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.

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 Least Square Regularized Regression for Multitask Learning

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yong-Li Xu ◽  
Di-Rong Chen ◽  
Han-Xiong Li
Keyword(s):  
Hilbert Space ◽  
Learning Algorithms ◽  
Multitask Learning ◽  
Least Square ◽  
Regularized Regression ◽  
Task Learning ◽  
Hypothesis Space ◽  
Learning Rates ◽  
Prediction Function ◽  
Optimal Function

The study of multitask learning algorithms is one of very important issues. This paper proposes a least-square regularized regression algorithm for multi-task learning with hypothesis space being the union of a sequence of Hilbert spaces. The algorithm consists of two steps of selecting the optimal Hilbert space and searching for the optimal function. We assume that the distributions of different tasks are related to a set of transformations under which any Hilbert space in the hypothesis space is norm invariant. We prove that under the above assumption the optimal prediction function of every task is in the same Hilbert space. Based on this result, a pivotal error decomposition is founded, which can use samples of related tasks to bound excess error of the target task. We obtain an upper bound for the sample error of related tasks, and based on this bound, potential faster learning rates are obtained compared to single-task learning algorithms.

REGULARIZED LEAST SQUARE ALGORITHM WITH TWO KERNELS

2012 ◽  
Vol 10 (05) ◽  
pp. 1250043 ◽  
Author(s):  
HONGWEI SUN ◽  
PING LIU
Keyword(s):  
Error Bounds ◽  
Learning Algorithm ◽  
Least Square ◽  
Covering Number ◽  
Mathematical Foundation ◽  
Hypothesis Space ◽  
Learning Rates ◽  
Regression Learning ◽  
Mercer Kernels ◽  
Dependent Error

A new multi-kernel regression learning algorithm is studied in this paper. In our setting, the hypothesis space is generated by two Mercer kernels, thus it has stronger approximation ability than the single kernel case. We provide the mathematical foundation for this regularized learning algorithm. We obtain satisfying capacity-dependent error bounds and learning rates by the covering number method.

scholarly journals Accelerating Reinforcement Learning by Composing Solutions of Automatically Identified Subtasks

2002 ◽  
Vol 16 ◽  
pp. 59-104 ◽  
Author(s):  
C. Drummond
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Learning Process ◽  
Learning Algorithm ◽  
Complete Solution ◽  
Learning Rate ◽  
Close Approximation ◽  
Order Of Magnitude ◽  
Abstract Level ◽  
Magnitude Increase

This paper discusses a system that accelerates reinforcement learning by using transfer from related tasks. Without such transfer, even if two tasks are very similar at some abstract level, an extensive re-learning effort is required. The system achieves much of its power by transferring parts of previously learned solutions rather than a single complete solution. The system exploits strong features in the multi-dimensional function produced by reinforcement learning in solving a particular task. These features are stable and easy to recognize early in the learning process. They generate a partitioning of the state space and thus the function. The partition is represented as a graph. This is used to index and compose functions stored in a case base to form a close approximation to the solution of the new task. Experiments demonstrate that function composition often produces more than an order of magnitude increase in learning rate compared to a basic reinforcement learning algorithm.

The consistency of least-square regularized regression with negative association sequence

2018 ◽  
Vol 16 (03) ◽  
pp. 1850019 ◽  
Author(s):  
Fen Chen ◽  
Bin Zou ◽  
Na Chen
Keyword(s):  
Learning Theory ◽  
Learning Process ◽  
Negative Association ◽  
Least Square ◽  
Learning Performance ◽  
Regularized Regression ◽  
Identical Distribution ◽  
Na Sequence ◽  
Mixing Sequences ◽  
Dependent Samples

In the last few years, many known works in learning theory stepped over the classical assumption that samples are independent and identical distribution and investigated learning performance based on non-independent samples, as mixing sequences (e.g., [Formula: see text]-mixing, [Formula: see text]-mixing, [Formula: see text]-mixing etc.), they derived similar results with the investigation based on classical sample assumption. Negative association (NA) sequence is a kind of significant dependent random variables and plays an important role in non-independent sequences. It is widely applied to various subjects such as probability theory, statistics and stochastic processes. Therefore, it is essential to study the learning performance of learning process for dependent samples drawn from NA process. Obviously, samples in this learning process are not independent and identical distribution. The results in classical learning theory are not applied directly. In this paper, we study the consistency of least-square regularized regression with NA samples. We establish the error bound of least-square regularized regression for NA samples, and prove that the learning rate of least-square regularized regression for NA samples is [Formula: see text], which is tend to [Formula: see text] when [Formula: see text] arbitrarily close to 0, where [Formula: see text] denote the number of the samples. The simulation experiment of convergence rate on NA samples reveals that the least-square regularized regression algorithm for NA samples is consistent. This result generalizes the classical result of independent and identical distribution.

