Basic Tools

Optimization

Optimization helps us to master the training.

• Convex Optimization
  • Yurii, Nesterov. Introductory lectures on convex optimization: A basic course. Vol. 87. Springer Science & Business Media, 2013.
  • Stephen P. Boyd, and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.
• Nonconvex Optimization
  • Prof. Sun’s website: https://sunju.org/research/nonconvex/

Statistic

Statistic characterizes the generalization property of the learning scheme.

• High-dimensional Probability
  • Roman Vershynin, High-dimensional probability: An introduction with applications in data science. Vol. 47. Cambridge university press, 2018.
  • Martin J. Wainwright, High-dimensional statistics: A non-asymptotic viewpoint. Vol. 48. Cambridge University Press, 2019.
• Statistic for machine learning
  • Vladimir Vapnik, The nature of statistical learning theory. Springer, 2013.

Geometry and Algebra

Geometry and Algebra provide a fundamental tool for understanding a machine learning process.

• Linear Algebra
  • Sheldon Axler, Linear algebra done right. springer, 2015.
• Advanced -Serge Lang, Fundamentals of differential geometry. Vol. 191. Springer Science & Business Media, 2012.
  • P.-A. Absil, R. Mahony, and R. Sepulchre. Optimization Algorithms on Matrix Manifolds. Princeton University Press, USA 2007.

Reading and Summary

TBA