The softassign quadratic assignment algorithm has recently emerged as an effective strategy for a variety of optimization problems in pattern recognition and combinatorial optimization. While the effectiveness of the algorithm was demonstrated in thousands of simulations, there was no known proof of convergence. Here, we provide a proof of convergence for the most general form of the algorithm.

In this paper we propose a model for the lateral connectivity of orientation-selective cells in the visual cortex based on informationtheoretic considerations. We study the properties of the input signal to the visual cortex and find new statistical structures which have not been processed in the retino-geniculate pathway. Applying the idea that the system optimizes the representation of incoming signals, we derive the lateral connectivity that will achieve this for a set of local orientation-selective patches, as well as the complete spatial structure of a layer of such patches. We compare the results with various physiological measurements.

We seek to analyze and manipulate two factors, which we call style and content, underlying a set of observations. We fit training data with bilinear models which explicitly represent the two-factor structure. These models can adapt easily during testing to new styles or content, allowing us to solve three general tasks: extrapolation of a new style to unobserved content; classification of content observed in a new style; and translation of new content observed in a new style.

To obtain classification systems with both good generalization performance and efficiency in space and time, we propose a learning method based on combinations of weak classifiers, where weak classifiers are linear classifiers (perceptrons) which can do a little better than making random guesses. A randomized algorithm is proposed to find the weak classifiers. They· are then combined through a majority vote. As demonstrated through systematic experiments, the method developed is able to obtain combinations of weak classifiers with good generalization performance and a fast training time on a variety of test problems and real applications.

We propose a novel approach to automatically growing and pruning Hierarchical Mixtures of Experts. The constructive algorithm proposed here enables large hierarchies consisting of several hundred experts to be trained effectively. We show that HME's trained by our automatic growing procedure yield better generalization performance than traditional static and balanced hierarchies. Evaluation of the algorithm is performed (1) on vowel classification and (2) within a hybrid version of the JANUS r9] speech recognition system using a subset of the Switchboard large-vocabulary speaker-independent continuous speech recognition database.

The power of sampling methods in Bayesian reconstruction of noisy signals is well known. The extension of sampling to temporal problems is discussed. Efficacy of sampling over time is demonstrated with visual tracking.

Further im- 528 F. Leisch and K. Hornik provements should be possible based on a better understanding of the theoretical properties of resample and combine techniques. These issues are currently being investigated.

We study the effect of noise and regularization in an online gradient-descent learning scenario for a general two-layer student network with an arbitrary number of hidden units. Training examples are randomly drawn input vectors labeled by a two-layer teacher network with an arbitrary number of hidden units; the examples are corrupted by Gaussian noise affecting either the output or the model itself. We examine the effect of both types of noise and that of weight-decay regularization on the dynamical evolution of the order parameters and the generalization error in various phases of the learning process.

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.

Probability models can be used to predict outcomes and compensate for missing data, but even a perfect model cannot be used to make decisions unless the utility of the outcomes, or preferences between them, are also provided. This arises in many real-world problems, such as medical diagnosis, where the cost of the test as well as the expected improvement in the outcome must be considered. Relatively little work has been done on learning the utilities of outcomes for optimal decision making. In this paper, we show how temporal-difference reinforcement learning (TO(A» can be used to determine decision theoretic utilities within the context of a mixture model and apply this new approach to a problem in medical diagnosis. TO(A) learning of utilities reduces the number of tests that have to be done to achieve the same level of performance compared with the probability model alone, which results in significant cost savings and increased efficiency.