One of the most important aspects of any machine learning paradigm is how i t scales according to problem size and complexity. Using a task with known optimal train ing error, and a pre-specified maximum number of training updates, we investigate the convergence of th backpropagation algorithm with respect to a) the complexity of the required function approximatio n, b) the size of the network in relation to the size required for an optimal solution, and c) the degree o f noise in the training data. In general, for a) the solution found is worse when the function to be app roximated is more complex, for b) oversized networks can result in lower training and generalization error in certain cases, and for c) the use of committee or ensemble techniques can be more beneficial as the level o f noise in the training data is increased. For the experiments we performed, we do not obtain the optimal solution in any case. We further support the observation that larger networks can produce bett er training and generalization error using a face recognition example where a network with many more par ameters than training points generalizes better than smaller networks.

What Size Neural Network Gives Optimal Generalization? Convergence Properties of Backpropagation

The purpose of this article is to investigate the causal relationship between economic growth and defense spending in fifty-five developing countries. Granger-causality tests are employed to analyze the presence and direction of causality between these two variables. Moreover, the study focuses upon the appropriate representation of the nature of nonstationarities apparent in these two economic time series across different countries. The results suggest that the relationship between defense spending and economic growth cannot be generalized across countries. The actual relationship may vary from one country to another due to the use of a different sample period, as well as differences in the socioeconomic structure and type of government in each country.

A Causal Analysis of Defense Spending and Economic Growth

https://in.bgu.ac.il/en/humsos/Econ/Working/163.pdf

Government expenditures, military spending and economic growth: causality evidence from Egypt, Israel, and Syria

Applications of hybrid models in chemical, petroleum, and energy systems: A systematic review

An increasingly popular alternative to the lecture-oriented “chalk-and-talk” approach to teaching principles of microeconomics is the use of classroom experiments. Like other alternatives to traditional teaching methods, there exists little more than anecdotal evidence supporting the effectiveness of the experimental approach. We estimate the effect of participating in classroom experiments on student achievement in a principles of microeconomics course. Nine sections (300 students) participated in the study, two of which (59 students) relied heavily on classroom experiments throughout the semester. The remaining seven sections (241 students) used no experiments. We find that students in the experimental sections experienced significantly higher gains in Test of Understanding in College Economics (TUCE) scores but differed little on other more qualitative outcomes. Additionally, results indicate that certain student characteristics, including gender, major, and grade point average, can be used to predict a student’s likely success when choosing between courses that rely on experiments and those that employ more traditional forms of pedagogy.

Comparing Student Achievement across Experimental and Lecture-Oriented Sections of a Principles of Microeconomics Course

Economic growth and defense spending: Granger Causality

Encoding a priori information in feedforward networks

Economics is characterized by well-developed predictive theories of human behavior. A wide variety of empirical tests of models based on those theories have been developed, as well as extensive and reliable data bases to test the theories. Thus, one can experiment with and simulate economic behavior. For these reasons, the conventional lecture-discussion format may be the least effective way to teach economics. Rather, the most effective teaching method may be as a laboratory science. We report here on two efforts to adapt economic instruction to a laboratory format. The purpose of adapting the lecture-laboratory format to economics is to permit a more active learning environment in which students can be meaningfully engaged by the material, with other students, and with the instructor. We report on two recent efforts to convert economics to a true, experimental, laboratory social science. The first, beginning in 1988, is a demonstration project conducted at Denison University for majors in economics. The second, beginning in 1993, is a true experiment conducted at Washington State University for all students taking introductory microand macroeconomics. I. The Demonstration Project for Economics Majors at Denison University

Laboratory-Based Experimental and Demonstration Initiatives in Teaching Undergraduate Economics

It seems natural to test feedforward networks on deterministic functions. Yet, some simple functions, notably polynomials, present some difficult problems for approximation by feedforward networks. The estimated parameters become unbounded and fail to follow any unique pattern. Furthermore, as the fit to the specified functions becomes closer, numerical problems may develop in the algorithm. This paper explains why these problems occur for polynomials of order less than or equal to the number of hidden units of a feedforward network. We show that other examples occur for functions mathematically related to the network's squashing function. These difficulties do not indicate problems with the training algorithm, but occur as an inherent consequence of the role of the connection weights in feedforward networks.

Wayne Joerding

Papers

Economic growth and defense spending: Granger Causality

Encoding a priori information in feedforward networks

Laboratory-Based Experimental and Demonstration Initiatives in Teaching Undergraduate Economics

Why some feedforward networks cannot learn some polynomials

Polymorphism in competitive strategies: Trading stamps