Volker Tresp*and Michiaki Taniguchi Siemens AG, Central Research Otto-Hahn-Ring 6 81730 Miinchen, Germany Abstract This paper discusses the linearly weighted combination of estimators inwhich the weighting functions are dependent on the input. We show that the weighting functions can be derived either by evaluating the input dependent variance of each estimator or by estimating how likely it is that a given estimator has seen data in the region of the input space close to the input pattern. The latter solutionis closely related to the mixture of experts approach and we show how learning rules for the mixture of experts can be derived from the theory about learning with missing features. The presented approaches are modular since the weighting functions can easily be modified (no retraining) if more estimators are added. Furthermore,it is easy to incorporate estimators which were not derived from data such as expert systems or algorithms. 1 Introduction Instead of modeling the global dependency between input x E D and output y E using a single estimator, it is often very useful to decompose a complex mapping -'\.t the time of the research for this paper, a visiting researcher at the Center for Biological and Computational Learning, MIT.

The TNM staging system has been used since the early 1960's to predict breast cancer patient outcome. In an attempt to increase putative prognostic factors haveprognostic accuracy, many the TNM stage model can not accommodatebeen identified.

Perceptual learning is defined as fast improvement in performance and retention of the learned ability over a period of time. In a set of psychophysical experimentswe demonstrated that perceptual learning occurs for the discrimination of direction in stochastic motion stimuli. Here we model this learning using two approaches: a clustering model that learns to accommodate the motion noise, and an averaging model that learns to ignore the noise. Simulations of the models show performance similar to the psychophysical results. 1 Introduction Global motion perception is critical to many visual tasks: to perceive self-motion, to identify objects in motion, to determine the structure of the environment, and to make judgements for safe navigation. In the presence of noise, as in random dot kinematograms, efficient extraction of global motion involves considerable spatial integration. Newsome and Colleagues (1989) showed that neurons in the macaque middle temporal area (MT) are motion direction-selective, and perform global integration ofmotion in their large receptive fields. Psychophysical studies in humans have characterized the limits of spatial and temporal integration in motion (Watamaniuk et.aI, 1984) and the nature of the underlying motion computations (Vaina et.

Experiments were performed to reveal some of the computational properties of the human motor memory system. We show that as humans practice reaching movements while interacting with a novel mechanical environment, they learn an internal model of the inverse dynamics of that environment. The representation of the internal model in memory is such that there is interference when there is an attempt to learn a new inverse dynamics map immediately after an anticorrelated mapping was learned. We suggest that this interference is an indication that the same computational elements used to encode the first inverse dynamics map are being used to learn the second mapping. We predict that this leads to a forgetting of the initially learned skill. 1 Introduction In tasks where we use our hands to interact with a tool, our motor system develops a model of the dynamics of that tool and uses this model to control the coupled dynamics of our arm and the tool (Shadmehr and Mussa-Ivaldi 1994). In physical systems theory, the tool is a mechanical analogue of an admittance, mapping a force as input onto a change in state as output (Hogan 1985).

Each year people spend a huge amount oftime typing. The text people type typically contains a tremendous amount of redundancy due to predictable word usage patterns and the text's structure. This paper describes a neural network system call AutoTypist that monitors a person's typing and predicts what will be entered next. AutoTypist displays the most likely subsequent word to the typist, who can accept it with a single keystroke, instead of typing it in its entirety. The multi-layer perceptron at the heart of Auto'JYpist adapts its predictions of likely subsequent text to the user's word usage pattern, and to the characteristics of the text currently being typed. Increases in typing speed of 2-3% when typing English prose and 10-20% when typing C code have been demonstrated using the system, suggesting a potential time savings of more than 20 hours per user per year. In addition to increasing typing speed, AutoTypist reduces the number of keystrokes a user must type by a similar amount (2-3% for English, 10-20% for computer programs). This keystroke savings has the potential to significantly reduce the frequency and severity of repeated stress injuries caused by typing, which are the most common injury suffered in today's office environment.

