Richard A. Olshen - US grants

The research proposed involves five different topics (i) the extension of tree-structured, recursive partitioning methods to the analysis of censored survival data from clinical trials or laboratory experiments; (ii) aggregated Markov models (in neurophysiology) that are crucial to the understanding of the acetylcholine receptor; (iii) the application of multivariate methods to the understanding of ocular micro-circulation and the early diagnosis of diabetes; (iv) binary regression with errors in variables and its use in evaluating burn care facilities; (v) estimation in pharmacokinetic models which arise in high dose intracavitary chemotherapy as it is administered at the UC San Diego Cancer Center.

The research we propose is all connected with extremely computer intensive statistics applied to cancer research, other medical problems and physiology. Olshen proposes studying problems in tree-structured methods and sample reuse techniques. In particular, he proposes study and implementation of a technique for producing unbiased estimates within the terminal nodes of a classification tree, and study of stratification and redesign of sample reuse methods. Investigations of asymptotic results on tree-structured methods that incorporate adaptiveness of splitting rules and rates of convergence for the algorithms are also proposed. Fredkin and Rice propose development of methodology for restoration of noisy single channel patch clamp data. A variety of issues arise in this regard: proper handling of filtering via deconvolution, data-based smoothing parameter estimates, extension of algorithms and computer code to handle multi conductance level channels, and special methods for dealing with flickering. Special attention will be given to the development of efficient computer code. Abramson proposes further study of a recursive technique for use in conditional analysis of models in which there are a large number of effects (for example, baseline measurements) that are not of primary interest and a small number of fixed effects that are. He proposes development of polished software for general distribution.

The research we propose is all connected with extremely computer intensive statistics applied to cancer research, other medical problems and physiology. Olshen proposes studying problems in tree-structured methods and sample reuse techniques. In particular, he proposes study and implementation of a technique for producing unbiased estimates within the terminal nodes of a classification tree, and study of stratification and redesign of sample reuse methods. Investigations of asymptotic results on tree-structured methods that incorporate adaptiveness of splitting rules and rates of convergence for the algorithms are also proposed. Fredkin and Rice propose development of methodology for restoration of noisy single channel patch clamp data. A variety of issues arise in this regard: proper handling of filtering via deconvolution, data-based smoothing parameter estimates, extension of algorithms and computer code to handle multi conductance level channels, and special methods for dealing with flickering. Special attention will be given to the development of efficient computer code. Abramson proposes further study of a recursive technique for use in conditional analysis of models in which there are a large number of effects (for example, baseline measurements) that are not of primary interest and a small number of fixed effects that are. He proposes development of polished software for general distribution.

Research will be conducted on variable rate tree-structured vector quantizers for image compression applications. The emphasis will be on tree-structured codes designed using extensions and variations of the tree design techniques of Breiman, Friedman, Olshen and Stone, but a variety of other vector quantization structures will be considered in combination with the tree- structured codes. In particular, both finite state and predictive vector quantizers will be considered for incorporating memory in the coding and two-dimensional subsampling techniques will be considered as a means of increasing effective vector size, improving prediction accuracy and providing a natural data structure. The dual use of trees for classification and compression in finite-state vector quantizers will be explored, as will be the combination of compression of image sequences such as video and multimodal images of a common object or view, as in multispectral and color imaging. Experiments will be conducted with medical images, computer image data consisting of mixed video, imagery, and graphics, and satellite imagery, especially multispectral.

The Principal Investigator will study statistical methods. These involve the optimal choices of sequences of binary questions for problems of classification, probability class estimation, regression, and survival analysis. Much of the computer- intensive research that is planned involves new capabilities and significant improvements of the algorithms and techniques given by Breiman, Friedman, Olshen, and Stone in Classification and Regression Trees and its associated CART software. Some computations will be done in an innovative distributed mode on a system of workstations. The investigators plan applications to test data sets, particularly a large data set concerning the quick diagnosis of heart attack. Details are given for an application to the enhancement of certain magnetic resonance images that are important to making prognoses for patients with lymphoma. (Support is not requested for the conduct of clinical trials; indeed, the data do not arise from conventional clinical trials.) The statistics research involved is of importance to a wide variety of applications, some of them medical.

Gray Tree-structured vector quantization is an approach to image compression that applies ideas from statistical clustering algorithms and tree-structured classification and regression algorithms to produce compression codes that trade off bit rate and average distortion in a near optimal fashion. This research is examining the explicit combination of these two forms of signal processing, compression and classification, into single tree-structured algorithms that permit a trade off between traditional distortion measures, such as squared error, with measures of classification accuracy such as Bayes risk. The intent is to produce codes with implicit classification information, that is, for which the stored or communicated compressed image incorporates classification information without further signal processing. Such systems can provide direct low level classification or provide an efficient front end to more sophisticated full-frame recognition algorithms. Vector quanitization algorithms for relatively large block sizes are also being developed with an emphasis on multiresolution compression algorithms. In order to improve the promising performance found in preliminary studies or combined compression and classification, it will be necessary to use larger block sizes or, equivalently, more context. Multiresolution or hierarchial quantizers provide a simple and effective means of accomplishing this. Other related issues are being explored, including improved prediction methods for predictive vector quantization and image sequence coding.

