Thesis (Th. M.)--Westminster Theological Seminary, Philadelphia, 1987. / Includes bibliographical references (leaves 122-127).

We present a set of techniques that can be used to represent anddetect shapes in images. Our methods revolve around a particularshape representation based on the description of objects usingtriangulated polygons. This representation is similar to the medialaxis transform and has important properties from a computationalperspective. The first problem we consider is the detection ofnon-rigid objects in images using deformable models. We present anefficient algorithm to solve this problem in a wide range ofsituations, and show examples in both natural and medical images. Wealso consider the problem of learning an accurate non-rigid shapemodel for a class of objects from examples. We show how to learn goodmodels while constraining them to the form required by the detectionalgorithm. Finally, we consider the problem of low-level imagesegmentation and grouping. We describe a stochastic grammar thatgenerates arbitrary triangulated polygons while capturing Gestaltprinciples of shape regularity. This grammar is used as a prior modelover random shapes in a low level algorithm that detects objects inimages.

To engineer complex synthetic biological systems will require modulardesign, assembly, and characterization strategies. The RNApolymerase arrival rate (PAR) is defined to be the rate that RNApolymerases arrive at a specified location on the DNA. Designing andcharacterizing biological modules in terms of RNA polymerase arrivalrates provides for many advantages in the construction and modeling ofbiological systems.PARMESAN is an in vitro method for measuring polymerase arrival ratesusing pyrrolo-dC, a fluorescent DNA base that can substitute forcytosine. Pyrrolo-dC shows a detectable fluorescence difference whenin single-stranded versus double-stranded DNA. During transcription,RNA polymerase separates the two strands of DNA, leading to a changein the fluorescence of pyrrolo-dC. By incorporating pyrrolo-dC atspecific locations in the DNA, fluorescence changes can be taken as adirect measurement of the polymerase arrival rate.

Array technologies have made it possible to record simultaneouslythe expression pattern of thousands of genes. A fundamental problemin the analysis of gene expression data is the identification ofhighly relevant genes that either discriminate between phenotypiclabels or are important with respect to the cellular process studied inthe experiment: for example cell cycle or heat shock in yeast experiments,chemical or genetic perturbations of mammalian cell lines,and genes involved in class discovery for human tumors. In this paperwe focus on the task of unsupervised gene selection. The problemof selecting a small subset of genes is particularly challengingas the datasets involved are typically characterized by a very smallsample size — in the order of few tens of tissue samples — andby a very large feature space as the number of genes tend to bein the high thousands. We propose a model independent approachwhich scores candidate gene selections using spectral properties ofthe candidate affinity matrix. The algorithm is very straightforwardto implement yet contains a number of remarkable properties whichguarantee consistent sparse selections. To illustrate the value of ourapproach we applied our algorithm on five different datasets. Thefirst consists of time course data from four well studied Hematopoieticcell lines (HL-60, Jurkat, NB4, and U937). The other fourdatasets include three well studied treatment outcomes (large celllymphoma, childhood medulloblastomas, breast tumors) and oneunpublished dataset (lymph status). We compared our approachboth with other unsupervised methods (SOM,PCA,GS) and withsupervised methods (SNR,RMB,RFE). The results clearly showthat our approach considerably outperforms all the other unsupervisedapproaches in our study, is competitive with supervised methodsand in some case even outperforms supervised approaches.

Among the various methods to combine classifiers, Boosting was originally thought as an stratagem to cascade pairs of classifiers through their disagreement. I recover the same idea from the work of Niyogi et al. to show how to loosen the requirement of weak learnability, central to Boosting, and introduce a new cascading stratagem. The paper concludes with an empirical study of an implementation of the cascade that, under assumptions that mirror the conditions imposed by Viola and Jones in [VJ01], has the property to preserve the generalization ability of boosting.

We give a one-pass, O~(m^{1-2/k})-space algorithm for estimating the k-th frequency moment of a data stream for any real k>2. Together with known lower bounds, this resolves the main problem left open by Alon, Matias, Szegedy, STOC'96. Our algorithm enables deletions as well as insertions of stream elements.

One of the reasons that it is difficult to plan and act in real-worlddomains is that they are very large. Existing research generallydeals with the large domain size using a static representation andexploiting a single type of domain structure. In this paper, wecreate a framework that encapsulates existing and new abstraction andapproximation methods into modules, and combines arbitrary modulesinto a system that allows for dynamic representation changes. We showthat the dynamic changes of representation allow our framework tosolve larger and more interesting domains than were previouslypossible, and while there are no optimality guarantees, suitablemodule choices gain tractability at little cost to optimality.

The zebra finch is a standard experimental system for studying learning and generation of temporally extended motor patterns. The first part of this project concerned the evaluation of simple models for the operation and structure of the network in the motor nucleus RA. A directed excitatory chain with a global inhibitory network, for which experimental evidence exists, was found to produce waves of activity similar to those observed in RA; this similarity included one particularly important feature of the measured activity, synchrony between the onset of bursting in one neuron and the offset of bursting in another. Other models, which were simpler and more analytically tractable, were also able to exhibit this feature, but not for parameter values quantitatively close to those observed.Another issue of interest concerns how these networks are initially learned by the bird during song acquisition. The second part of the project concerned the analysis of exemplars of REINFORCE algorithms, a general class of algorithms for reinforcement learning in neural networks, which are on several counts more biologically plausible than standard prescriptions such as backpropagation. The former compared favorably with backpropagation on tasks involving single input-output pairs, though a noise analysis suggested it should not perform so well. On tasks involving trajectory learning, REINFORCE algorithms meet with some success, though the analysis that predicts their success on input-output-pair tasks fails to explain it for trajectories.

In this paper, we present and analyze a novel regularization technique based on enhancing our dataset with corrupted copies of the original data. The motivation is that since the learning algorithm lacks information about which parts of thedata are reliable, it has to produce more robust classification functions. We then demonstrate how this regularization leads to redundancy in the resulting classifiers, which is somewhat in contrast to the common interpretations of the Occam’s razor principle. Using this framework, we propose a simple addition to the gentle boosting algorithm which enables it to work with only a few examples. We test this new algorithm on a variety of datasets and show convincing results.

Matrices that can be factored into a product of two simpler matricescan serve as a useful and often natural model in the analysis oftabulated or high-dimensional data. Models based on matrixfactorization (Factor Analysis, PCA) have been extensively used instatistical analysis and machine learning for over a century, withmany new formulations and models suggested in recent years (LatentSemantic Indexing, Aspect Models, Probabilistic PCA, Exponential PCA,Non-Negative Matrix Factorization and others). In this thesis weaddress several issues related to learning with matrix factorizations:we study the asymptotic behavior and generalization ability ofexisting methods, suggest new optimization methods, and present anovel maximum-margin high-dimensional matrix factorizationformulation.