STATS 202B: Matrix Algebra and Optimization

2022-04-19

This course is a survey of computational methods that are especially useful for statistical analysis, with implementations in statistical package R. Topics include matrix analysis, multivariate regression, principal component analysis, multivariate analysis, and deterministic optimization methods.

The Bruin Learn course page is here.

A detailed description of the class is available here.

Motivation and Synopsis

During the twentieth century, the development of statistical computing played a crucial facilitating role for the growth of the statistics discipline and the adoption of statistical methods within the scientific community and beyond. In the twenty-first century digital age, the amounts of data available for statistical analysis has grown tremendously, yielding new opportunities for statistical computing, as well as new challenges. Statistical computing constitutes an important part of a statistics education, and is highly valuable for statisticians in both academia and industry.

This course is an introduction computational methods that are useful for statistical analysis, with implementations in the statistical package R.

Computational methods are essential to both understand and implement modern statistical ideas. Often the computation methods are a translation of the statistical methods into another language, one that computer understand. In this class we will consider this process for key statistical models and techniques. These include multivariate regression, principal component analysis, and multivariate analysis. In doing so, we study the core mathematical and numerical ideas that make this possible including matrix analysis and deterministic optimization methods.

The course has various parts:

  • We’ll do some matrix algebra (not linear algebra), emphasizing what is available in R.
  • We apply the matrix algebra to multivariate data analysis, in particular to regression, principal component analysis, canonical analysis, correspondence analysis.
  • We discuss optimization methods. These will be mainly deterministic but also stochastic methods
  • We finally apply both optimization and linear algebra to discuss statistical techniques such as multidimensional scaling, independent component analysis, tomography, and generalized mixed linear models. Well, maybe not all.

The primary purpose of this course is to provide students with a common set of core knowledge about statistical computing computing for their class work and research. The course will have an applied focus on tools. The course will involve the practical application of the ideas of statistical computing and their implementation through statistical software, particularly R.

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