Darcy Problem: Discretisations and Coercivity

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Kernel Methods: Neural Networks

Covers the fundamentals of neural networks, focusing on RBF kernels and SVM.

Learning the Kernel: Convex Optimization

Explores learning the kernel function in convex optimization, focusing on predicting outputs using a linear classifier and selecting optimal kernel functions through cross-validation.

Kernel Methods: Efficient Dot Product Computation

Demonstrates efficient dot product computation and introduces nonlinear boundaries in the original space.

Nonparametric Regression

Covers nonparametric regression, scatterplot smoothing, kernel methods, and bias-variance tradeoff.

Nonlinear SVM: Kernels and Dual Optimization

Explores transforming data with nonlinear maps, kernels, dual optimization, and interpreting SVM results.

Kernel Trick: Understanding Machine Learning

Explores the kernel trick in machine learning, enabling high-dimensional operations without explicit coordinate calculations.

Multivariate Methods I

Explores multivariate methods like PCA, SVD, PLS, and ICA for dimensionality reduction in functional brain imaging.

Neural Network: Random Features and Kernel Regression

Covers random features in neural networks and kernel regression equivalence.

Unitary Representations: Schur's Lemma

Explains Schur's Lemma on unitary representations and their irreducibility and invariance properties.

Optimal Linear Response: Stochastic Dynamical Systems

Explores optimal linear response for stochastic dynamical systems, addressing perturbations and mixing rate optimization.