Kukjin Kang and Jong-Hoon Oh Department of Physics Pohang University of Science and Technology Hyoja San 31, Pohang, Kyongbuk 790-784, Korea Email: kkj.jhohOgalaxy.postech.ac.kr Abstract We study generalization capability of the mixture of experts learning fromexamples generated by another network with the same architecture. When the number of examples is smaller than a critical value,the network shows a symmetric phase where the role of the experts is not specialized. Upon crossing the critical point, the system undergoes a continuous phase transition to a symmetry breakingphase where the gating network partitions the input space effectively and each expert is assigned to an appropriate subspace. Wealso find that the mixture of experts with multiple level of hierarchy shows multiple phase transitions. 1 Introduction Recently there has been considerable interest among neural network community in techniques that integrate the collective predictions of a set of networks[l, 2, 3, 4]. The mixture of experts [1, 2] is a well known example which implements the philosophy ofdivide-and-conquer elegantly.

This paper describes a new technique for object recognition based on learning appearance models. The image is decomposed into local regions which are described by a new texture representation called "Generalized Second Moments" that are derived from the output of multiscale, multiorientation filter banks. Class-characteristic local texture features and their global composition is learned by a hierarchical mixture of experts architecture (Jordan & Jacobs). The technique is applied to a vehicle database consisting of 5 general car categories (Sedan, Van with backdoors, Van without backdoors, old Sedan, and Volkswagen Bug). This is a difficult problem with considerable in-class variation.

A typical problem in experiments performed at high energy accelerators aimed at studying novel effects in the field of Elementary Particle Physics is that of preselecting interesting interactions at as early a stage as possible, in order to keep the data volume manageable. One class of events that have to be eliminated is due to cosmic muons that pass all trigger conditions.

The classes in classification tasks often have a natural ordering, and the training and testing examples are often incomplete. We propose a nonlinear ordinal model for classification into ordered classes. Predictive, simulation-based approaches are used to learn from past and classify future incomplete examples. These techniques are illustrated by making prognoses for patients who have suffered severe head injuries.

We propose and analyze an algorithm that approximates solutions to the problem of optimal stopping in a discounted irreducible aperiodic Markov chain. The scheme involves the use of linear combinations of fixed basis functions to approximate a Q-function. The weights of the linear combination are incrementally updated through an iterative process similar to Q-Iearning, involving simulation of the underlying Markov chain. Due to space limitations, we only provide an overview of a proof of convergence (with probability 1) and bounds on the approximation error. This is the first theoretical result that establishes the soundness of a Q-Iearninglike algorithm when combined with arbitrary linear function approximators to solve a sequential decision problem.

By now it is widely accepted that learning a task from scratch, i.e., without any prior knowledge, is a daunting undertaking. Humans, however, rarely attempt to learn from scratch. They extract initial biases as well as strategies how to approach a learning problem from instructions and/or demonstrations of other humans. For learning control, this paper investigates how learning from demonstration can be applied in the context of reinforcement learning. We consider priming the Q-function, the value function, the policy, and the model of the task dynamics as possible areas where demonstrations can speed up learning. In general nonlinear learning problems, only model-based reinforcement learning shows significant speedup after a demonstration, while in the special case of linear quadratic regulator (LQR) problems, all methods profit from the demonstration. In an implementation of pole balancing on a complex anthropomorphic robot arm, we demonstrate that, when facing the complexities of real signal processing, model-based reinforcement learning offers the most robustness for LQR problems. Using the suggested methods, the robot learns pole balancing in just a single trial after a 30 second long demonstration of the human instructor.

A new reinforcement learning architecture for nonlinear control is proposed. A direct feedback controller, or the actor, is trained by a value-gradient based controller, or the tutor. This architecture enables both efficient use of the value function and simple computation for real-time implementation. Good performance was verified in multidimensional nonlinear control tasks using Gaussian softmax networks.

High frequency foreign exchange data can be decomposed into three components: the inventory effect component, the surprise infonnation (news) component and the regular infonnation component. The presence of the inventory effect and news can make analysis of trends due to the diffusion of infonnation (regular information component) difficult. We propose a neural-net-based, independent component analysis to separate high frequency foreign exchange data into these three components. Our empirical results show that our proposed multi-effect decomposition can reveal the intrinsic price behavior.

We present a mixture of experts (ME) approach to interpolate sparse, spatially correlated earth-science data. Kriging is an interpolation method which uses a global covariation model estimated from the data to take account of the spatial dependence in the data. Based on the close relationship between kriging and the radial basis function (RBF) network (Wan & Bone, 1996), we use a mixture of generalized RBF networks to partition the input space into statistically correlated regions and learn the local covariation model of the data in each region. Applying the ME approach to simulated and real-world data, we show that it is able to achieve good partitioning of the input space, learn the local covariation models and improve generalization.

This paper describes how the early visual process of contour organisation can be realised using the EM algorithm. The underlying computational representation is based on fine spline coverings. According to our EM approach the adjustment of spline parameters draws on an iterative weighted least-squares fitting process. The expectation step of our EM procedure computes the likelihood of the data using a mixture model defined over the set of spline coverings. These splines are limited in their spatial extent using Gaussian windowing functions.