Reports

Most of these papers are based upon work supported by the National Science Foundation under Grants DMS-0072445, DMS-0306612, and DMS-0604939. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Each article goes under the year when it was first written, usually as a technical report. Revisions don't usually make an article move up the list.

2008

Southworth, L.K., Kim. S.K. and Owen, A.B. Properties of balanced permutations PDF
Balanced permutations are a fascinating idea for microarray analyses. But we find that they can give very misleading p values.

2007

Perry, P.O. and Owen, A.B. A rotation test to verify latent structure PDF
We test the presence of a latent variable in correlated noise by employing projection pursuit non-normality measures.
Zahn, Poosala, Owen, Ingram, Lustig, Carter, Weeratna, Taub, Gorospe, Mazan-Mamczarz, Lakatta, Boheler, Zu, Mattson, Falco, Ko, Schlessinger, Firman, Kummerfeld, Wood, Longo, Zonderman, Kim, Becker
"AGEMAP: a gene expression database for aging in mice" PLOS Genetics
This is a preliminary online version of the article. There may be changes.
We look at patterns of aging in mice for 16 different tissues, as measured by gene expression.
Owen, A.B. and Perry, P.O. "Bi-cross-validation of the SVD and the non-negative matrix factorization" PDF | Slides
We look at how to pick the rank k when approximating a matrix by a truncated SVD. We hold out a rectangular submatrix, fit an SVD to a complementary submatrix, truncate it and predict. The method extends to the non-negative matrix factorization among other models.
Owen, A.B. "Pearson's test in a large scale multiple meta-analysis" PDF
The AGEMAP study generated an 8932 x 16 matrix of p values. We apply meta-analysis to each row. A method originally proposed by Pearson (1934) and thought for over 50 years to be inadmissible performs best in a simulation. We also show that Pearson's test really is admissible.
Owen, A.B. "The pigeonhole bootstrap" Annals of Applied Statistics | PDF | Slides
McCullagh (2000) showed that large crossed random effects data sets, such as are now studied for recommender engines and information retrieval are impossible to bootstrap. This means that even for balanced homoscedastic random effects models with no missing data, no bootstrap correctly estimates the variance of a sample mean (let alone a more complicated procedure). But one of the methods he studied, that of independently resampling rows and columns, comes pretty close. This article shows the expected bootstrap variance in that method tracks the desired variance, even for severely unbalanced and heteroscedastic data sets.

2006

Owen, A.B. "A robust hybrid of lasso and ridge regression" PDF | Slides
A penalty that behaves like lasso for small coefficients and like ridge for large coefficients is developed. This penalty is a reversed Huber function. The penalty is convex. Like the Huber function it requires scaling. The scaling parameter can be incorporated into a criterion that is jointly convex in it and the regression coefficient vector.
Owen, A.B. "Infinitely imbalanced logistic regression" JMLR
Many binary classfication problems are very unbalanced with one category much more common than the other. This paper shows what happens to logistic regression in the limit where one category's sample size tends to infinity while the other remains finite. For example one could use logistic regression to separate a Gaussian measure from a finite data set. Under mild conditions, the limiting coefficient vector (apart from the intercept) is finite. It can be expressed in terms of an exponential tilt and solved for by a convex optimization.
Journal of Machine Learning Research (v 8, pp 761-773, 2007)
Zahn, Sonu, Vogel, Crane, Mazan-Mamczarz, Rabkin, Davis, Becker, Owen, Kim
"Transcriptional profile of aging in human muscle reveals a common aging signature" PLOS Genetics
This paper relates human aging to various genes and gene groups. It includes a new version of Gene Set Enrichment Analysis (GSEA) geared to handle regressions and covariates. The electron transport group of genes are found to be age related in human kidney, muscle and brain, and in other species.

