SCIENTIFIC PROGRAMS AND ACTIVITIES

September  2, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
August 12-15, 2013
22nd International Workshop on Matrices and Statistics
Location :
Bahen Centre, 40 St. George St. , Room 1180 (map)


ABSTRACTS
REGISTRATION
**On-site Aug. 12-15**

After July 1
Fees: $300,
Students & Postdocs $200

Registration fees include conference material, morning refreshments, coffee breaks, and 2 catered lunches


Tickets to the Workshop Dinner on August 14, $60 for registrants,
$75 for guests
Abstract Submissions
Housing in Toronto
History of the IWMS
IWMS series
Journal of Statistical computation and simulation (JSCS).
Related Conferences
Map to Bahen Centre

Back to main index

Invited Speakers

Mohamed Amezziane, Central Michigan University
Semiparametric Smoothing through Preliminary Test Estimation
Coauthors: S. Ejaz Ahmed


Pre-test estimation is implemented to develop a semiparametric function estimator by shrinking a nonparametric function estimator towards a fully known parametric function. We demonstrate that this semiparametric estimator outperforms the nonparametric estimator under certain conditions. We also derive the asymptotic properties of the estimator and discuss the smoothing parameter selection.

Oskar Maria Baksalary (Adam Mickiewicz)
On certain subspace distances determined by the Frobenius norm
Coauthors: Goetz Trenkler, Faculty of Statistics, Dortmund University of Technology, Dortmund, Germany

From among functions introduced so far to characterize a "separation" of two vector subspaces, a distinguished role is played by the notions of an angle and minimal angle, which were originally defined in a Hilbert space. Inspired by known characterizations of the angles, we specify two new measures of a separation between two subspaces of a finite dimensional complex vector space, say M, N ? Cn, 1. The measures are based on the Frobenius norm of certain functions of orthogonal projectors onto subspaces determined by M and N. Several properties of the measures are identified and discussed, mostly by exploiting partitioned representations of matrices.
With this talk we are pleased to celebrate the 70th birthday of Professor Goetz Trenkler on 14 July 2013.


Somnath Datta
(Louisville)
Robust Regression Analysis of Longitudinal Data Under Censoring

We consider regression analysis of longitudinal data when the temporal correlation is modeled by an autoregressive process.Robust R estimators of regression and autoregressive parameters are obtained. Our estimators are valid under censoring caused by detection limits. Theoretical and simulation studies of the estimators are presented. We analyze a real data set on air pollution using our methodology.

Susmita Datta (University of Louisville)
Rank Aggregation in Bioinformatics Problems

High-throughput technologies in genomics and proteomics promoted the need to develop novel statistical methods for handling and analyzing enormous amounts of high dimensional data that are being produced on a daily bases in laboratories around the world. In this work, we propose novelmethodology to summarize the information in the data in terms of clustering techniques. In particular, we find the optimal clustering algorithm for a given data amongst a collection of algorithms in terms of multiple performance criteria. We use stochastic optimization technique of cross entropy to rank aggregate a list of distances of multiple ordered lists to achieve this. We illustrate the methodologies through simulated and real life microarray and mass spectrometry data.

Kai-Tai Fang (United International College, Zhuhai)
The Magic Square - Historical Review and Recent Development
Coauthors: Yanxun Zheng

If an n×n matrix of numbers in which the sum of entries along each row, each column, the main diagonal and the cross diagonal is the same constant, it is called a magic square. If the elements of the magic square are consecutive integers from 1 through n2, then it is called a classical magic square. Magic squares were known to Chinese mathematicians, as early as 650 B.C. There are so many mystical properties of the magic matrix in the literature. In this talk a historical review is given and some recent developments are mentioned. Some applications of the magic square are discussed also.

Ali Ghodsi, University of Waterloo
Nonnegative Matrix Factorization via Rank-One Downdate

Nonnegative matrix factorization (NMF) was popularized as a tool for data mining by Lee and Seung in 1999. NMF attempts to approximate a matrix with nonnegative entries by a product of two low-rank matrices, also with nonnegative entries. In this talk, I introduce an algorithm called rank-one downdate (R1D) for computing an NMF that is partly motivated by the singular value decomposition. This algorithm computes the dominant singular values and vectors of adaptively determined submatrices of a matrix. On each iteration, R1D extracts a rank-one submatrix from the original matrix according to an objective function. I establish a theoretical result that maximizing this objective function corresponds to correctly classifying articles in a nearly separable corpus. I also provide computational experiments showing the success of this method in identifying features in realistic datasets. The method is also much faster than other NMF routines.

