Fuzzy ART: Fast Stable Learning and Categorization of Analog Patterns by an Adaptive Resonance System

A Fuzzy ART model capable of rapid stable learning of recognition categories in response to arbitrary sequences of analog or binary input patterns is described. Fuzzy ART incorporates computations from fuzzy set theory into the ART 1 neural network, which learns to categorize only binary input patterns. The generalization to learning both analog and binary input patterns is achieved by replacing appearances of the intersection operator (n) in AHT 1 by the MIN operator (Λ) of fuzzy set theory. The MIN operator reduces to the intersection operator in the binary case. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy set theory play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Learning stops when the input space is covered by boxes. With fast learning and a finite input set of arbitrary size and composition, learning stabilizes after just one presentation of each input pattern. A fast-commit slow-recode option combines fast learning with a forgetting rule that buffers system memory against noise. Using this option, rare events can be rapidly learned, yet previously learned memories are not rapidly erased in response to statistically unreliable input fluctuations.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-90-00530); Air Force Office of Scientific Research (90-0175

Portfolio Choice and Health Status

This paper analyzes the role that health status plays in household portfolio decisions using data from the Health and Retirement Study. The results indicate that health is a significant predictor of both the probability of owning different types of financial assets and the share of financial wealth held in each asset category. Households in poor health are less likely to hold risky financial assets, other things (including the level of total wealth) being the same. Poor health is associated with a smaller share of financial wealth held in risky assets and a larger share in safe assets. We find no evidence that the relationship between health status and portfolio allocation is driven by third variables' that simultaneously affect health and financial decisions. Further, the relationship between health status and portfolio choice does not appear to operate through the effect of poor health on individuals' attitudes toward risk, their planning horizons, or their health insurance status.

ART 2-A: An Adaptive Resonance Algorithm for Rapid Category Learning and Recognition

This article introduces ART 2-A, an efficient algorithm that emulates the self-organizing pattern recognition and hypothesis testing properties of the ART 2 neural network architecture, but at a speed two to three orders of magnitude faster. Analysis and simulations show how the ART 2-A systems correspond to ART 2 dynamics at both the fast-learn limit and at intermediate learning rates. Intermediate learning rates permit fast commitment of category nodes but slow recoding, analogous to properties of word frequency effects, encoding specificity effects, and episodic memory. Better noise tolerance is hereby achieved without a loss of learning stability. The ART 2 and ART 2-A systems are contrasted with the leader algorithm. The speed of ART 2-A makes practical the use of ART 2 modules in large-scale neural computation.BP (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-90-00530); Air Force Office of Scientific Research (90-0175, 90-0128); Army Research Office (DAAL-03-88-K0088

Altruistic Behavior and Habit Formation

This paper examines whether altruistic behavior is habit forming. We take advantage of a data set that includes a rich set of information concerning individuals’ donations of cash and time as adults as well as information about whether they were involved with charitable activities when they were young. The basic premise is that if altruistic behavior when young is a good predictor of such behavior in adulthood, then this is consistent with the notion that altruistic behavior is habit forming. Using U.S. data, we examine both donations of money and time, and find that engaging in charitable behavior when young is a strong predictor of adult altruistic behavior, ceteris paribus. A major issue in the interpretation of this result is that the correlation between youthful and adult altruistic behavior may be due to some third variable that affects both. While it is impossible to rule out such a possibility, we are able to control for family influences that likely could affect lifetime attitudes toward altruism. We find that, even taking this factor into account, altruistic behavior as a youth plays a significant role in explaining adult behavior. This result applies to donations of money and time to a variety of types of non-profit organizations.altruistic behavior, donations, nonprofit fundraising

Fuzzy ART: An Adaptive Resonance Algorithm for Rapid, Stable Classification of Analog Patterns

The Fuzzy ART system introduced herein incorporates computations from fuzzy set theory into ART 1. For example, the intersection (n) operator used in ART 1 learning is replaced by the MIN operator (A) of fuzzy set theory. Fuzzy ART reduces to ART 1 in response to binary input vectors, but can also learn stable categories in response to analog input vectors. In particular, the MIN operator reduces to the intersection operator in the binary case. Learning is stable because all adaptive weights can only decrease in time. A preprocessing step, called complement coding, uses on-cell and off-cell responses to prevent category proliferation. Complement coding normalizes input vectors while preserving the amplitudes of individual feature activations.Air Force Office of Scientific Research (90-0175, 90-0128); Army Research Office (DAAL-03-88-K0088); BP (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-90-00530

A Neural Network Realization of Fuzzy ART

A neural network realization of the fuzzy Adaptive Resonance Theory (ART) algorithm is described. Fuzzy ART is capable of rapid stable learning of recognition categories in response to arbitrary sequences of analog or binary input patterns. Fuzzy ART incorporates computations from fuzzy set theory into the ART 1 neural network, which learns to categorize only binary input patterns, thus enabling the network to learn both analog and binary input patterns. In the neural network realization of fuzzy ART, signal transduction obeys a path capacity rule. Category choice is determined by a combination of bottom-up signals and learned category biases. Top-down signals impose upper bounds on feature node activations.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (90-0175

Strategic Traditions for the Asia-Pacific Region

Tradition has both positive and negative implications. It may be valuable lessons learned, lessons paid for with blood, but tradition may also be habits of the last war that make it difficult to see and react to change. There is good reason to think that future conditions in the Asia-Pacific region will not be consistent with what the strategic traditions of the U.S. military tell us we can expect

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (90-0175

Health Status and Portfolio Choice

This paper analyzes the role that health status plays in household portfolio decisions using data from the first wave of the Health and Retirement Study. The results indicate that health is a significant predictor of both the probability of owning different types of financial assets and the share of financial wealth held in each asset category. Households in poor health are less likely to hold both safe and risky financial assets, other things (including the level of total wealth) being the same. Poor health is associated with a smaller share of financial wealth held in risky assets and a larger share in safe assets. We find no evidence that the cross sectional relationship between health status and portfolio allocation is driven by “third variables” that simultaneously affect health and financial decisions. Further, the relationship between health status and portfolio choice does not appear to operate through the effect of poor health on individuals’ attitudes toward risk or their planning horizons.