The purpose of the Institute of Mathematical Statistics (IMS) is to foster the development and dissemination of the theory and applications of statistics and probability. The Institute was formed at a meeting of interested persons on September 12, 1935, in Ann Arbor, Michigan, as a consequence of the feeling that the theory of statistics would be advanced by the formation of an organization of those persons especially interested in the mathematical aspects of the subject. The Annals of Statistics and The Annals of Probability (which supersede The Annals of Mathematical Statistics), Statistical Science, and The Annals of Applied Probability are the scientific journals of the Institute. These and The IMS Bulletin comprise the official journals of the Institute. The Institute has individual membership and organizational membership.

The field of AI is directed at the fundamental problem of how the mind works; its approach, among other things, is to try to simulate its working -- in bits and pieces. History shows us that mankind has been trying to do this for certainly hundreds of years, but the blooming of current computer technology has sparked an explosion in the research we can now do. The center of AI is the wonderful capacity we call learning, which the field is paying increasing attention to. Learning is difficult and easy, complicated and simple, and most research doesn't look at many aspects of its complexity. However, we in the AI field are starting. Let us now celebrate the efforts of our forebears and rejoice in our own efforts, so that our successors can thrive in their research. This article is the substance, edited and adapted, of the keynote address given at the 1992 annual meeting of the Association for the Advancement of Artificial Intelligence on 14 July in San Jose, California. AI Magazine 14(2): 36-48.

Touretzky (1984) proposed a formalism for nonmonotonic multiple inheritance reasoning which is sound in the presence of ambiguities and redundant links. We show that Touretzky's inheritance notion is NPhard, and thus, provided P#NP, computationally intractable. This result holds even when one only considers unambiguous, totally acyclic inheritance networks. A direct consequence of this result is that the conditioning strategy proposed by Touretzky to allow for fast parallel inference is also intractable. Therefore, it follows that nonmonotonic multiple inheritance hierarchies, although compact representations, may not allow for efficient retrieval of information as has been suggested in attempts to use such hierarchies, e.g., in NETL (Fahlman 1979). We also analyze the influence of various design choices made by Touretzky. We show that all versions of downward (coupled) inheritance, i.e., on-path or off-path preemption and skeptical or credulous reasoning, are intractable. However, tractability can be achieved when using upward (decoupled) inheritance.

Animal locomotion patterns are controlled by recurrent neural networks called central pattern generators (CPGs). Although a CPG can oscillate autonomously, its rhythm and phase must be well coordinated with the state of the physical system using sensory inputs. In this paper we propose a learning algorithm for synchronizing neural and physical oscillators with specific phase relationships. Sensory input connections are modified by the and input signals. Simulations showcorrelation between cellular activities that the learning rule can be used for setting sensory feedback connections to a CPG as well as coupling connections between CPGs. 1 CENTRAL AND SENSORY MECHANISMS IN LOCOMOTION CONTROL Patterns of animal locomotion, such as walking, swimming, and fiying, are generated by recurrent neural networks that are located in segmental ganglia of invertebrates and spinal cords of vertebrates (Barnes and Gladden, 1985).

Do you want your neural net algorithm to learn sequences? Do not limit yourself to conventional gradient descent (or approximations thereof). Instead, use your sequence learning algorithm (any will do) to implement the following method for history compression. No matter what your final goals are, train a network to predict its next input from the previous ones. Since only unpredictable inputs convey new information, ignore all predictable inputs but let all unexpected inputs (plus information about the time step at which they occurred) become inputs to a higher-level network of the same kind (working on a slower, self-adjusting time scale). Go on building a hierarchy of such networks.

"Best-first model merging" is a general technique for dynamically choosing the structure of a neural or related architecture while avoiding overfitting. It is applicable to both leaming and recognition tasks and often generalizes significantly better than fixed structures. We demonstrate the approach applied to the tasks of choosing radial basis functions for function learning, choosing local affine models for curve and constraint surface modelling, and choosing the structure of a balltree or bumptree to maximize efficiency of access.

During waking and sleep, the brain and mind undergo a tightly linked and precisely specified set of changes in state. At the level of neurons, this process has been modeled by variations of Volterra-Lotka equations for cyclic fluctuations of brainstem cell populations. However, neural network models based upon rapidly developing knowledge ofthe specific population connectivities and their differential responses to drugs have not yet been developed. Furthermore, only the most preliminary attempts have been made to model across states. Some of our own attempts to link rapid eye movement (REM) sleep neurophysiology and dream cognition using neural network approaches are summarized in this paper.

It is shown that both changes in viewing position and illumination conditions can be compensated for, prior to recognition, using combinations of images taken from different viewing positions and different illumination conditions. It is also shown that, in agreement with psychophysical findings, the computation requires at least a sign-bit image as input - contours alone are not sufficient. 1 Introduction The task of visual recognition is natural and effortless for biological systems, yet the problem of recognition has been proven to be very difficult to analyze from a computational point of view. The fundamental reason is that novel images of familiar objects are often not sufficiently similar to previously seen images of that object. Assuming a rigid and isolated object in the scene, there are two major sources for this variability: geometric and photometric. The geometric source of variability comes from changes of view position. A 3D object can be viewed from a variety of directions, each resulting with a different 2D projection. The difference is significant, even for modest changes in viewing positions, and can be demonstrated by superimposing those projections (see Figure 1, first row second image). Much attention has been given to this problem in the visual recognition literature ([9], and references therein), and recent results show that one can compensate for changes in viewing position by generating novel views from a small number of model views of the object [10, 4, 8].

Three methods for improving the performance of (gaussian) radial basis function (RBF) networks were tested on the NETtaik task. In RBF, a new example is classified by computing its Euclidean distance to a set of centers chosen by unsupervised methods. The application of supervised learning to learn a non-Euclidean distance metric was found to reduce the error rate of RBF networks, while supervised learning of each center's variance resulted in inferior performance. The best improvement in accuracy was achieved by networks called generalized radial basis function (GRBF) networks. In GRBF, the center locations are determined by supervised learning. After training on 1000 words, RBF classifies 56.5% of letters correct, while GRBF scores 73.4% letters correct (on a separate test set). From these and other experiments, we conclude that supervised learning of center locations can be very important for radial basis function learning.

Connections between spline approximation, approximation with rational functions, and feedforward neural networks are studied. The potential improvement in the degree of approximation in going from single to two hidden layer networks is examined. Some results of Birman and Solomjak regarding the degree of approximation achievable when knot positions are chosen on the basis of the probability distribution of examples rather than the function values are extended.