2005

Tribble, S.D and Owen, A.B. "Constructions of weakly CUD sequences for MCMC PDF
An earlier paper below showed that MCMC can be driven by completely uniformly distributed (CUD) or weakly CUD (WCUD) point sequences. This paper shows that a construction of Liao's that permutes QMC vectors leads to WCUD point sequences. A theorem of Niederreiter (1977) implies that certain lattice constructions satisfy a triangular array version of CUD. We find QMC methods for MCMC reduce variance by factors ranging from 10 to several hundred in a 42 dimensional Gibbs sampling probit example. A proposal of Liao's for incorporating acceptance rejection into QMC-MCMC
Owen, A.B. "Local antithetic sampling with scrambled nets" PDF
A local antithetic reflection strategy can improve the variance rate of scrambled nets from n^(-3/2+epsilon) to n^(-3/2-2/d+epsilon) in dimension d. The benefit is similar to that which Haber gets when moving from stratified sampling to stratified antithetic sampling. The method also looks like a merger of scrambled nets and monomial cubature.
Owen, A.B. "On the Warnock-Halton quasi-standard error" PDF
Warnock and Halton have proposed a method of treating multiple QMC estimates as replicates. This paper reproduces an example where the method seems to work, but cautions that the method can fail arbitrarily badly
Lin, Z & Owen, A.B. & Altman, R. Science Reply to letters about "Genetic research and human subject privacy".

2004

Owen, A.B. and Tribble, S.D "A quasi-Monte Carlo Metropolis algorithm" pnas
This paper proves that QMC methods can be applied to Metropolis-Hastings style MCMC. The key idea is to use QMC points that are "completely uniformly distributed". This is like using the entire period of a small random number generator.
Rodwell,Sonu,Zahn,Lund,Wilhelmy,Wang,Xiao,Mindrinos,Crane,Segal,Myers,Brooks,Davis,Higgins,Owen, and Kim "A transcriptional profile of aging in the human kidney" Public Library of Science
We found genes that change expression with age, in the human kidney. These genes do not tend to be the ones that serve to distinguish kidney from other tissue types, consistent with a model that aging is similar in different tissue types. The genes do not overlap with aging related genes in other species that we looked at.
Owen, A.B. "Randomized QMC and point singularities" PDF
Randomized QMC is shown to have a superior rate of convergence to ordinary MC on some functions with square integrable singularities at unknown locations. Surprisingly that means RQMC will generally beat importance sampling asymptotically. Of course one might combine them.
Lin, Z & Owen, A.B. & Altman, R. "Genetic research and human subject privacy" Science, Vol 305, Issue 5681, 183, 9 July 2004
Owen, A. B. "Variance of the number of false discoveries". PDF | R functions (beta) | R function documentation (beta)
Given d hypothesis tests at level alpha we expect d alpha false positives. When the tests are dependent, the variance of the number of false positives can be O(d^2) higher than the independence value of d alpha(1-alpha). This paper shows how to estimate such a variance taking account of dependency in the tests. The R functions are beta and very subject to change. Feedback is welcomed.
Owen, A. B. "Halton sequences avoid the origin". PDF
Gives rates of convergence for QMC on unbounded integrands, using growth conditions on f and a singularity avoidance pattern for x's. Halton sequences and randomized QMC avoid the origin suitably.
Owen, A. B. "Multidimensional variation for quasi-Monte Carlo". PDF | BiBTeX

Survey, and some new results, on multidimensional variation (Vitali and Hardy-Krause) for Quasi-Monte Carlo.

