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Lecture
Principal Component Analysis: Properties and Applications
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Generative Models: Self-Attention and Transformers
Covers generative models with a focus on self-attention and transformers, discussing sampling methods and empirical means.
Multivariate Methods I
Explores multivariate methods like PCA, SVD, PLS, and ICA for dimensionality reduction in functional brain imaging.
Principal Component Analysis: Dimension Reduction
Covers Principal Component Analysis for dimension reduction in biological data, focusing on visualization and pattern identification.
Quantitative Risk Management: Distributions and Techniques
Covers distributions and techniques in Quantitative Risk Management for financial modeling.
Discriminant Analysis: Bayes Rule
Covers the Bayes discriminant rule for allocating individuals to populations based on measurements and prior probabilities.
Multivariate Normal Distribution: Correlation and Covariance
Covers correlation, covariance, empirical estimates, eigenvalues, normality testing, and factor models.
Maximum Likelihood Theory & Applications
Covers maximum likelihood theory, applications, and hypothesis testing principles in econometrics.
Gaussian Mixture Regression: Modeling and Prediction
Covers Gaussian Mixture Regression principles, modeling joint and conditional densities for multimodal datasets.
Causal Systems & Transforms: Delay Operator Interpretation
Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.
Characteristic Polynomials and Similar Matrices
Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.