In this paper, we incorporate the Hierarchical Mixtures of Experts (HME) method of probability estimation, developed by Jordan [1], into an HMMbased continuousspeech recognition system. The resulting system can be thought of as a continuous-density HMM system, but instead of using gaussian mixtures, the HME system employs a large set of hierarchically organized but relatively small neural networks to perform the probability density estimation. The hierarchical structure is reminiscent of a decision tree except for two important differences: each "expert" or neural net performs a "soft" decision rather than a hard decision, and, unlike ordinary decision trees, the parameters of all the neural nets in the HME are automatically trainable using the EM algorithm. We report results on the ARPA 5,OOO-word and 4O,OOO-word Wall Street Journal corpus using HME models. 1 Introduction Recent research has shown that a continuous-density HMM (CD-HMM) system can outperform amore constrained tied-mixture HMM system for large-vocabulary continuous speech recognition (CSR) when a large amount of training data is available [2]. In other work, the utility of decision trees has been demonstrated in classification problems by using the "divide and conquer" paradigm effectively, where a problem is divided into a hierarchical set of simpler problems. We present here a new CD-HMM system which **MIT, Cambridge MA 02139 860 YingZhao, Richard Schwartz, Jason Sroka, John Makhoul has similar properties and possesses the same advantages as decision trees, but has the additional important advantage of having automatically trainable "soft" decision boundaries. 2 Hierarchical Mixtures of Experts The method of Hierarchical Mixtures of Experts (HME) developed recently by Jordan [1] breaks a large scale task into many small ones by partitioning the input space into a nested set of regions, then building a simple but specific model (local expert) in each region.

Motivated by difficulties in analog VLSI implementation of back-propagation [Rumelhart et al., 1986] and related algorithms that calculate gradients based on detailed knowledge of the neural network model, there were several similar recent papersproposing to use a parallel [Alspector et al., 1993, Cauwenberghs, 1993, Kirk et al., 1993] or a semi-parallel [Flower and Jabri, 1993] perturbative technique which has the property that it measures (with the physical neural network) rather than calculates the gradient. This technique is closely related to methods of stochastic approximation[Kushner and Clark, 1978] which have been investigated recently by workers in fields other than neural networks.

The performance of online algorithms for learning dichotomies is studied. In online learning, thenumber of examples P is equivalent to the learning time, since each example is presented only once. The learning curve, or generalization error as a function of P, depends on the schedule at which the learning rate is lowered. For a target that is a perceptron rule, the learning curve of the perceptron algorithm can decrease as fast as p-1,if the schedule is optimized. If the target is not realizable by a perceptron, the perceptron algorithm does not generally converge to the solution with lowest generalization error.

The TNM staging system has been used since the early 1960's to predict breast cancer patient outcome. In an attempt to increase prognosticaccuracy, many putative prognostic factors have been identified. Because the TNM stage model can not accommodate thesenew factors, the proliferation of factors in breast cancer has lead to clinical confusion. What is required is a new computerized prognostic system that can test putative prognostic factors and integrate the predictive factors with the TNM variables inorder to increase prognostic accuracy. Using the area under the curve of the receiver operating characteristic, we compare the accuracy of the following predictive models in terms of five year breast cancer-specific survival: pTNM staging system, principal componentanalysis, classification and regression trees, logistic regression, cascade correlation neural network, conjugate gradient descent neural, probabilistic neural network, and backpropagation neural network. Several statistical models are significantly more ac- 1064 HarryB.

Understanding the response of neural nets to structural/functional damage is important fora variety of reasons, e.g., in assessing the performance of neural network hardware, and in gaining understanding of the mechanisms underlying neurological andpsychiatric disorders. Recently, there has been a growing interest in constructing neuralmodels to study how specific pathological neuroanatomical and neurophysiological changes can result in various clinical manifestations, and to investigate thefunctional organization of the symptoms that result from specific brain pathologies (reviewed in [1, 2]). In the area of associative memory models specifically, earlystudies found an increase in memory impairment with increasing lesion severity (in accordance with Lashley's classical'mass action' principle), and showed that slowly developing lesions have less pronounced effects than equivalent acute lesions [3]. Recently, it was shown that the gradual pattern of clinical deterioration manifested in the majority of Alzheimer's patients can be accounted for, and that different synaptic compensation rates can account for the observed variation in the severity and progression rate of this disease [4]. However, this past work is limited in that model elements have no spatial relationships to one another (all elements are conceptually equidistant).