Data compression aims at producing an efficient representation for storage or transmission in order to communicate or store the smallest possible number of bits while retaining high quality in the reconstructed image. Statistical classification and segmentation are both concerned with labeling parts of an image as being of a certain type or class, such as tumor or normal tissue in a medical image or text, graphics, or photographs in a document page. Classification and segmentation can be used to assist human users of images, as in highlighting suspicious tissue in a medical image or defects in an imaged circuit, or they can be used for the automatic extraction of features in intelligent browsing of large databases. All three operations have in common the goal of efficiently representing an image as a whole, by optimally trading off quality and cost or distortion, an din decomposing the image into useful components. Most of the systems involving these operations, however, focus on each separate operation rather than on combining them into common algorithms with multiple goals. This project is devoted to the development of theory and algorithms for jointly performing these operations and related signal processing such as the estimation of probability distributions or models from observed data. The approach involves optimizing single combined systems subject to possibly conflicting combined goals, such as maximizing signal-to-noise ratios and minimizing bit rates and Bayes risk. Theory will be reinforced by simulations for both artificial sources, where theoretical performance bounds can be used for comparison, and real-world examples drawn from medical and document applications.

The research is concerned with techniques from statistical signal processing and information theory as they apply to communication systems with multiple goals. Such systems arise in multimedia communications networks like the Internet. The decomposition of data streams into different types is critical to finding information desired by a user among vast available sources, and it can also provide methods for displaying, rendering, printing, or playing the received signal that take advantage of its particular structure. Signal processing and coding theory have provided powerful mathematical models of information sources and algorithms by which these sources can be communicated and processed. Typically systems are designed as a collection of separate, unrelated, components. This can result in much less than optimal overall performance. Furthermore, it can hamper theoretical understanding of the fundamental limits on achievable performance.We treat the simultaneous design of mathematical models that account at once for information sources, data compression, and signal processing and apply to extracting information from the received data. Our emphasis is on image communication and processing. Because, the techniques draw heavily from demonstrably successful methods in speech coding and recognition they are natural for both signal types, individually or together.


The research involves a unified approach to data compression, statistical classification and regression, and density estimation. It is based on a novel combination of vector quantization, Gauss mixture models, measures of minimum discrimination information (relative entropy), and universal coding. Vector quantization provides both a theoretical framework and a method for implementation. Gauss mixture models are a flexible class by which to describe information sources. They can be fit to real data by clustering with respect to a minimum discrimination information measure of distortion. A primary objective is the development and application of conditional versions of rate-distortion extremal properties of Gaussian models in order to design robust algorithms for compression, classification, modeling, and combinations thereof. There are many open questions about relations among modeling, compression, and classification/regression. Our goal is to provide answers to as many of them as possible and in so doing to contribute to understanding the interplay of modeling, signal processing, and coding. We describe optimized and implementable robust codes for compression and classification for a variety of information sources, especially for multimodal imagery. Part of our efforts are devoted to purely mathematical aspects of tree-structured regression, which is related to martingale theory and to the differentiation of integrals.

Abstract
0309701
Robert M. Gray
Stanford University

The research is about the theory and design of systems for communicating and interpreting information bearing signals such as images, video, and speech. The main focus is on methods for reducing the complexity of signals while retaining or extracting essential information. The algorithms typically quantize or compress the data efficiently into a simpler signal that can be transmitted or stored efficiently and then used in place of the original. They can facilitate identification of the data as belonging to some class or type. Examples of such signal processing include analog-to-digital conversion, speech and image coding, speech recognition, and segmenting images into distinct regions of interest. The research involves the fundamental theory of such systems and draws on ideas from information theory, statistical signal processing, and statistics. It also involves applications, especially algorithms for classifying and segmenting images and for content-addressable browsing through image databases.
The basic tools come from modeling, density estimation, compression, coding, classification, and segmentation. They enable both theoretical characterizations of optimal performance and associated algorithms by which codes are optimized for specific applications, for example, systems for compression and segmentation of images for communications, analysis, and retrieval. Tools are drawn from four fundamental ideas of information theory and signal processing: vector quantization, mixture models, relative entropy (Kullback-Leibler information) measures of distortion or distance between probability distributions, and universal coding. Of particular interest is the theory of high rate vector quantization and its applications to statistical image classification and segmentation. Specific applications of interest include automatic
segmentation of multimodal images and of categorizing images taken internally in gas pipelines in order to quantify pipeline integrity.

The Biostatistics Core of this project will be led by Professor Richard Olshen, who will be joined in supportive efforts by Professors Bradley Efron and Lu Tian. There will be high level statistical consulting on all projects and all investigators of SHIMR by these investigators. All data made available to these individuals will be anonymized compliant with HIPPA rules. Open source computer programs written in the popular R language http://www.r-project.org/ will be made available to SHIMR investigators. Stanford's Data Coordinating Center (DCC) is the umbrella organization that will supervise writing these open source computer programs. In most instances the programs will call existing routines, available for downloading from CRAN http://cran.r proiect.org/, though occasionally we will create the ingredient routines ourselves.

DESCRIPTION (provided by applicant): This proposal outlines a new pre-doctoral training program in biostatistics that emphasizes applications to genomics and personalized medicine. Primary faculty members are from the Departments of Health Research & Policy and Statistics at Stanford University. A group of affiliate faculty from biochemistry, genetics, cardiology and other areas provide the necessary breadth for interdisciplinary research. The trainees in the program pursue a PhD in the Department of Statistics, with a concentration in Biostatistics; this option currently not available at Stanford. In addition to fulfilling the requirements of the PhD i Statistics, the proposed program will include additional course work in biomedical sciences, mentored research experienced in a collaborative setting, and training in the responsible conduct of research.