On the sample complexity of various learning strategies in the probabilistic PAC learning paradigms

2006 ◽  
pp. 89-106
Author(s):  
Naoki Abe
Keyword(s):  
Learning Strategies ◽  
Pac Learning ◽  
Sample Complexity

On Learning Perceptrons with Binary Weights

1993 ◽  
Vol 5 (5) ◽  
pp. 767-782 ◽  
Author(s):  
Mostefa Golea ◽  
Mario Marchand
Keyword(s):  
Learning Curve ◽  
Uniform Distribution ◽  
Pac Learning ◽  
Sample Complexity ◽  
Average Case Analysis ◽  
Average Case ◽  
Hebb Rule ◽  
Product Distributions ◽  
Training Examples ◽  
Learning Analysis

We present an algorithm that PAC learns any perceptron with binary weights and arbitrary threshold under the family of product distributions. The sample complexity of this algorithm is of O[(n/ε)4 ln(n/δ)] and its running time increases only linearly with the number of training examples. The algorithm does not try to find an hypothesis that agrees with all of the training examples; rather, it constructs a binary perceptron based on various probabilistic estimates obtained from the training examples. We show that, under the restricted case of the uniform distribution and zero threshold, the algorithm reduces to the well known clipped Hebb rule. We calculate exactly the average generalization rate (i.e., the learning curve) of the algorithm, under the uniform distribution, in the limit of an infinite number of dimensions. We find that the error rate decreases exponentially as a function of the number of training examples. Hence, the average case analysis gives a sample complexity of O[n ln(1/ε)], a large improvement over the PAC learning analysis. The analytical expression of the learning curve is in excellent agreement with the extensive numerical simulations. In addition, the algorithm is very robust with respect to classification noise.

scholarly journals STATISTICAL SIGNIFICANCE OF PREDICTING THE PRODUCTION PROCESS RESULTS BY MEANS OF AN ARTIFICIAL NEURAL NETWORK

2018 ◽  
Vol 3 (3) ◽  
pp. 117-123
Author(s):  
Александр Макаров ◽  
Aleksandr Makarov
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Lower Bound ◽  
Confidence Interval ◽  
Production Process ◽  
Statistical Significance ◽  
Test Sample ◽  
Pac Learning ◽  
Sample Complexity ◽  
Artificial Neural

As a result of the research of production process organization for the roof construction of residential multi-storey buildings, an artificial neural network (ANN) was designed, the purpose of which is to predict the labor productivity based on organizational factors. One of the main tasks on the way to this purpose is the training of ANN on precedents of the sample extracted from the research object. In view of the deficiency of training data, the main problem is to determine the conditions for the statistical significance of the predictions of the model trained on limited sample. This article is devoted to solving this problem within the research of production organization. The paper uses the provisions of the statistical learning theory, the notion of the Vapnik-Chervonenkis dimension for describing the sample complexity, and also the approaches of probably approximately correct learning (PAC-learning). The technologies of statistical bootstrapping and bagging are described, which allow expanding the training sample. ANN training is conducted using a computer experiment on the programming language Python. The bounds of the theoretical sample complexity, which is necessary for obtaining of ANN results within a given confidence interval with a confidence level of 0,95, were estimated. The sample was transformed by an order comparable to the theoretical lower bound. ANN was trained and the mean square error (MSE) in the test sample was defined, which amounted to . The theoretical bounds of the sample complexity to ensure a given statistical significance are determined in the article. After the ANN training on the sample, the order of which corresponds to theoretical lower bound, a prediction error was obtained on the test sample within the given confidence interval.

The Role of Test Anticipation in the Link Between Performance-Approach Goals and Academic Achievement

2016 ◽  
Vol 75 (3) ◽  
pp. 123-132 ◽  
Author(s):  
Marie Crouzevialle ◽  
Fabrizio Butera
Keyword(s):  
Learning Strategies ◽  
Test Performance ◽  
Longitudinal Design ◽  
Study Strategies ◽  
High Achievers ◽  
Course Content ◽  
And Mathematics ◽  
Set Up ◽  
Approach Goals ◽  
Goal Endorsement

Abstract. Performance-approach goals (i.e., the desire to outperform others) have been found to be positive predictors of test performance, but research has also revealed that they predict surface learning strategies. The present research investigates whether the high academic performance of students who strongly adopt performance-approach goals stems from test anticipation and preparation, which most educational settings render possible since examinations are often scheduled in advance. We set up a longitudinal design for an experiment conducted in high-school classrooms within the context of two science, technology, engineering, and mathematics (STEM) disciplines, namely, physics and chemistry. First, we measured performance-approach goals. Then we asked students to take a test that had either been announced a week in advance (enabling strategic preparation) or not. The expected interaction between performance-approach goal endorsement and test anticipation was moderated by the students’ initial level: The interaction appeared only among low achievers for whom the pursuit of performance-approach goals predicted greater performance – but only when the test had been scheduled. Conversely, high achievers appeared to have adopted a regular and steady process of course content learning whatever their normative goal endorsement. This suggests that normative strivings differentially influence the study strategies of low and high achievers.

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