This is a joint work with Michael Biggs and Stephen Vavasis.

Karl E. Gustafson (Colorado at Boulder)
A New Financial Risk Ratio

Randomness in Financial Markets has been recognized for over a century: Bachelier(1900), Cowles(1932), Kendall(1953), Samuelson(1959). Risk thus enters into efficient Portfolio design: Fisher(1906), Williams(1936), Working(1948), Markowitz(1952). Reward versus Risk decisions then depend upon Utility to the Investor: Bernoulli(1738), Kelly(1956), Sharpe(1964), Modigliani(1997). Returns of a Portfolio adjusted to Risk are measured by a number of Ratios: Treynor, Sharpe, Sortino, M2, among others. I will propose a refinement of such ratios. This possibility was mentioned in my recent book: Antieigenvalue Analysis , World-Scientific (2011).

Abdulkadir Hussein (Windsor)
Efficient estimation in high dimensional spatial regression models

We consider Some spatial regression models and develop an array of shrinkage and absolute penalty estimators for the regression coefficients. We compare the estimators analytically and by means of Monte Carlo simulations. We illustrate the usefulness of the proposed estimation methods by using data sets on crime distribution and housing prices.
Keywords: Spatial regression, penalty estimation, shrinkage

Tõnu Kollo (University of Tartu)
Matrix star-product and skew elliptical distributions

Multivariate skew elliptical distributions have usually three parameters: vectors of location and shape and a positive definite matrix as the scale parameter. Often distributions have some additional matrix parameters. In Kollo, Selart, Visk (2013) an estimation method for three parameter skew elliptical distributions is suggested based on moments' expressions. The construction of point estimates uses star product of matrices. In the talk we examine possibility of deriving confidence regions for these estimates using matrix derivative technique. Reference: Kollo, T., Selart, A. Visk, H. (2013). From multivariate skewed distributions to copulas. In: Combinatorial Matrix Theory and Generalized Inverses of Matrices. Eds.: R. B. Bapat et al. Springer, 63-72.

Steven N. MacEachern (Ohio State University)
Efficient Quantile Regression for Linear Heterogenous Models
Coauthors: Yoonsuh Jung (University of Waikato) and Yoonkyung Lee (Ohio State University)

Quantile regression provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques which focus on a single conditional mean function. Lee et al. (2012) modified quantile regression by combining notions from least squares regression and quantile regression. The combination of methods results in a modified loss function where the sharp corner of the quantile-regression loss is rounded. The main modification involves an asymmetric l2 adjustment of the loss function around zero. We extend the idea of l2 adjusted quantile regression to linear heterogeneous models. The l2 adjustment is constructed to diminish as sample size grows. The modified method is evaluated both empirically and theoretically.

Ingram Olkin (Stanford)
A Linear Algebra Biography

This talk is a review of my travels through linear algebra -- how it started and how it continued from 1948 to the present.

Jianxin Pan (University of Manchester)
Covariance matrix modeling: recent advances

When analyzing longitudinal/clustered data, misspecification of covariance matrix structures may lead to very inefficient estimates of parameters in the mean. In some circumstances, for example, when missing data are present, it may yield very biased estimates of the mean parameters. Hence, correct modeling of covariance matrix structures play a very important role in statistical inferences. Like the mean, covariance matrix structures can be modeled using linear or nonlinear regression models. Various estimation methods were proposed recently to model the mean and covariance structures, simultaneously. In this talk, I will review these methods on joint modeling of the mean and covariance structures for longitudinal or clustered data, including linear, nonparametric regression models and semiparametric models. Missing data and variable selection will be addressed too. Real examples and simulation studies will be provided for illustration.

