Eric B. Baum

Bio: Eric B. Baum is an academic researcher from Princeton University. The author has contributed to research in topics: Blocks world & Probability distribution. The author has an hindex of 16, co-authored 26 publications receiving 5861 citations.

On genetic algorithms

Abstract: We analyze the performance of a Genetic Type Algorithm we call Culling and a variety of other algorithms on a problem we refer to as ASP. Culling is near optimal for this problem, highly noise tolerant, and the best known a~~roach . . in some regimes. We show that the problem of learning the Ising perception is reducible to noisy ASP. These results provide an example of a rigorous analysis of GA’s and give insight into when and how C,A’s can beat competing methods. To analyze the genetic algorithm, we view it as a special type of submartingale. We prove some new large deviation bounds on this submartingale w~ich enable us to determine the running time of the algorithm.

What Size Net Gives Valid Generalization

Abstract: We address the question of when a network can be expected to generalize from m random training examples chosen from some arbitrary probability distribution, assuming that future test examples are drawn from the same distribution. Among our results are the following bounds on appropriate sample vs. network size. Assume 0 < e ≤ 1/8. We show that if m ≥ O(W/e log N/e) random examples can be loaded on a feedforward network of linear threshold functions with N nodes and W weights, so that at least a fraction 1 - e/2 of the examples are correctly classified, then one has confidence approaching certainty that the network will correctly classify a fraction 1 - e of future test examples drawn from the same distribution. Conversely, for fully-connected feedforward nets with one hidden layer, any learning algorithm using fewer than Ω(W/e) random training examples will, for some distributions of examples consistent with an appropriate weight choice, fail at least some fixed fraction of the time to find a weight choice that will correctly classify more than a 1 - e fraction of the future test examples.

Constructing Hidden Units using Examples and Queries

Abstract: While the network loading problem for 2-layer threshold nets is NP-hard when learning from examples alone (as with backpropagation), (Baum, 91) has now proved that a learner can employ queries to evade the hidden unit credit assignment problem and PAC-load nets with up to four hidden units in polynomial time. Empirical tests show that the method can also learn far more complicated functions such as randomly generated networks with 200 hidden units. The algorithm easily approximates Wieland's 2-spirals function using a single layer of 50 hidden units, and requires only 30 minutes of CPU time to learn 200-bit parity to 99.7% accuracy.

Neural networks for pattern recognition

Abstract: From the Publisher: This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts, the book examines techniques for modelling probability density functions and the properties and merits of the multi-layer perceptron and radial basis function network models. Also covered are various forms of error functions, principal algorithms for error function minimalization, learning and generalization in neural networks, and Bayesian techniques and their applications. Designed as a text, with over 100 exercises, this fully up-to-date work will benefit anyone involved in the fields of neural computation and pattern recognition.

A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting

Abstract: In the first part of the paper we consider the problem of dynamically apportioning resources among a set of options in a worst-case on-line framework. The model we study can be interpreted as a broad, abstract extension of the well-studied on-line prediction model to a general decision-theoretic setting. We show that the multiplicative weight-update Littlestone?Warmuth rule can be adapted to this model, yielding bounds that are slightly weaker in some cases, but applicable to a considerably more general class of learning problems. We show how the resulting learning algorithm can be applied to a variety of problems, including gambling, multiple-outcome prediction, repeated games, and prediction of points in Rn. In the second part of the paper we apply the multiplicative weight-update technique to derive a new boosting algorithm. This boosting algorithm does not require any prior knowledge about the performance of the weak learning algorithm. We also study generalizations of the new boosting algorithm to the problem of learning functions whose range, rather than being binary, is an arbitrary finite set or a bounded segment of the real line.

Approximation by superpositions of a sigmoidal function

Abstract: In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks.

A training algorithm for optimal margin classifiers

Abstract: A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of the classification functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters is adjusted automatically to match the complexity of the problem. The solution is expressed as a linear combination of supporting patterns. These are the subset of training patterns that are closest to the decision boundary. Bounds on the generalization performance based on the leave-one-out method and the VC-dimension are given. Experimental results on optical character recognition problems demonstrate the good generalization obtained when compared with other learning algorithms.