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# Research Training Group

### Research Training Group: Data-Oriented Mathematical and Statistical Sciences

Acknowledgment of the challenges of extracting useful information from ever-growing torrents and oceans of raw data has become nearly ubiquitous over the past decade. Mathematical and statistical reasoning are central to addressing these challenges, and the mathematical sciences have established an impressive track record in providing methodology for “big data” problems as they have emerged in recent decades. The ASU Research Training Group (RTG) program is sponsored by the National Science Foundation to keep pace with these challenges. The program includes training in three areas:

1. Statistics is by its nature concerned with analysis of data. Concepts like development of sufficient statistics for hypothesis tests and identifying estimators for critical model parameters that make efficient use of collected data remain among the most powerful in the modern arsenal.
2. Computational Mathematics has been primarily responsible for algorithmic speedups that have rivaled Moore's law advances in processing technology in enabling meaningful processing of data. It also provides a bridge between exact'' solutions and heuristic algorithms by providing rigorous approximate solutions with certificates of fidelity and complexity.
3. Harmonic Analysis has underpinned most of the advances in data compression over the past thirty years, providing mechanisms for dimensionality reduction through parsimonious representation of high-dimensional data in judiciously chosen bases or frames. More recently, this area of mathematics has been instrumental in advancing ways to identify and exploit compressibility, not just in through low-dimensional subspaces of linear spaces but also by capitalizing on other kinds of low-dimensional structure.

The RTG program fosters integration across these areas to cultivate mathematical scientists who have skills in all three of them and can furthermore understand how to draw on concepts from multiple areas in addressing data-oriented problems. Examples of research questions to be addressed by the synergy of these disciplines include (but are not limited to):

1. finding and analyzing efficient and adaptive data collection strategies in sequential experimental design
2. reconstructing signals and/or images from incomplete and/or noisy data sources
3. devising measurement and other data collection strategies that optimize the value of the data in subsequent statistical tests or estimators

All ASU undergraduate students, graduate students, and postdoctoral fellows are welcome to participate in the RTG seminar, which will include both research and professional development components.

Undergraduate students, graduate students, and postdoctoral fellows participating in the RTG program will have the opportunity to complete some research activity at an off-site location, typically during the summer at a national research laboratory or medical center. This will give participants a chance to collaborate with research from diverse backgrounds and other scientific disciplines on real data-data oriented problems.

Those interested in participating should contact Rodrigo Platte.

Funding is provided by the National Science Foundation and the School of Mathematical and Statistical Sciences.

Faculty affiliiated with RTG include:

##### RTG Applied Mathematics Curriculum
 Semester 1 STP 501 Theory of Statistics IAPM 505 Applied Linear AlgebraAPM 503 Applied AnalysisRTG Seminar Semester 2 STP 502 Theory of Statistics IIRTG SeminarTwo of the following APM courses approved by student's supervisory committee. Note that APM 598 is a comprehensive level course:APM 506 Computational MethodsAPM 504 Applied Probability and Stochastic ProcessesAPM 598 Fourier Analysis and Wavelets Summer 1 Research Projects/Internship Semester 3 STP 598 Computational StatisticsRTG SeminarOne of the following APM elective courses approved by the student’s supervisory committee (note APM 520, 523, and 525 are comprehensive level courses):APM 501 Differential Equations 1APM 520 Advanced Linear AlgebraAPM 523 OptimizationAPM 525 High-Performance Computing Semester 4 One elective at comprehensive level approved by the student's supervisory committee Course to complete 5 of 6 APM core curriculum (see PhD Applied Mathematics)RTG Seminar Summer 2 Comprehensive Examination (requires completion of two comprehensive level courses)Research Projects/Internship
##### RTG Statistics Curriculum
 Semester 1 STP 501 Theory of Statistics ISTP 530 Applied Regression Analysis (or IEE 578)APM 503 Applied AnalysisRTG Seminar Semester 2 STP 502 Theory of Statistics IISTP 531 Applied Analysis of Variance (or IEE 572)APM 504 Applied Probability and Stochastic ProcessesRTG Seminar Summer 1 Qualifying ExaminationResearch Projects/Internship Semester 3 STP 526 Theory of Statistical Linear ModelsSTP 598 Computational StatisticsRTG SeminarOne of the following APM elective courses approved by the student’s supervisory committee:APM 505 Applied Linear AlgebraAPM 523 OptimizationAPM 525 High-Performance Computing Semester 4 STP 527 Statistical Large Sample Theory (or equivalent comprehensive examination course)One of elective statistics (STP/ECN/IEE) courses approved by the student’s supervisory committeeOne of the following APM elective courses approved by the student’s supervisory committee:APM 506 Computational methodsAPM 526 Advanced Numerical Methods for Partial Differential EquationsAPM 598 Fourier Analysis and WaveletsRTG Seminar Summer 2 Comprehensive ExaminationResearch Projects/Internship