Serge B. Provost (Western University)
On Improving Density Estimates by Means of Polynomial Adjustments

A moment-based methodology is proposed for obtaining accurate density estimates and approximants. This technique which involves applying a polynomial adjustment to an initial functional representation of a target density, relies on the inversion of a matrix that is often ill-conditioned. This approach will be applied to certain saddlepoint density approximations and extended to density estimates by making use of empirical cumulant-generating functions. The bivariate case which is tackled via a standardizing transformation, relies on inverting a high-dimensional matrix. The resulting representation of the joint density functions gives rise to a very flexible copula family. Several illustrative examples will be presented.


Shuangge Ma
(Yale University)
Contrasted Penalized Integrative Analysis

Single-dataset analysis of high-throughput omics data often leads to unsatisfactory results. The integrative analysis of heterogeneous raw data from multiple independent studies provides an effective way to increase sample size and improve marker selection results. In integrative analysis, the regression coefficient matrix has certain structures. In our study, we use group penalization for one- or two-dimensional marker selection and introduce contrast penalties to accommodate the subtle coefficient structures. Simulations show that the proposed methods have significantly improved marker selection properties. In the analysis of cancer genomic data, important markers missed by the existing methods are identified.


Fuzhen Zhang
(Nova Southeastern University)
Integer Partition, Young Diagram, and Majorization
Coauthors: Geir Dahl (University of Oslo, Norway)

We relate the integer partitions to Young diagram and majorization, that is, we describe integer partition problem via Young diagram and in terms of integral vector majorization. In the setting of majorization, we study the polytope of integral vectors. We present several properties of the cardinality function of the integral vector majorization polytopes. This is a joint work with G. Dahl,(University of Oslo, Norway).

Invited Special Sessions

Special Session to celebrate Lynn Roy LaMotte's 70th Birthday

Speakers:
David A. Harville (IBM Thomas J. Watson Research Center )
Prediction: a "Nondenominational" Model-Based Approach

Prediction problems are ubiquitous. In a model-based approach to predictive inference, the values of random variables that are presently observable are used to make inferences about the values of random variables that will become observable in the future, and the joint distribution of the random variables or various of its characteristics are assumed to be known up to the value of a vector of unknown parameters. Such an approach has proved to be highly effective in many important applications.
It is argued that the performance of a prediction procedure in repeated application is important and should play a significant role in its evaluation. A ``nondenominational'' model-based approach to predictive inference is described and discussed; what in a Bayesian approach would be regarded as a prior distribution is simply regarded as part of a model that is hierarchical in nature. Some specifics are given for mixed-effects linear models, and an application to the prediction of the outcomes of basketball or football games (and to the ranking and rating of basketball or football teams) is included for purposes of illustration.

Lynn Roy LaMotte, LSUHSC School of Public Health
On Formulation of Models for Factor Effects

In linear models, effects of combinations of levels of categorical factors are modeled in several ways: dummy variables (also called GLM coding), reference-level coding, effect coding, and others. The conventional way to parse multi-factor effects is in terms of sets of main-effect and interaction-effect contrasts among the cell means, e.g., A effects, B effects, AB interaction effects. Call these ANOVA effects.
Depending on the formulation, the full-model vs. restricted-model computation of the numerator sum of squares may not provide a test statistic that tests the ANOVA effects in question. In some, the hypothesis tested depends on the within-cell sample sizes and empty cells. In others, it has been asserted that the test statistic tests the target hypothesis when all its degrees of freedom are estimable. There does not seem to be a general description of the relation between the test statistic and the target hypothesis.
A framework is described in this paper by which some order and clarification of such questions can be had. Building on the cell-means approach to models of effects, models are formulated in terms of sums of orthogonal projection matrices for ANOVA effects. Other formulations can be expressed equivalently in these terms, providing a common bridge among different model formulations.
Using this framework, several questions and widely-held beliefs will be addressed.

J. N. K. Rao, Carleton University
Robust estimation of variance components in linear mixed and semi-parametric mixed models

Maximum likelihood (ML) method is often used for estimating variance components in a linear mixed model. However, ML estimators are sensitive to outliers in the random effects or the unit errors in the model. We propoe a robust fixed point approach to robust ML estimation and show that it overcomes covnergence problems with the Newton-Raphson method. We also consider semi-parametric mixed models using penalized splines to approximate the mean function. In this case, robust ML approach runs into problems and we propose a method simialr to a method of Fellner (1986) to estimate the random effects and model parameters simultaneously.

