CiteULike: pdlug's mathematics

Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)

Gene Golub — 2005-07-12T18:58:24-00:00

(15 October 1996)

<P>Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.</P>

Bayesian Classification and Regression with High Dimensional Features

Longhai Li — 2008-07-07T22:16:13-00:00

(18 Sep 2007)

This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional measurements are available, for example, gene expression data produced by microarray techniques. For computational or other reasons, people may select only a small subset of features when modelling such data, by looking at how relevant the features are to predicting the response, based on some measure such as correlation with the response in the training data. Although it is used very commonly, this procedure will make the response appear more predictable than it actually is. In Chapter 2, we propose a Bayesian method to avoid this selection bias, with application to naive Bayes models and mixture models. High dimensional features also arise when we consider high-order interactions. The number of parameters will increase exponentially with the order considered. In Chapter 3, we propose a method for compressing a group of parameters into a single one, by exploiting the fact that many predictor variables derived from high-order interactions have the same values for all the training cases. The number of compressed parameters may have converged before considering the highest possible order. We apply this compression method to logistic sequence prediction models and logistic classification models. We use both simulated data and real data to test our methods in both chapters.

Elements of Linear and Real Analysis

Stephen Semmes — 2008-03-28T16:47:12-00:00

(18 Sep 2001)

This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond linear algebra and beginning analysis. In particular, this should be accessible to undergraduates or readers whose main focus is not necessarily pure mathematics. One could easily accommodate Lebesgue integrals and so forth if one wanted to, but they are not really needed.

Large Deviations for Heavy-Tailed Factor Models

Boualem Djehiche — 2007-12-21T15:22:45-00:00

(4 Dec 2007)

We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms contribute to the behaviour of the tail-probability of the sum. A simple conditional Monte Carlo algorithm is also provided together with a comparison between the simulations and the large deviation approximation. We also study large deviation probabilities for stochastic processes with factor structure. The processes involved are assumed to be Levy processes with regularly varying jump measures. Based on the results of the first part of the paper, we show that large deviations on a finite time interval are due to one large jump that can come from either the factor or the idiosyncratic part of the process.

Robust portfolio selection problems

G Iyengar — 2006-05-13T09:26:08-00:00

In this paper we show how to formulate and solve robust portfolio selection problems. The objective of these robust formulations is to systematically combat the sensitivity of the optimal portfolio to statistical and modeling errors in the estimates of the relevant market parameters. We introduce "uncertainty structures" for the market parameters and show that the robust portfolio selection problems corresponding to these uncertainty structures can be reformulated as second-order cone programs...

Physics of Econophysics

Yougui Wang — 2006-10-09T14:18:27-00:00

(4 Jan 2004)

Econophysics is a new area developed recently by the cooperation between economists, mathematicians and physicists. It's not a tool to predict future prices of stocks and exchange rates. It applies idea, method and models in Statistical Physics and Complexity to analyze data from economical phenomena. In this paper, three examples from three active main topics in Econophysics are presented first. Then using these examples, we analyze the role of Physics in Econophysics. Some comments and emphasis on Physics of Econophysics are included. New idea of network analysis for economy systems is proposed, while the actual analysis is still in progress.

Mathematics for Economists

Carl Simon — 2005-02-27T09:43:39-00:00

(08 June 1994)

Graph mining: Laws, generators, and algorithms

Deepayan Chakrabarti — 2006-07-21T13:00:13-00:00

ACM Comput. Surv., Vol. 38, No. 1. (2006)