MAT/STP 591 Topic: Data-Oriented Mathematical and Statistical Sciences

Schedule: Mondays 1:30 - 2:30pm in WXLR 021 (lower level)

Description: This seminar series is part of the NSF-RTG Data-Oriented Mathematical and Statistical Sciences. Seminar speakers will include ASU faculty and post-docs, outside visitors, and students. The RTG seminar will focus on both research and professional development. Topics of interest include mathematical and statistical challenges related to data problems that have emerged in recent years.

The seminar is open to all ASU students and faculty. In addition, students may register for 1 credit hour (pass/fail) or 3 credit hours (standard grading). Students registering for 1 credit must attend all talks. Students registering for 3 credits must attend all talks and present two regular length seminar talks on pre-approved topics (or two parts of the same topic). Under special circumstances, the course instructor may propose a different set of requirements. RTG fellows are required to register for three credit hours.

Prerequisite: Degree- or nondegree-seeking graduate student. Registration for three credit hours requires instructor approval.

The RTG seminar is open to everyone. ASU students may register for 1 or 3 credits. Further information is available on the Seminar tab.

RTG Seminar - Spring 2017

Jan 09, Toby Sanders
Inverse and Imaging Problems -- Introduction

Jan 23, Rodrigo Platte
Condition Numbers and Inverse Problems (pdf)

Jan 30, Part I, Rodrigo Platte
l2 and l1 Regularization of Ill-Conditioned Problems (pdf)

Jan 30, Part II, Toby Sanders
l1 Optimization and the Alternating Direction Method of Multipliers (ADMM)

Feb 06, Toby Sanders

Feb 13, Doug Cochran
Foundations of Analytic Data Compression

Feb 20, Doug Cochran
Compression with Overcomplete Libraries and Frames

Feb 27, Doug Cochran
Building Frames, Best Basis Algorithm, and Lossless Coding

Mar 13, John Stufken
Introduction to the Design of Experiments, Part I

Mar 20, John Stufken
Introduction to the Design of Experiments, Part II

Mar 27, Rob McCulloch, Invited Speaker, SoMSS
Trees in Machine Learning, Part I

Apr 03, Rob McCulloch, Invited Speaker, SoMSS
Trees in Machine Learning, Part II

Apr 10, Part I, Tony Liu, student
Optimal Sampling for Polynomial Data Fitting on Complex Regions

Apr 10, Part II, John Stockton, student
Model Selection and Data with Asymmetric Distribution Testing Using the IBOSS Approach

Apr 17, Part I, Genesis Islas, student
Function Approximation on Spherical Domains

Apr 17, Part II, Lauren Crow, student
Leverage Subsampling in Multivariate-Multinormally-Distributed Data

Tomography and Sampling

RTG Seminar - Fall 2016

Aug 22
Introduction to the RTG

Aug 29, Rodrigo Platte
Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) (pdf)

Sep 12, Toby Sanders
Introduction to the Mathematics of Computed Tomography

Sep 19, Doug Cochran
Sensing, Statistics, and Closed-loop Data Collection

Sep 26, Ming-Hung (Jason) Kao
Introduction to Optimal Experimental Designs for Functional Brain Imaging Studies

Oct 03, Kenneth Buetow, Invited Speaker, School of Life Sciences
Biomedical Informatics and Information Technology

Oct 17, Al Boggess
Introduction to Wavelets and Fourier Analysis with Application to Data Compression

Oct 31, Part I, Tony Liu , student
Nonuniform Fast Fourier Transforms

Oct 31, Part I, John Stockton, student
Data Conditions and Variable Order Testing Using IBOSS Approach

Nov 07, John Stufken
Ideas from optimal design of experiments for subdata selection from big data: Part I

Nov 14, John Stufken
Ideas from optimal design of experiments for subdata selection from big data: Part II

Nov 21, Part I, Genesis Islas, student
Signal Reconstruction using Least Absolute Error

Nov 21, Part II, Lauren Crow, student
Comparison and Implementation of Big Data Analytic Methods

Nov 28, Part I, Hope Yao, student
Deep Learning on 3D Geometries

Nov 28, Part II, John Chang, student
Bootstrapping in the Context of Big Data