2003

Delayed graft function in transplanted kidneys Article
Be sure to see Tao Jiang's Thesis: Compressed PostScript | PDF
Liu, R. Owen, A.B. "Estimating Mean Dimensionality of ANOVA decompositions (revised)" PDF Relationships between Sobol's sensitivity indices and moments of the dimension distribution are established. The mean dimension is computed for some functions arising in finance and extreme value theory. The minimum of d independent uniform random variables is seen to have strong low dimensional components.
Troyanskaya, O.G., Dolinski, K., Owen, A.B., Altman, R.B., Botstein, D. "A Bayesian framework for combining heterogeneous data sources for gene function prediction (in S. cerevisiae)" Online Supplement
Owen, A.B. "Quasi-Monte Carlo Sampling" PDF |BiBTeX
A Chapter on QMC for a SIGGRAPH 2003 course. It motivates QMC as a deterministic law of large numbers. The algorithms are presented as extensions of stratification methods, like those already well known in graphics (jittering, n rooks, multi-jittered sampling).

2002

Owen, A.B., Stuart, J., Mach, K. Villeneuve, A,M., Kim, S. "A gene recommender algorithm to identify co-expressed genes in C elegans" Paper| Software
This paper imitates algorithms from movie and book recommenders to find new genes related to a group of old genes. Given a query of genes with common function, we identify experiments in which the query genes are strongly co-expressed. Then we rank all the organisms genes according to the extent to which they agree with the query group, in the selected experiments. RNA interference knockouts confirmed two new Retinoblastoma related genes in C elegans.
Owen, A.B. "Variance and discrepancy with alternative scramblings" PostScript | PDF
There are many computationally efficient proposals for scrambling digital nets. Generally they preserve mean squared discrepancy. This paper shows that one alternative can be detrimental to the sampling variance, adversely affecting the rate of convergence. Another scrambling improves the rate of convergence, at least for d=1.
Owen, A.B. "Necessity of low effective dimension" PostScript | PDF
This paper explores the extent to which low superposition dimension is necessary for QMC to beat MC.
Jiang, T. and Owen, A.B. "Quasi-regression for visualization and interpretation of black box functions" PostScript | PDF
Quasi-regression is applied to the output of a support vector machine and to a neural network. The method allows one to peer into a black box and identify important variables and interactions. The most vexing issue is how to reconcile a decomposition derived for independent variables with a function fit to highly dependent data.
Hickernell, F. and Lemieux, C. and Owen, A.B. "Control variates for quasi-Monte Carlo" PostScript | PDF
It is easy and natural to combine quasi-Monte Carlo with control variates. But the proper control variate coefficients can change, as can the choice of what constitutes a good control variate. In MC a good control variate correlates with the integrand. In QMC it is better to correlate with some derivative or high frequency component of the target integrand.

2001

Jiang, T. and Owen, A.B. "Quasi-regression with shrinkage" PostScript | PDF | Software | Slides
Quasi-regression is a method of Monte Carlo approximation useful for global sensitivity analysis. This paper presents a new version, incorporating shrinkage parameters of the type used in wavelet approximation. As an example application, a black box function from machine learning is analyzed. That function is nearly a superposition of functions of one and two variables and the first variable acting alone accounts for more than half of the variance.
Owen, A.B. "The dimension distribution and quadrature test functions" PostScript | PDF
A "dimension distribution" is introduced through which various measures of effective dimension of a function can be defined. The idea is explored on some widely used quadrature test functions. Some isotropic functions are shown to be of low effective dimension, explaining the success of QMC methods on them.
@article{dimdist, author = {A. B. Owen}, title = {The dimension distribution and quadrature test functions}, journal = {Statistica Sinica}, volume = 13, number = 1, note = {In press}, year = 2003 }
Owen, A.B. "Empirical Likelihood" Book | Software
Lemieux, C. and Owen, A.B. "Quasi-Regression and the Relative Importance of the ANOVA Components of a Function" PostScript | PDF

2000

Lazzeroni, L. and Owen, A.B. "Plaid Models for Gene Expression Data" PostScript version PDF version. Published as: "Plaid Models for Gene Expression Data", Laura Lazzeroni and Art Owen Statistica Sinica Vol. 12, No. 1, pp. 61-86. January, 2002.
Related research course
Here are the figures for the plaid paper. Figures 1 and 2 are LARGE. The compressed versions download faster. But when uncompressed they can take a long time to print or to come up in a postscript viewer. Figure 1 40.3 Mb PostScript Figure 1 4.11 Mb Zip compressed PostScript
Figure 2 33.4 Mb PostScript Figure 2 3.16 Mb Zip compressed PostScript
Figures 3 and 4 31.9 Kb PostScript

