Hierarchical Mixtures of Experts and the EM Algorithm

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 (GLIM's). 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 on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain.

Formal Multilevel Hierarchical Verification of Synchronous MOS Circuits

I have designed and implemented a system for the multilevel verification of synchronous MOS VLSI circuits. The system, called Silica Pithecus, accepts the schematic of an MOS circuit and a specification of the circuit's intended digital behavior. Silica Pithecus determines if the circuit meets its specification. If the circuit fails to meet its specification Silica Pithecus returns to the designer the reason for the failure. Unlike earlier verifiers which modelled primitives (e.g., transistors) as unidirectional digital devices, Silica Pithecus models primitives more realistically. Transistors are modelled as bidirectional devices of varying resistances, and nodes are modelled as capacitors. Silica Pithecus operates hierarchically, interactively, and incrementally. Major contributions of this research include a formal understanding of the relationship between different behavioral descriptions (e.g., signal, boolean, and arithmetic descriptions) of the same device, and a formalization of the relationship between the structure, behavior, and context of device. Given these formal structures my methods find sufficient conditions on the inputs of circuits which guarantee the correct operation of the circuit in the desired descriptive domain. These methods are algorithmic and complete. They also handle complex phenomena such as races and charge sharing. Informal notions such as races and hazards are shown to be derivable from the correctness conditions used by my methods.

Model-Based Matching by Linear Combinations of Prototypes

We describe a method for modeling object classes (such as faces) using 2D example images and an algorithm for matching a model to a novel image. The object class models are "learned'' from example images that we call prototypes. In addition to the images, the pixelwise correspondences between a reference prototype and each of the other prototypes must also be provided. Thus a model consists of a linear combination of prototypical shapes and textures. A stochastic gradient descent algorithm is used to match a model to a novel image by minimizing the error between the model and the novel image. Example models are shown as well as example matches to novel images. The robustness of the matching algorithm is also evaluated. The technique can be used for a number of applications including the computation of correspondence between novel images of a certain known class, object recognition, image synthesis and image compression.

Model-Based Matching of Line Drawings by Linear Combinations of Prototypes

We describe a technique for finding pixelwise correspondences between two images by using models of objects of the same class to guide the search. The object models are 'learned' from example images (also called prototypes) of an object class. The models consist of a linear combination ofsprototypes. The flow fields giving pixelwise correspondences between a base prototype and each of the other prototypes must be given. A novel image of an object of the same class is matched to a model by minimizing an error between the novel image and the current guess for the closest modelsimage. Currently, the algorithm applies to line drawings of objects. An extension to real grey level images is discussed.