Peningkatan Hasil Belajar Fisika Melalui Pendekatan Numbered Head Together Dengan Pemberian Reward di SMP Negeri 5 Kota Jambi

2012 ◽  
Vol 1 (1) ◽  
Author(s):  
Delismar Delismar
Keyword(s):  
Action Research ◽  
Active Learning ◽  
Learning Outcomes ◽  
Learning Process ◽  
Learning Outcome ◽  
Class Action ◽  
Learning Approach ◽  
Physics Learning ◽  
Lecture Method ◽  
Student Observation

In classical learning approach, conventional lecture method is commonly used by teachers in implementing learning process in classes.  The teacher becomes the main source of learning.  The current student’s habit that tends to be passive and individualistic resulted in a passive and monotone learning.      To overcome these problems, I was interested to implement the model of numbered heads together in learning Physics in the Class VII B of SMP Negeri 5 Kota Jambi. The purpose of this learning approach is to enable students to develop cooperative skill and more active learning of physics and to improve learning results. This research is a class action research, which were performed in two cycles.  All students’ activities in the class were observed and recorded in observation sheet, consisting of teacher observation sheet and student observation sheet. To find out the learning outcomes, formative test was performed using a written instrument form.  The results show the increase of students’ discipline, cooperation, liveliness, timeliness in learning Physics.  In addition, the learning model also increases the students’ learning outcomes. The average learning results increased to 75.38 (increase 3.25 points).  To conclude, the implementation of Number Head Together increase students’ discipline, cooperation, activities, and timeliness.  The model also increase the Physics learning outcome of student in SMP Negeri 5 Kota  Jambi.

scholarly journals Mechatronics: Experiential Learning and the Stimulation of Thinking Skills

2021 ◽  
Vol 11 (2) ◽  
pp. 46
Author(s):  
Maki K. Habib ◽  
Fusaomi Nagata ◽  
Keigo Watanabe
Keyword(s):  
Critical Thinking ◽  
Experiential Learning ◽  
Learning Process ◽  
Laboratory Experiments ◽  
Thinking Skills ◽  
Project Based Learning ◽  
Critical Thinking Skills ◽  
Learning Approach ◽  
Learning Approaches ◽  
Experimental Systems

The development of experiential learning methodologies is gaining attention, due to its contributions to enhancing education quality. It focuses on developing competencies, and build-up added values, such as creative and critical thinking skills, with the aim of improving the quality of learning. The interdisciplinary mechatronics field accommodates a coherent interactive concurrent design process that facilitates innovation and develops the desired skills by adopting experiential learning approaches. This educational learning process is motivated by implementation, assessment, and reflections. This requires synergizing cognition, perception, and behavior with experience sharing and evaluation. Furthermore, it is supported by knowledge accumulation. The learning process with active student’s engagement (participation and investigation) is integrated with experimental systems that are developed to facilitate experiential learning supported by properly designed lectures, laboratory experiments, and integrated with course projects. This paper aims to enhance education, learning quality, and contribute to the learning process, while stimulating creative and critical thinking skills. The paper has adopted a student-centered learning approach and focuses on developing training tools to improve the hands-on experience and integrate it with project-based learning. The developed experimental systems have their learning indicators where students acquire knowledge and learn the target skills through involvement in the process. This is inspired by collaborative knowledge sharing, brainstorming, and interactive discussions. The learning outcomes from lectures and laboratory experiments are synergized with the project-based learning approach to yield the desired promising results and exhibit the value of learning. The effectiveness of the developed experimental systems along with the adopted project-based learning approach is demonstrated and evaluated during laboratory sessions supporting different courses at Sanyo-Onoda City University, Yamaguchi, Japan, and at the American University in Cairo.

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.

THE WORK HARD ETHIC OF TEACHER (ETOS KERJA KERAS GURU) DALAM PEMBELAJARAN SEBAGAI PILAR PENDIDIKAN YANG BERKARAKTE

2013 ◽  
Vol 1 (1) ◽  
pp. 36
Author(s):  
Sutarman Sutarman
Keyword(s):  
Learning Process ◽  
Learning Approach ◽  
Information Communication ◽  
Teaching Process ◽  
Teacher Needs ◽  
Strong Motivation ◽  
Communication And Technology

Teacher isn‘t one of all source of science in learning process. So, if the teacher needs survive in his or her contribution in the learning teaching process, they must do some innovations. Its means, the teacher  must have work hard ethic in doing to do the innovation, learning approach, chosing the metode and media. In order to make the learning teaching process run well, therefore the teacher is not only has mastered his or her competence but also has mastered the emotion quotion, spiritual quotion and has mastered the information, communication and technology. Beside that, the teacher who has work hard ethic,  is the teacher who has optimism. It means, in doing his task of the learning teaching process must have the strong motivation. So, the teacher will get the best achievement.

scholarly journals Kecakapan Berpikir Dalam Konteks Pendekatan Pembelajaran Pada Kurikulum Sekolah Di Indonesia

2019 ◽  
Vol 14 (01) ◽  
pp. 63-84
Author(s):  
Marwan Salahuddin ◽  
Fatimatul Asroriyah
Keyword(s):  
Learning Process ◽  
Thinking Skills ◽  
School Curriculum ◽  
Learning Activities ◽  
Learning Approach ◽  
Scientific Thinking ◽  
Thinking Process ◽  
And Behavior ◽  
Previous Learning

The thinking skills are indispensable in the context of the learning approach, as it is a scientific thinking process aimed at growing the expected personality. It also affects the learning process and the ability to develop its goals through strengthening attitudes, skills and knowledge in an integrated way. The process includes activities: observing, asking, trying, reasoning, and communicating. In the course of the school curriculum in Indonesia and its learning process, the strengthening of cognitive and skill aspects is still dominant, while the attitude (spiritual and social) is still lacking, but this attitude will support the learning activities oriented to cultivation of character. Because the curriculum and the previous learning process still appear to be opposite and have not indicated the process of achieving competence in the attitude aspect, the curriculum of the school applied today is tailored to that need. So as to accommodate the elements of personality that include: beliefs, values, and behavior as a whole.

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