Special Session on Applied Probability
(Organized by Jeffrey Hunter)

Speakers:
Iddo Ben-Ari, University of Connecticut
A Probabilistic Approach to Generalized Zeckendorf Decompositions
Coauthors: Steven J. Miller

Zeckendorf's Theorem states that every positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers, if we start the sequence 1, 2, 3, 5,... This result has been generalized to decompositions arising from other recurrence relations, and to properties of the decompositions, most notabley, Lekkerkerker's Theorem which gives the mean number of summands. The theorem was originally proved using continued fraction techniques, but recently a more combinatorial approach has had great success in attacking this and related problems, such as the distribution between gaps of summands. We introduce a unified probabilistic framework and show how this machinery allows to reprove and generalize all existing results and obtain new results. The main idea is that the digits appearing in the decomposition are obtained by a simple change of measure for some Markov chain.

Minerva Catral, Xavier University
The Kemeny constant for a Markov chain on a given directed graph

Let T be the transition matrix of an n-state homogeneous ergodic Markov chain. The Kemeny constant K(T) gives a measure of the expected time to mixing or time to stationarity of the chain, and has representations in terms of the group generalized inverse of A=I-T and the inverses of the (n-1) ×(n-1) principal submatrices of A. We give an overview of these representations and present several perturbation results. Finally, we consider the effect of the directed graph structure of T on the value of K(T).

Sophie Hautphenne, University of Melbourne
An Expectation-Maximization algorithm for the model fitting of Markovian binary trees
Coauthors: Mark Fackrell

In this paper, we consider the parameter estimation of Markovian binary trees, a class of branching processes where the lifetime and reproduction epochs of individuals are controlled by an underlying Markov process. We develop an Expectation-Maximization (EM ) algorithm to estimate the parameters of the Markov process from the continuous observation of some populations, first with information about which individuals reproduce or die, and second without this information.

Jeffrey Hunter, Auckland University of Technology
Generalized inverses of Markovian kernels in terms of properties of the Markov chain

All one-condition generalized inverses of the Markovian kernel I - P, where P is the transition matrix of a finite irreducible Markov chain, can be uniquely specified in terms of the stationary probabilities and the mean first passage times of the underlying Markov chain. Special sub-families include the group inverse of I - P, Kemeny and Snell’s fundamental matrix of the Markov chain and the Moore- Penrose g-inverse. The elements of some sub-families of the generalized inverses can also be re-expressed involving the second moments of the recurrence time variables. Some applications to Kemeny’s constant and perturbations of Markov chains are also considered

*Jianhong Xu, Southern Illinois University Carbondale
An Iterative Algorithm for Computing Mean First Passage Matrices of Markov Chains

For an ergodic Markov chain, the mean first passage matrix and the stationary distribution vector are among its most important characteristics. There are various iterative algorithms in the literature for computing the stationary distribution vector without resorting to any explicit matrix inversion (in either the regular or the generalized form). This, however, is not the case in general when it comes to computing the mean first passage matrix. In particular, various formulations of this matrix involve one or multiple explicit matrix inversions if implemented directly. In this talk, we present an iterative algorithm that computes the mean first passage matrix and, moreover, that can be readily implemented free of explicit matrix inversions.

Special Session of Statistical Inference on GLM
(Organized by Krishna Saha, Central CT State University)

Speakers:
Dianliang Deng, University of Regina
Goodness of fit of product multinomial regression models to sparse data

Tests of goodness of t of sparse multinomial models with non-canonical links is proposed by using approximations to the first three moments of the conditional distribution of a modifed Pearson Chi-square statistic. The modifed Pearson statistic is obtained using a supplementary estimating equation approach. Approximations to the first three conditional moments of the modifed Pearson statistic are derived. A simulation study is conducted to compare, in terms of empirical size and power, the usual Pearson Chi-square statistic, the standardized modifed Pearson Chi-square statistic using the first two conditional moments, a method using Edgeworth approximation of the p-values based on the first three conditional moments and a score test statistic. There does not seems to be any qualitative difference in size of the four methods. However, the standardized modifed Pearson Chi-square statistic and the Edgeworth approximation method of obtaining p-values using the first three conditional moments show power advantages compared to the usual Pearson Chi-square statistic, and the score test statistic. In some situations, for example, for small nominal level, the standardized modifed Pearson Chi-square statistic shows some power advantage over the method using Edgeworth approximation of the p-values using the first three conditional moments. Also, the former is easier to use and so is preferable. Two data sets are analyzed and a discussion is given.

