Statistical Computing
STAT 538 Winter Quarter 2008

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Course description

Optimization -- finding maxima or minima of functions -- is necessary in most cases when a problem has been "solved on paper" or just formulated, but we need to follow with computing the value of its solution. Most practically interesting problems and many theoretical ones do not have analytical solutions. Therefore, optimization in the technical sense deals with the algorithms for numerically finding extrema of functions and with finding conditions when these extrema exist. In this course we will focus on continuous optimization (that is, over continuous multidimensional domains) and, within this area, on convex optimization. We will look at applications in statistics (e.g estimating parameters by maximizing likelihood) and in related machine learning methods (support vector machines, boosting). Convexity is intimately related to a class of statistical models called exponential family models and to the information theoretic concepts of entropy and Kullback-Liebler divergence; our course will also examine these from a computational point of view. Below is a list of topics that we are likely to cover (the ordering being logical, rather than chronological)
  • Exponential family models -- parameters, sufficient statistics, link functions
  • Entropy, KL divergence, and their optimization. Maximum entropy estimation
  • Unconstrained optimization and descent methods
  • Boosting as gradient descent
  • Convex constrained optimization
    • Convex sets and functions and their relevance to optimization and to statistics
    • Duality and Lagrange multipliers
    • Algorithms
  • Approximate inference in graphical models and convexity
  • Support Vector Machines as convex optimization

Contact the instructor at: mmp@stat.washington.edu