The Plaid program is available for noncommercial research purposes. Plaid only runs on the Wintel platform. To get a time limited copy or to learn how to license Plaid for commercial research purposes, visit this link .
Owen, A.B. "Plaid User's Guide" PostScript | PDF | HTML
Owen, A.B. "Data squashing by empirical likelihood" PostScript | PDF

1999

Owen, A.B. and Zhou, Y. "Adaptive Importance Sampling by Mixtures of Products of Beta Distributions" PostScript | PDF
An, J. and Owen, A.B. "Quasi-Regression", Computer experiments are used commonly in engineering design problems, arising in semiconductor, aerospace and other fields, with accurate deterministic simulators. The purposes of computer experiments vary...they might be thought of as "function mining" in analogy to data mining. The goals include approximation, interpretation and visualization. Quasi-regression is a frequentist simulation based tool for computer experiments. It is aimed at building approximations for those problems for which kriging, (often called DACE) is computationally infeasible. PostScript | PDF
Owen, A.B. "Assessing linearity in high dimensions" Revised. PostScript | PDF
Owen, A.B. and Zhou, Y. "Safe and effective importance sampling", revised. PostScript | PDF
Owen, A.B. "Tubular Neighbors for Regression and Classification" PostScript | PDF

1998

Owen, A.B. and Zhou, Y. "Safe and effective importance sampling" Importance sampling can be nearly perfect with a well chosen sampling density. Or it can give an infinite variance even when the sampling density closely matches the integrand. This paper shows that by combining importance sampling and control variates it is possible to get a method that is never much worse than importance sampling and never much worse than ordinary monte carlo. It is also well known that the importance sampling variance can approach zero for a nonnegative integrand as the sampling density becomes more nearly proportional to the integrand. This paper shows that it is possible to approach zero variance for integrands taking both positive and negative signs, by using two or more importance samples. PostScript | PDF
Owen, A.B. "Monte Carlo Extension of Quasi-Monte Carlo" Monte Carlo methods can be used to advantage in combination with quasi-Monte Carlo. This paper surveys some recent results: randomized QMC can give sample based error estimates, randomized QMC can also increase accuracy by a factor of roughly n^-.5 over QMC for smooth integrands, and Latin supercube sampling can extend the reach of QMC into higher, even infinite, dimensions. PostScript | PDF To appear: 1998 Winter Simulation Conference Proceedings. (D. J. Medieiros, E.F. Watson, M. Manivannan, and J. Carson, Eds.), pages 571--577. I thank WSC'98 for allowing its republication.

1997

Owen, A.B. "Scrambling Sobol and Niederreiter-Xing Points". PostScript
Owen, A.B. "How nearly linear is a function?". Many high dimensional numerical problems become tractable for nearly linear functions. The problem is, how can you tell if a given function is nearly linear? This paper presents a method based on quasi-regression for estimating the amount of linear structure in a function. Quasi-regression allows one to estimate regression coefficients without matrix inversion, at least in controlled settings, in the same way that quasi-interpolation allows fast approximate interpolation. In an example, the amount of linear structure in a 1,000,000 dimensional function is accurately estimated from only 90,000 observations. A more thorough experimental investigation finds a variant of quasi-regression that gives consistently good results on 64 functions (defined by varying 6 binary features) over 1,000 dimensions. PostScript
Owen, A.B. "Latin supercube sampling for very high dimensional simulations". In very high dimensional simulations quasi-Monte Carlo (QMC) methods can begin to lose their effectiveness or break down completely. One response is to use QMC on a few key dimensions and something else on the other dimensions. Latin supercube sampling allows one to use QMC on more than one independent set of dimensions. The paper also considers Latin hypercube sampling for infinite dimensional problems. Motivating applications: particle transport simulations, computational finance, graphical rendering, queuing systems. PostScript
Caflisch, R.E., Morokoff, W. and Owen, A.B. "Valuation of Mortgage Backed Securities using Brownian Bridges to Reduce Effective Dimension". We study a 360 dimensional integration problem motivated by collateralized mortgage obligations. The integral is tractable because it is of lower effective dimension (as defined in the paper) than 360. A Brownian bridge encoding of Brownian motion reduces the effective dimension further. As a result quasi-Monte Carlo sampling of the leading input dimensions is made more effective. PostScript

