PROFESSOR RICHARD GOLDEN

 

RESEARCH INTERESTS

 

 

 

MATHEMATICAL METHODS FOR NEURAL NETWORK ANALYSIS AND DESIGN: GOLDEN RICHARD


Overview

My specific research interests are divided into two complementary areas. First, basic research in understanding statistical machine learning algorithms.  Many important mathematical models of human and animal behavior as well as mathematical models in the field of computational neuroscience have been developed using statistical machine learning algorithms. An improved understanding of statistical machine learning algorithms then directly translates into an improved understanding of a large class of mathematical models in the Behavioral and Brain Science field. And second, the empirical application of statistical machine learning algorithms in the fields of mathematical psychology and computational neuroscience as well as other areas including: biomedical data analysis, artificial intelligence, computer science, and control theory.  These two lines of research are highly synergistic. The theoretical  statistical machine learning research component supports new solutions to mathematical modeling applications, and the applications component supports new directions in theoretical statistical machine learning research. 

 

Theoretical  Research in Statistical Machine Learning

A recent book chapter published in a Feschrift for the late Halbert L. White discusses an entirely new collection of mathematical tools for determining if a given probability model is an adequate representation of the process which generated the data (Golden et al., 2013).  Despite best intentions, however, the possibility of model misspecification (i.e., the presence of flaws in a probability model) is always present.  This observation has motivated an additional research strand which is concerned with the development of methods for robust estimation and inference in the presence of possible model misspecification in the presence of partially observable data (see Golden, 1995, for a review).  In addition, many fundamental problems in models of the brain and behavioral sciences as well as machine learning are forced to deal with the presence of  only partially observable state variables due to either unavoidable limitations of measurement methodologies and/or lack of knowledge of model structure. My recent research is concerned with the development of a unified mathematical theory for supporting robust estimation and inference in the simultaneous presence of both model misspecification and partially observable state variables. Another on-going research thread which dates back to Golden (2000, 2003) is my long-term interest in model selection criteria for determining which of two competing probability models provides a better representation of the data generating process.  For over two decades I have pursued the development of a unified probabilistic framework for interpreting learning machines (Golden, 1988a, 1988b, 1996; Rumelhart et al., 1996). My book Mathematical Methods for Neural Network Analysis and Design (1996, MIT Press)  provides a useful introduction to my research program in the area of statistical machine learning which includes work in dynamical systems theory, deterministic and stochastic nonlinear optimization theory, deterministic and stochastic control theory, Markov fields, and statistical pattern recognition. Selected list of theoretical statistical machine learning publications.

 

Text Comprehension and Memory

An on-going component of my research program involves investigating human text comprehension and memory.  Currently, I am evaluating a constrained multinomial logistic regression time-series modeling methodology for the  purpose of analyzing semantic structural relations in human recall, summarization, and question-answering data (Ismaili and Golden, 2008; Golden, 1998) as well as semi-automated methods for the analysis of human free response data (Golden and Ghiasinejad, 2013; Durbin, Earwood, and Golden, 2000). 

Visit Text Comprehension Website.

Visit Knowledge Digraph Contribution Analysis Website.

 

Statistical Machine Learning Applications

My research program additionally involves the application of statistical machine learning methods to a wide range of mathematical modeling problems. These empirical applications are an important supportive component of the theoretical research program component which is concerned with the analysis and design of statistical machine learning algorithms. Empirical applications include: identification of clinical predictors of deep venous thrombosis and pulmonary embolus after severe injury (Brakenridge et al., 2013), document clustering (Dasgupta, Golden, and Ng, 2012), predicting risk of multiple organ failures after severe injury (Brakenridge et al., 2011),  evaluating the effects of duty hour limits on resident physician satisfaction (Kashner et al., 2010), automated detection of software bugs (Wong, Shi, Qi, and Golden, 2008), smart antenna blind adaptive CDMA processing (Paik, Golden, Tolak, and Dowling, 2006), smart antenna multiuser interference suppression (Jani, Dowling, and Golden, 2000), automated analog circuit design (Golden, 2000), predicting quality of life in patients with benign prostate hyperplasia or prostate cancer (Krongrad et al., 1997; Michaels et al., 1998), and automated aircraft landing (Schley et al., 1991). Currently, I am an Invited Consultant to the National Panel on Statistics and Analytics for Veteran Health Administration. Selected list of statistical machine learning applications and list of patents.