Lectures related to Principal component regression

Principal Component Analysis: Dimensionality Reduction

Covers Principal Component Analysis for dimensionality reduction, exploring its applications, limitations, and importance of choosing the right components.

Principal Component Analysis: Properties and Applications

Explores Principal Component Analysis theory, properties, applications, and hypothesis testing in multivariate statistics.

Ridge Regression: Penalised Least Squares

Explores Ridge Regression for handling multicollinearity and the LASSO method for model selection.

Non-Negative Definite Matrices and Covariance Matrices

Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.

Kernel Methods and Regression

Covers kernel methods, kernel regression, RBF kernel, and SVM for classification.

Atomic-scale Modeling: Interactive Exercises and Graded Assignments

Explores atomic-scale modeling through interactive exercises and graded assignments, covering crystallography, diffraction, defects, and regression models.

Kernel Methods

Covers overfitting, model selection, validation methods, kernel functions, and SVM concepts.

Kernel Ridge Regression and the Kernel Trick

Explores Kernel Ridge Regression, the Kernel Trick, Representer Theorem, feature spaces, kernel matrix, predicting with kernels, and building new kernels.

Financial Time Series: ARCH and GARCH Models

Covers regression analysis, multivariate linear regression, principal component analysis, and factor models.

Model Selection: Least Squares

Explores model selection in least squares regression, addressing multicollinearity challenges and introducing shrinkage techniques.

Functional Linear Regression: Sparse Estimation and Adaptive Methods

By Angelina Roche covers adaptive and sparse estimation in functional linear regression models.

Data Representations: Learning Methods

Covers polynomial feature expansion, kernel functions, regression, and SVM, emphasizing the importance of choosing functions for feature expansion.

Neural Network: Random Features and Kernel Regression

Covers random features in neural networks and kernel regression equivalence.

Applying the learning bound to kernel regression

Discusses the application of the main theorem to least square regression in a RKHS, focusing on LR of the Rademacher bound and Lipschitz constant.

Gradient Descent Methods: Theory and Computation

Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.

PCA: Directions of Largest Variance Log in to Mediaspace to watch this video

Covers PCA, finding directions of largest variance, data dimensionality reduction, and limitations of PCA.

Principal Component Analysis: Applications and Limitations Log in to Mediaspace to watch this video

Explores the applications and limitations of Principal Component Analysis, including denoising, compression, and regression.

Clustering Methods Log in to Mediaspace to watch this video

Covers K-means, hierarchical, and DBSCAN clustering methods with practical examples.

Kernel Regression: K-nearest Neighbors Log in to Mediaspace to watch this video

Covers the concept of kernel regression and K-nearest neighbors for making data linearly separable.

Data Representations & Processing Log in to Mediaspace to watch this video

Explores data representations, overfitting, model selection, cross-validation, and imbalanced data challenges.