Showing papers by "Michael I. Jordan published in 1993"

Hierarchical mixtures of experts and the EM algorithm

Abstract: We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIMs). Learning is treated as a maximum likelihood problem; in particular, we present an expectation-maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an online learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain.

Convergence of Stochastic Iterative Dynamic Programming Algorithms

Abstract: Recent developments in the area of reinforcement learning have yielded a number of new algorithms for the prediction and control of Markovian environments. These algorithms, including the TD(λ) algorithm of Sutton (1988) and the Q-learning algorithm of Watkins (1989), can be motivated heuristically as approximations to dynamic programming (DP). In this paper we provide a rigorous proof of convergence of these DP-based learning algorithms by relating them to the powerful techniques of stochastic approximation theory via a new convergence theorem. The theorem establishes a general class of convergent algorithms to which both TD(λ) and Q-learning belong.

Supervised learning from incomplete data via an EM approach

Abstract: Real-world learning tasks may involve high-dimensional data sets with arbitrary patterns of missing data. In this paper we present a framework based on maximum likelihood density estimation for learning from such data set.s. We use mixture models for the density estimates and make two distinct appeals to the Expectation-Maximization (EM) principle (Dempster et al., 1977) in deriving a learning algorithm--EM is used both for the estimation of mixture components and for coping with missing data. The resulting algorithm is applicable to a wide range of supervised as well as unsupervised learning problems. Results from a classification benchmark--the iris data set--are presented.

Learning piecewise control strategies in a modular neural network architecture

Abstract: The authors describe a multinetwork, or modular, neural network architecture that learns to perform control tasks using a piecewise control strategy. The architecture's networks compete to learn the training patterns. As a result, a plant's parameter space is adaptively partitioned into a number of regions, and a different network learns a control law in each region. This learning process is described in a probabilistic framework and learning algorithms that perform gradient ascent in a log-likelihood function are discussed. Simulations show that the modular architecture's performance is superior to that of a single network on a multipayload robot motion control task. >

Trading relations between tongue-body raising and lip rounding in production of the vowel /u/: a pilot "motor equivalence" study.

Abstract: Articulatory and acoustic data were used to explore the following hypothesis for the vowel /u/: The objective of articulatory movements is an acoustic goal; varying and reciprocal contributions of different articulators may help to constrain acoustic variation in achieving the goal. Previous articulatory studies of similar hypotheses, expressed entirely in articulatory terms, have been confounded by interdependencies of the variables being studied (e.g., lip and mandible displacements). One case in which this problem may be minimized is that of lip rounding and tongue-body raising (formation of a velo-palatal constriction) for the vowel /u/. Lip rounding and tongue-body raising should have similar acoustic effects for /u/, mainly to lower F2. In multiple repetitions, reciprocal contributions of lip rounding and tongue-body raising could help limit F2 variability for /u/; thus this experiment looked for complementary covariation (negative correlations) in measures of these two parameters. An electro-magnetic midsagittal articulometer (EMMA) was used to track movements of midsagittal points on the tongue body, upper and lower lips, and mandible for large numbers of repetitions of utterances containing /u/. (Interpretation of the data was aided by results from area-function-to-formant modeling.) Three of four subjects showed weak negative correlations, tentatively supporting the hypothesis; a fourth showed the opposite pattern: positive correlations of lip rounding and tongue raising. The results are discussed with respect to ideas about motor equivalence, the nature of speech motor programming, and potential improvements to the paradigm.

The Cascade Neural Network Model and a Speed-Accuracy Trade-Off of Arm Movement.

Abstract: We propose a hybrid neural network model of aimed arm movements that consists of a feedforward controller and a postural controller. The cascade neural network of Kawato, Maeda, Uno, and Suzuki (1990) was employed as a computational implementation of the feedforward controller. This network computes feedforward motor commands based on a minimum torque-change criterion. If the weighting parameter of the smoothness criterion is fixed and the number of relaxation iterations is rather small, the cascade model cannot calculate the exact torque, and the hand does not reach the desired target by using the feedforward control alone. Thus, one observes an error between the final position and the desired target location. By using a fixed weighting parameter value and a limited iteration number to simulate target-directed arm movements, we found that the cascade model generated a planning time–accuracy trade-off, and a quasi–power-law type of speed–accuracy trade-off. The model provides a candidate neural m...

Task Decompostiion Through Competition in a Modular Connectionist Architecture: The What and Where Vision Tasks

Abstract: A novel modular connectionist architecture is presented in which the networks composing the architecture compete to learn the training potterns. An outcome of the competition is that different networks learn different training patterns and, thus, learn to compute different functions. The architecture performs task decomposition in the sense that it learns to partition a task into two or more functionally independent tasks and allocates distinct networks to learn each task. In addition, the architecture tends to allocate to each task the network whose topology is most appropriate to that task. The architecture’s performance on “what” and “where” vision tasks is presented and compared with the performcmce of two multilayer networks. Finally, it is noted that function decomposition is an underconstrained problem, and, thus, different modular architectures may decompose a function in different ways. A desirable decomposition con be achieved if the architecture is suitably restricted in the types of functions that it can compute. Finding appropriate restrictions is possible through the application of domain knowledge. A strength of the modular architecture is that its structure is well suited for incorporating domain knowledge.

Supervised learning and divide-and-conquer: a statistical approach

Abstract: We present a novel statistical model for supervised learning. The model is based on the principle of divide-and-conquer, and is similar in spirit to models such as CART, ID3 and MARS. We formulate the problem of learning the parameters of the model as a maximum likelihood estimation problem and develop an Expectation-Maximization (EM) algorithm for the model. Comparative simulation results are presented in the robot dynamics domain.

Constraints on underspecified target trajectories

Abstract: Much of the recent interest in artificial neural networks is founded on the development of supervised learning algorithms for nonlinear problems [1, 30, 39, 42, 47]. These algorithms, the most well-known being backpropagation, are able to model a large class of nonlinear transformations by assigning credit to internal “hidden” units. The remaining units—those connected directly to the environment—are generally assumed to be provided with target states. This assumption appears to be a liability; it is by no means clear that such desired outputs can always be provided. Consider, for example, a network serving as a feedforward controller for a robot. Such a network must produce torques as a function of the environmental goal and the current state of the robot. In general, however, the environment provides only the goal and not the torques that achieve the goal. Furthermore, if we assume the existence of an oracle that provides the torques as training data, then there appears to be little reason (other than perhaps speed) not to use the oracle as the controller in place of the network.

Myths of the World : A Thematic Encyclopedia

Abstract: Divided into mythological themes, rather than in A-Z format, this reference book relates each myth to its culture and period of origin, and has detailed cross-referencing and indexing. It is intended to appeal to the serious student and general reader alike, whether they are seeking information on a particular mythological concept, or on a culture, or on an individual character. Michael Jordan is the author of "Gods of the Earth" and "Encyclopedia of Gods".