1996

Owen, A.B. and Tavella, D.A. "Scrambled Nets for Value at Risk Calculations" Some low discrepancy point sets are used to compute the value at risk of two simple financial derivatives. Low discrepancy point sets converge faster than Monte Carlo on these problems. By randomizing the low discrepancy point sets, we get a data based estimate of the variance of the value at risk. BiBTeX
Owen, A.B. "Scrambled Net Variance for Integrals of Smooth Functions". This paper shows how a hybrid of Monte Carlo and Quasi-Monte Carlo methods can integrate smooth functions (over the s dimensional cube) with a variance of order n^(-3) (log n)^(s-1). This improves on both Monte Carlo and Quasi-Monte Carlo. Published in BiBTeX

1995

Koehler, J.R. and Owen, A.B. "Computer Experiments" BiBTeX This paper is a survey of Bayesian and sampling methods for computer experiments.
Owen, A.B. "Empirical Likelihood" " PostScript"| "PDF" This paper is an introduction to empirical likelihood, to appear as an Encyclopedia of Statistical Sciences entry.
Stork, Wolff and Owen "Empirical Error-Confidence Curves for Neural Networks and Gaussian Classifiers" This poster describes some simulations running neural networks and linear discriminant analysis. Some simulations had a net as the "ground truth", others satisfied the assumptions of the LDA.

1994

Owen, Art B. "Monte Carlo Variance of Scrambled Equidistribution Quadrature." This paper studies the variance of a hybrid of Equidistribution and Monte Carlo techniques for high dimensional integration. It features a multidimensional Haar-like wavelet decomposition of the integrand.
Owen, Art B. "Randomly permuted $(t,m,s)$-Nets and $(t,s)$-sequences." BiBTeX This paper proposes the method studied in the paper above, and shows on some simulated examples that it improves on both Monte Carlo and equidistribution.
Owen, Art B. "Overfitting in Neural Networks." With figures. To appear in Proc. of 1994 "Stat. and Comp. Sci., The Interface."

1993

Owen, Art B. "Nonparametric Likelihood Confidence Bands for a Distribution Function." The confidence bands described in this paper have better Bahadur efficiency than any weighted Kolmogorov-Smirnov test at any alternative distribution. Their coverage level is exact, not asymptotic. This paper has appeared in JASA volume 90 number 430 pages 516-521. Accordingly the hyperlink above gives only the abstract of the paper.
Owen, Art B. "Redundant Units in High Dimensions." Technical Report 432 (July 1993). This This paper uses Aldous's Poisson clumping heuristic to investigate theoretically the behavior of connectionist models. It extends the work from Report 427 below to high dimensional settings.
Owen, Art B. "Poisson Clumping and Redundant Units." Technical Report 427 (June 1993). This This paper uses Aldous's Poisson clumping heuristic to investigate theoretically the behavior of connectionist models. It gives asymptotic probabilities of finding spurious features in noise. The result in fact describes the expected number to be found in noise. Different networks types are differently sensitive to noise.

Every minute spent doing the research reported here was a minute somebody was, with good reason, waiting for me to do something else. I thank them all for their patience.

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