Severien Nkurunziza, Windsor
Optimal inference in linear model with multiple change-points

Krishna Saha, Central CT State University
Inference concerning a common dispersion of several treatment groups in the analysis of count response data from clinical trials

Samiran Sinha, Texas A&M University
Semiparametric analysis of linear transformation model in the presence of errors-in-covariates

*Jihnhee Yu, University at Buffalo
A maximum likelihood approach to analyzing incomplete longitudinal data in mammary tumor development experiments with mice

Longitudinal mammary tumor development studies using mice as experimental units are affected by i) missing data towards the end of the study by natural death or euthanasia, and ii) the presence of censored data caused by the detection limits of instrumental sensitivity. To accommodate these characteristics, we investigate a test to carry out K-group comparisons based on maximum likelihood methodology. We derive a relevant likelihood ratio test based on general distributions, investigate its properties of based on theoretical propositions, and evaluate the performance of the test viaa simulation study. We apply the results to data extracted from a study designed to investigate the development of breast cancer in mice.

Memorial Session to honor Shayle R. Searle
(Organized by Jeffrey J. Hunter)

Speakers:
David A. Harville

Jeffrey J. Hunter

J. N. K. Rao

Robert Rodriguez

Susan Searle

Heather Selvaggio

Special Session on Perspectives on High Dimensional Data Analysis
(Organized by: Muni Srivastava)

Speakers:

Shota Katayama, Osaka University
Model Selection in High-Dimensional Multivariate Linear Regression Analysis with Sparse Inverse Covariance Structure

Abbas Khalili, McGill University
Sparse mixture of regression models in high dimensional spaces

*J. S. Marron, University of North Carolina
Object Oriented Data Analysis: HDLSS Asymptotics

Takahiro Nishiyama, Senshu University
Multivariate multiple comparison procedure among mean vectors in high-dimensional settings

Martin Singull, Linköping University
Test for the mean in a Growth Curve model in high dimension

Muni Srivastava, University of Toronto
Test for Covariance Matrices in High Dimension with Less Sample Size

Anand Vidyashankar, George Mason University
Inference for high-dimensional data accounting for model selection variability

Takayuki Yamada, Nihon University
Test for assessing multivariate normality available for high-dimensional data

Hirokazu Yanagihara, Hiroshima University
Conditions for Consistency of a Log-likelihood- Based Information Criterion in High-Dimensional Multivariate Linear Regression Models under the Violation of Normality Assumption

Invited Special Session on Open-Source Statistical Computing (Organized by Reijo Sund)

Speakers:

Antti Liski, National Institute for Health and Welfare, Finland
The effect of data constraints on the normalized maximum likelihood criterion with numerical examples using Survo R

The stochastic complexity for the data, relative to a suggested model, serves as a criterion for model selection. The normalized maximum likelihood (NML) formulation of the stochastic complexity contains two components: the maximized log likelihood and a component that may be interpreted as the parametric complexity of the model. In Gaussian linear regression the use of the normalized maximum likelihood criterion is problematic because the parametric complexity is not finite. Rissanen has proposed an elegant solution to constrain the data space. Liski and Liski (2009) proposed alternative constraints for the data space and Giurcaneanu, Razavi and Liski (2011) investigated the use of these constraints further. In this paper we study and illustrate the effects of data constraints on the proposed model selection criterion using Survo R software. We focus especially on the case when there is multicollinearity present in the data.

