Least Square Regression with lp-Coefficient Regularization

2010 ◽  
Vol 22 (12) ◽  
pp. 3221-3235 ◽  
Author(s):  
Hongzhi Tong ◽  
Di-Rong Chen ◽  
Fenghong Yang
Keyword(s):  
Error Analysis ◽  
Learning Algorithm ◽  
Learning Rate ◽  
Least Square ◽  
Explicit Learning ◽  
Regularization Term ◽  
Least Square Regression ◽  
Primary Focus ◽  
Selection Of

The selection of the penalty functional is critical for the performance of a regularized learning algorithm, and thus it deserves special attention. In this article, we present a least square regression algorithm based on lp-coefficient regularization. Comparing with the classical regularized least square regression, the new algorithm is different in the regularization term. Our primary focus is on the error analysis of the algorithm. An explicit learning rate is derived under some ordinary assumptions.

scholarly journals Error analysis of regularized least-square regression with Fredholm kernel

2017 ◽  
Vol 249 ◽  
pp. 237-244
Author(s):  
Yanfang Tao ◽  
Peipei Yuan ◽  
Biqin Song
Keyword(s):  
Error Analysis ◽  
Least Square ◽  
Least Square Regression ◽  
Fredholm Kernel

scholarly journals Selecting Milk Spectra to Develop Equations to Predict Milk Technological Traits

Foods ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 3084
Author(s):  
Maria Frizzarin ◽  
Isobel Claire Gormley ◽  
Alessandro Casa ◽  
Sinéad McParland
Keyword(s):  
Principal Component ◽  
Fixed Number ◽  
Prediction Performance ◽  
Partial Least Square ◽  
Least Square ◽  
Partial Least Square Regression ◽  
Local Approach ◽  
Mahalanobis Distances ◽  
Least Square Regression ◽  
Selection Of

Including all available data when developing equations to relate midinfrared spectra to a phenotype may be suboptimal for poorly represented spectra. Here, an alternative local changepoint approach was developed to predict six milk technological traits from midinfrared spectra. Neighbours were objectively identified for each predictand as those most similar to the predictand using the Mahalanobis distances between the spectral principal components, and subsequently used in partial least square regression (PLSR) analyses. The performance of the local changepoint approach was compared to that of PLSR using all spectra (global PLSR) and another LOCAL approach, whereby a fixed number of neighbours was used in the prediction according to the correlation between the predictand and the available spectra. Global PLSR had the lowest RMSEV for five traits. The local changepoint approach had the lowest RMSEV for one trait; however, it outperformed the LOCAL approach for four traits. When the 5% of the spectra with the greatest Mahalanobis distance from the centre of the global principal component space were analysed, the local changepoint approach outperformed the global PLSR and the LOCAL approach in two and five traits, respectively. The objective selection of neighbours improved the prediction performance compared to utilising a fixed number of neighbours; however, it generally did not outperform the global PLSR.

The performance of semi-supervised Laplacian regularized regression with the least square loss

2017 ◽  
Vol 15 (02) ◽  
pp. 1750016 ◽  
Author(s):  
Baohuai Sheng ◽  
Daohong Xiang
Keyword(s):  
Convergence Rate ◽  
Learning Process ◽  
Learning Algorithm ◽  
Learning Rate ◽  
Least Square ◽  
Learning Approach ◽  
Regularized Regression ◽  
Scale Parameters ◽  
Hypothesis Space ◽  
Suitable Structure

The capacity convergence rate for a kind of kernel regularized semi-supervised Laplacian learning algorithm is bounded with the convex analysis approach. The algorithm is a graph-based regression whose structure shares the feature of both the kernel regularized regression and the kernel regularized Laplacian ranking. It is shown that the kernel reproducing the hypothesis space has contributions to the clustering ability of the algorithm. If the scale parameters in the Gaussian weights are chosen properly, then the learning rate can be controlled by the unlabeled samples and the algorithm converges with the increase of the number of the unlabeled samples. The results of this paper show that choosing suitable structure the semi-supervised learning approach can not only increase the learning rate, but also finish the learning process by increasing the number of unlabeled samples.

