Statistical Learning: Advanced Data Analysis Techniques

Module 1 offers an in-depth exploration of statistical learning, beginning with the rationale behind choosing a pre-defined family of functions and optimizing the expected prediction error (EPE). It covers the essentials of statistical learning, including the loss function, the bias-variance tradeoff in model selection, and the significance of model evaluation.

This module explores linear regression, covering the model's construction, parameter estimation, statistical tests, subset selection, regularization methods (Ridge Regression and LASSO), and data transformations. It provides a comprehensive understanding of linear regression and its variations.

This module covers linear classification methods, including adapting linear regression for classification tasks, Linear Discriminant Analysis (LDA), and logistic regression. It introduces classification metrics and explores how these methods create linear decision boundaries.

This module focuses on advanced methods in statistical modeling, including Basis Expansion Methods, Piecewise Polynomials, Smoothing Splines, and Regularization and Kernel Functions. It explores how these techniques enhance linear models by incorporating non-linear relationships.

This module covers advanced techniques in non-linear data modeling, focusing on Kernel Smoothers, k-Nearest Neighbors (kNN), and Local Regression methods. It examines how these techniques adapt to complex data relationships and addresses challenges in hyperparameter selection.

This module delves into model evaluation and selection, covering Bias-Variance Decomposition, model complexity, selection metrics (AIC, BIC, MDL), VC Dimension, Cross-Validation, and Bootstrapping. It focuses on balancing model complexity with predictive performance and estimating test error.

This module introduces advanced inferential techniques, focusing on Maximum Likelihood Inference and Bayesian Inference. It covers the process of finding optimal model parameters, Bayes' Theorem, and the construction and updating of Bayesian models.

This module covers diverse advanced machine learning techniques, including Decision Trees, Support Vector Machines (SVM), k-Means Clustering, and Neural Networks. It provides a deep dive into each technique, showcasing their unique advantages and applications in statistical learning.

This module contains the summative course assessment that has been designed to evaluate your understanding of the course material and assess your ability to apply the knowledge you have acquired throughout the course.