Reijo Sund, National Institute for Health and Welfare (THL), Finland
Survo R for open-source statistical computing

For centuries, a core principle of scientific research has been intersubjective verifiability. A structured version of this principle demands that a thorough description of methodology required for the replication of findings is made publicly available. For a statistician this means publication of data, theoretic-mathematical justification of the statistical methods and code required for the replication of the actual analyses. Statistical software packages have revolutionalized the use of statistical methods in empirical research: nowadays extremely complicated methods can be easily applied by any skilled researcher on the cost that many important computational details may remain hidden inside a black box of the potentially expensive statistical software. To overcome this problem, open-source statistical software is becoming a cornerstone of scientific inference, and is an important element of the modern scientific method. The open-source software development process also makes the method development global in the sense that software and source codes are freely available to anyone and the development is open to collaborative efforts of scientists worldwide.
R is the most common open-source software environment for statistical computing and graphics. It runs on a wide variety of platforms and is highly extensible, with thousands of user-contributed packages available. One extensive package is Survo R. Survo is an integrated environment for statistical computing and related areas developed since the early 1960s by professor Seppo Mustonen. First version was for the Elliott 803 and later generations include versions for Wang 2200, PC and Windows. Survo R is a sophisticated mixture of Mustonen’s original C sources and rewritten I/O functions that utilize R and Tcl/Tk extensively to provide multiplatform support.
Features of Survo include file-based data operations, flexible data preprocessing and manipulation tools, various plotting and printing facilities, a teaching friendly matrix interpreter, so-called editorial arithmetics for instant calculations, a powerful macro language, plenty of statistical modules and an innovative text editor based GUI (originally invented in 1979) that allows to freely mix commands, data and natural text encouraging towards reproducible research with ideas similar to literate programming. In addition, several properties have been developed to make the interplay with R from the GUI seamless.
By giving direct access to these additional useful features of Survo for every R user, the options available for data processing and analysis as well as teaching within R are significantly expanded. Text editor based user interface suits well for interactive use and offers flexible tools to deal with issues that may be challenging to approach using standard R programming. This new version of Survo also concretely shows the power and possibilities of open-source software: the functionality of full-featured statistical software Survo has been fully incorporated into the open-source statistical software R.

Kimmo Vehkalahti, University of Helsinki
Teaching matrix computations using SURVO R
Coauthors: Reijo Sund (National Institute for Health and Welfare, Helsinki)

We demonstrate the possibilities of SURVO R in teaching matrix computations. SURVO R (Sund et al 2012) is an open-source implementation representing the newest generation of the Survo computing environment, the lifework of prof. Seppo Mustonen since the early 1960s (Mustonen 1992).
Survo binds together a selection of useful tools through its unique editorial approach, invented by Mustonen in 1979 (Mustonen 1981). This approach, inherited to all subsequent generations of Survo, lets the user freely create mixtures of work schemes and documentation (Mustonen 1992, Mustonen 1999, Vehkalahti 2005). Our focus is on Survo puzzles (Mustonen 2006) and an exciting method for solving them with matrices, involving restricted integer partitions and Khatri-Rao products, for example. We employ the matrix interpreter and other tools of SURVO R to demonstrate the power of the editorial approach in teaching matrix computations.
References
Mustonen, S. (1981). On Interactive Statistical Data Processing. Scandinavian Journal of Statistics, 8, 129-136.
Mustonen, S. (1992). Survo - An Integrated Environment for Statistical Computing and Related Areas. Survo Systems, Helsinki. http://www.survo.fi/books/1992/Survo_Book_1992_with_comments.pdf
Mustonen, S. (1999). Matrix computations in Survo. Proceedings of the 8th IWMS, Department of Mathematical Sciences, University of Tampere, Finland. http://www.helsinki.fi/survo/matrix99.html
Mustonen, S. (2006). On certain cross sum puzzles. http://www.survo.fi/papers/puzzles.pdf
Sund, R., Vehkalahti, K. and Mustonen, S. (2012). Muste - editorial computing environment within R. Proceedings of COMPSTAT 2012, 20th International Conference on Computational Statistics, 27-31 August 2012, Limassol, Cyprus. pp. 777-788. http://www.survo.fi/muste/publications/sundetal2012.pdf
Vehkalahti, K. (2005). Leaving useful traces when working with matrices. Proceedings of the 14th IWMS, ed. by Paul S. P. Cowpertwait, Massey University, Auckland, New Zealand, pp. 143-154.

*awaiting confirmation

back to top