Introduction to Optimization for Data Analysis
Stub. Why data analysis is, almost always, an optimization problem in disguise — surveyed through the running examples the rest of the book builds algorithms for: least squares, matrix factorization, support vector machines, logistic regression, and deep learning.
Corresponds to Chapter 1. Frames essentially every data-analysis task covered in the rest of the book as “minimize a loss function over a parameter vector,” and previews the five running examples that recur throughout: least squares (the linear, quadratic-loss case — simple enough to solve in closed form, but the template every iterative method is first tested against), matrix factorization (e.g. low-rank approximation, recommender systems), support vector machines (margin-based classification), logistic regression (probabilistic classification), and deep learning (the nonconvex case motivating most of the book’s later, more sophisticated machinery). Closes with the book’s stated emphasis — algorithms with convergence guarantees, not just heuristics.
Outline (TODO — flesh out each)
- Data analysis and optimization — the general framing
- Least squares
- Matrix factorization problems
- Support vector machines
- Logistic regression
- Deep learning
- Emphasis of the book