Johnson-Lindenstrauss Theorem

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Nonlinear Dimension Reduction Methods

Explores nonlinear dimension reduction methods preserving neighborhoods in lower-dimensional spaces.

Unsupervised Learning: Dimensionality Reduction

Explores unsupervised learning techniques for reducing dimensions in data, emphasizing PCA, LDA, and Kernel PCA.

Unsupervised learning: Young-Eckart-Mirsky theorem and intro to PCA

Introduces the Young-Eckart-Mirsky theorem and PCA for unsupervised learning and data visualization.

PCA: Key Concepts

Covers the key concepts of PCA, including reducing data dimensionality and extracting features, with practical exercises.

Gaussian Naive Bayes & K-NN

Covers Gaussian Naive Bayes, K-nearest neighbors, and hyperparameter tuning in machine learning.

Monte Carlo: Markov Chains

Covers unsupervised learning, dimensionality reduction, SVD, low-rank estimation, PCA, and Monte Carlo Markov Chains.

Maximum Entropy Modeling: Applications & Inference

Explores maximum entropy modeling applications in neuroscience and protein sequence data.

PCA: Key Concepts

Covers the key concepts of Principal Component Analysis (PCA) and its practical applications in data dimensionality reduction and feature extraction.

Unsupervised Learning: Dimensionality Reduction and Clustering

Covers unsupervised learning, focusing on dimensionality reduction and clustering, explaining how it helps find patterns in data without labels.

Support Vector Machines: Non-Linear Data Mapping

Explores mapping non-linear data to higher dimensions using SVM and covers polynomial feature expansion, regularization, noise implications, and curve-fitting methods.