Research 

"Ask and it will be given to you; seek and you will find; knock and the door will be opened to you".
Matthew 7:7

Research Interests

My primary research interest is function estimation in high dimensional spaces with an emphasis on the construction of estimators that yield optimal prediction.  I invest an equal amount of research/thinking energy on both the theoretical foundation and the applicability of the methods that I work on.  I was first exposed to Machine Learning and Statistical Learning Theory back in 1991 in Cameroon from Professor Patrick Gallinari who is currently at Universite Pierre et Marie Curie in France. I later obtained a scholarship to join the Neural Computing Research Group then headed by Professor Christopher Bishop. While at the NCRG, I was very fortunate to work with Professor Manfred Opper on my Master's Thesis, concentrating on Mean Field Methods for Gaussian Process Classifiers. After my Master's, I was fortunate enough yet again to be awarded a PhD scholarship by the University of Glasgow where I completed my PhD in Statistics under the supervision of Professor Mike Titterington. My research naturally belongs to Statistical Learning Theory/Machine Learning Theory. My work can be applied to problems in classification, regression and dimensionality reduction, especially when the goal is optimal prediction. Considering the unusually high dimensionality of the spaces that I deal with, a substantial part of my work has a numerical analysis flavor to it, in the sense that  I need to address such issues as computational stability, computational scalability and computational speed/complexity.  Theoretically, my work sits at the confluent of statistics, mathematics, computer science and engineering, and I enjoy such natural interdisciplinarity, being at my core something of a philosopher  who easily sees the interconnectedness of most things. After my PhD, I move to The Ohio State University where I worked for four years as an Assistant Professor of Statistics. Still true to my first love with Machine Learning, I took a leave of absence in my third year at OSU to work as a Postdoctoral Research Fellow at the Statistical and Applied Mathematical Sciences Institute (SAMSI) within the Data Mining and Machine Learning program. 

Interest 1: One aspect of my current research that I find particularly interesting is model selection for optimal prediction. One is given a family of models along with a predictive optimality criterion, and the goal is the select amongst the models the one that yields the best performance on unseen data. For various model family specifications, this problem can be approached from either the Bayesian or the frequentist perspective. I have personally been exploring various aspects of this interesting problem from the Bayesian perspective with the model family being the general linear model, and the loss function being the square error loss. More specifically, consider a response variable of interest, say Y. In this case, Y could be binary, as in classification problems, for instance Y = +1 (credit worthy) or Y = -1 (not credit worthy). For the experimenter, it is interesting to decide as accurately as possible whether a person applying for credit should be granted it. At his/her disposal, the experimenter has on a collection of potential explanatory variables X1, X2, X3, ...,Xp believed to be potential predictors of credit worthiness (Y) through some functional transformation f. In the presence of a large or extremely large number of Xj's, it is very highly likely that a substantial number of them are really not good predictors of Y. This triggers the need to define a measure of the importance of a given predictor variable Xi. If one assumes that each predictor variable Xj has measure of importance p_j attached to it in connection with the accurate prediction of the desired response Y,

  • What are good techniques (consistent, stable/robust, scalable and fast) for estimating the p_j's ?

  • Once the p_j's have been estimated and ranked, how many of them should be retained?

  • How does one prove theoretically that the retained set of predictors does indeed achieve optimal prediction?

  • How does one go about choosing f in the first place?

"Fundamental progress has to do with the reinterpretation of basic ideas."

Alfred North Whitehead (1861-1947)

 

"Contradiction is not a sign of falsity, nor the lack of contradiction a sign of truth."
Blaise Pascal

Machine Learning Resources
Important Papers &  Websites Journals, Conferences and Workshops Institutions and Departments
  • Neural Computation

  • Journal of Machine Learning Research

  • Machine Learning

  • Stanford - Statistics Dept

  • Berkeley - Statistics Dept

  • Berkeley - CS Dept

  • MIT

  • Wisconsin

"All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident."

Arthur Schopenhauer (1788-1860)

 
Interesting Research Resources
Guidance on writing good research papers Research Institutions Research Grant Institutes
   

 

Functional Analysis and Its Applications

"I believe that numbers and functions of Analysis are not the arbitrary result of our minds; I think that they exist outside of us, with the same character of necessity as the things of objective reality, and we meet them or discover them, and study them, as do the physicists, the chemists and the zoologists."
David Hilbert (1862-1943)

"To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession."
Blaise Pascal

"The student of mathematics has to develop a tolerance for ambiguity. Pedantry can be the enemy of insight."
Gila Hanna

Copyright © 2001-2006, Ernest Parfait Fokoué