created and trained an NN with the stochastic gradient descent algorithm, optimized by the Adam update rule, which was proved to be the best, using a trainset of 16,750 handwritten image samples of 28 × 28 each and a testset of 7947 samples. The final accuracy achieved is 90.13%. The general methodology followed consists of two stages: the image processing and the NN design and training. Finally, an application has been created that implements the methodology and automatically recognizes handwritten logic formulas. An interesting feature of the application is that it allows for creating new, user-oriented training sets and parameter settings, and thus new NN models.

MapReduce and Optimized Deep Network for Rainfall Prediction in Agriculture

2020 ◽  
Vol 63 (6) ◽  
pp. 900-912
Author(s):  
Oswalt Manoj S ◽  
Ananth J P
Keyword(s):  
Deep Learning ◽  
Gradient Descent ◽  
Prediction Models ◽  
Short Term Memory ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Mean Square ◽  
Rainfall Prediction ◽  
Gradient Descent Algorithm ◽  
Major Factors

Abstract Rainfall prediction is the active area of research as it enables the farmers to move with the effective decision-making regarding agriculture in both cultivation and irrigation. The existing prediction models are scary as the prediction of rainfall depended on three major factors including the humidity, rainfall and rainfall recorded in the previous years, which resulted in huge time consumption and leveraged huge computational efforts associated with the analysis. Thus, this paper introduces the rainfall prediction model based on the deep learning network, convolutional long short-term memory (convLSTM) system, which promises a prediction based on the spatial-temporal patterns. The weights of the convLSTM are tuned optimally using the proposed Salp-stochastic gradient descent algorithm (S-SGD), which is the integration of Salp swarm algorithm (SSA) in the stochastic gradient descent (SGD) algorithm in order to facilitate the global optimal tuning of the weights and to assure a better prediction accuracy. On the other hand, the proposed deep learning framework is built in the MapReduce framework that enables the effective handling of the big data. The analysis using the rainfall prediction database reveals that the proposed model acquired the minimal mean square error (MSE) and percentage root mean square difference (PRD) of 0.001 and 0.0021.

scholarly journals Stochastic Subgradient for Large-Scale Support Vector Machine Using the Generalized Pinball Loss Function

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1652
Author(s):  
Wanida Panup ◽  
Rabian Wangkeeree
Keyword(s):  
Support Vector Machine ◽  
Loss Function ◽  
Gradient Descent ◽  
Large Scale ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Support Vector ◽  
Hinge Loss ◽  
Gradient Descent Algorithm ◽  
Pinball Loss

In this paper, we propose a stochastic gradient descent algorithm, called stochastic gradient descent method-based generalized pinball support vector machine (SG-GPSVM), to solve data classification problems. This approach was developed by replacing the hinge loss function in the conventional support vector machine (SVM) with a generalized pinball loss function. We show that SG-GPSVM is convergent and that it approximates the conventional generalized pinball support vector machine (GPSVM). Further, the symmetric kernel method was adopted to evaluate the performance of SG-GPSVM as a nonlinear classifier. Our suggested algorithm surpasses existing methods in terms of noise insensitivity, resampling stability, and accuracy for large-scale data scenarios, according to the experimental results.

scholarly journals Parameter calibration with stochastic gradient descent for interacting particle systems driven by neural networks

2021 ◽  
Author(s):  
Simone Göttlich ◽  
Claudia Totzeck
Keyword(s):  
Gradient Descent ◽  
Interacting Particle Systems ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Force Model ◽  
Data Sets ◽  
Optimal Controls ◽  
Parameter Calibration ◽  
Descent Algorithm ◽  
Gradient Descent Algorithm

AbstractWe propose a neural network approach to model general interaction dynamics and an adjoint-based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem that is investigated from a theoretical and numerical point of view. We prove the existence of optimal controls, derive the corresponding first-order optimality system and formulate a stochastic gradient descent algorithm to identify parameters for given data sets. To validate the approach, we use real data sets from traffic and crowd dynamics to fit the parameters. The results are compared to forces corresponding to well-known interaction models such as the Lighthill–Whitham–Richards model for traffic and the social force model for crowd motion.

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