Ease of Doing Business and Its Impact on Inward FDI

2018 ◽  
Vol 1 (1) ◽  
pp. 52 ◽  
Author(s):  
Mohamed Tareq Hossain ◽  
Zubair Hassan ◽  
Sumaiya Shafiq ◽  
Abdul Basit
Keyword(s):  
Regression Model ◽  
Causal Relationship ◽  
World Bank ◽  
Least Square ◽  
Doing Business ◽  
Least Square Regression ◽  
Foreign Countries ◽  
Ease Of Doing Business ◽  
The Impact ◽  
Starting A Business

This study investigates the impact of Ease of Doing Business on Inward FDI over the period from 2011 to 2015 across the globe. This study measures ease of doing business using starting a business, getting credit, registering property, paying taxes and enforcing contracts. The research used a sample of 177 countries from 190 countries listed in World Bank. Least square regression model via E-views software used to examine causal relationship. The study found that ease of doing business indicators ‘Enforcing Contracts’ was found to have a positive significant impact on Inward FDI. Nevertheless, ‘Getting Credit’ and ‘Registering Property’ were found to have a negative significant impact on Inward FDI. However, ‘Starting a Business’ and ‘Paying Taxes’ have no significant impact on Inward FDI in the studied timeframe of this research. The findings of the study suggested the ease of doing business enables inward FDI through better contract enforcements, getting credit and registering property. The findings of the research will assist international managers and companies to know the importance of ease of doing business when investing in foreign countries through FDI.

scholarly journals Monotonic Functions Method and Its Application to Staging of Patients with Prostate Cancer According to Pretreatment Data

2021 ◽  
Vol 11 (9) ◽  
pp. 3836
Author(s):  
Valeri Gitis ◽  
Alexander Derendyaev ◽  
Konstantin Petrov ◽  
Eugene Yurkov ◽  
Sergey Pirogov ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Learning Algorithm ◽  
Binary Classification ◽  
Preoperative Staging ◽  
Threshold Value ◽  
Logical Function ◽  
Adequate Treatment ◽  
Monotonic Functions ◽  
Selection Of

Prostate cancer is the second most frequent malignancy (after lung cancer). Preoperative staging of PCa is the basis for the selection of adequate treatment tactics. In particular, an urgent problem is the classification of indolent and aggressive forms of PCa in patients with the initial stages of the tumor process. To solve this problem, we propose to use a new binary classification machine-learning method. The proposed method of monotonic functions uses a model in which the disease’s form is determined by the severity of the patient’s condition. It is assumed that the patient’s condition is the easier, the less the deviation of the indicators from the normal values inherent in healthy people. This assumption means that the severity (form) of the disease can be represented by monotonic functions from the values of the deviation of the patient’s indicators beyond the normal range. The method is used to solve the problem of classifying patients with indolent and aggressive forms of prostate cancer according to pretreatment data. The learning algorithm is nonparametric. At the same time, it allows an explanation of the classification results in the form of a logical function. To do this, you should indicate to the algorithm either the threshold value of the probability of successful classification of patients with an indolent form of PCa, or the threshold value of the probability of misclassification of patients with an aggressive form of PCa disease. The examples of logical rules given in the article show that they are quite simple and can be easily interpreted in terms of preoperative indicators of the form of the disease.

Modeling CO2 exchange and meteorological factors of an apple orchard using partial least square regression

2020 ◽  
Vol 27 (35) ◽  
pp. 43439-43451 ◽  
Author(s):  
Jianfeng Yang ◽  
Yumin Duan ◽  
Xiaoni Yang ◽  
Mukesh Kumar Awasthi ◽  
Huike Li ◽  
...  
Keyword(s):  
Meteorological Factors ◽  
Co2 Exchange ◽  
Apple Orchard ◽  
Partial Least Square ◽  
Least Square ◽  
Partial Least Square Regression ◽  
Least Square Regression

scholarly journals A Simpler Approach to Coefficient Regularized Support Vector Machines Regression

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongzhi Tong ◽  
Di-Rong Chen ◽  
Fenghong Yang
Keyword(s):  
Support Vector Machines ◽  
Convergence Analysis ◽  
Learning Rate ◽  
Support Vector ◽  
Explicit Learning ◽  
Stepping Stone ◽  
Mild Conditions ◽  
Hypothesis Space ◽  
Vector Machines

We consider a kind of support vector machines regression (SVMR) algorithms associated withlq  (1≤q<∞)coefficient-based regularization and data-dependent hypothesis space. Compared with former literature, we provide here a simpler convergence analysis for those algorithms. The novelty of our analysis lies in the estimation of the hypothesis error, which is implemented by setting a stepping stone between the coefficient regularized SVMR and the classical SVMR. An explicit learning rate is then derived under very mild conditions.

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