Some advanced topics and theories related to statistics and machine learning are taught. More specifically, a nonparametric method called kernel method, statistical properties of training and prediction errors, prediction error bound using Rademacher complexity, universl approximation theorem of neural networks, adversarial training of generative models are taught.
[Objectives] Statistical science and machine learning are disciplines in which useful information is extracted from data to aid
prediction and decision making. Students will learn methodology not simply as knowledge but also learning the background theory including the validity of those methods to promote understanding the essence. Students will broadly apply all kinds of techniques to a variety of problems, learning to construct new techniques on one's own.
[Topics] Students in this course will learn several of statistical science's more advanced techniques, based on their connection to various application fields. We will focus in particular on the connection with machine learning, introducing central topics from both statistical science and machine learning.
machine learning, statistics, kernel methods, prediction error, Rademacher complexity, statistical consistency, neural networks, universal approximation theorem, adversarial training
|✔ Specialist skills||Intercultural skills||Communication skills||✔ Critical thinking skills||Practical and/or problem-solving skills|
Lectures using slides.
|Course schedule||Required learning|
|Class 1||Introduction and regression analysis I||Introduction of Statistical Mathematics. Understand the problem setup of machine learning through some practical examples. Learn the problem setup of regression analysis.|
|Class 2||Regression Analysis II||Understand the statistical modeling with kernels, regularization, and kernel ridge regressions in regression analysis.|
|Class 3||Kernel methods I: positive definite kernels||Review positive definite matrix. Understand the definition of positive definite kernels, and learn some properties of kernel functions and examples.|
|Class 4||Kernel methods II: reproducing property, representer theorem, etc.||Understand reproducing property, representer theorem, etc used in statistical learning with kernels.|
|Class 5||Spline smoothing and kernel methods I||Learn the relationship between spline smoothing methods and kernel methods.|
|Class 6||Spline smoothing and kernel methods II||Learn B-spline and multi-dimensional spline regression|
|Class 7||Review of Probability theory||Review the probability theory used in Machine Leaning|
|Class 8||Inequalities in Probability Theory.||Understand some probabilistic inequalities used in machine learning.|
|Class 9||Prediction error and Model Selection||Learn the prediction error of statistical learning and model selection methods.|
|Class 10||Rademacher Complexity||Learn Rademacher complexity to measures the statistical models|
|Class 11||Prediction error and Model Uniform law of large numbers and statistical consistency of learning algorithms||Learn Uniform law of large numbers that is an extension of the law of large numbers, and Understand the proof on statistical consistency of learning algorithms.|
|Class 12||Learning with Neural networks||Learn the universal approximation theorem for neural networks|
|Class 13||Adversarial training of generative models||Learn the adversarial training of generative models with neural networks and regularization methods.|
|Class 14||Summary||Summarize Stasistical Learning|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Course materials are provided during class.
Reference book: Shai Shalev-Shwartz and Shai Ben-David, Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, 2014.
Evaluated by report submission.
It is preferred that students know the basics of statistics and probability theory.