| • Estimation and Statistical Learning Theory (k5) Students can apply methods from estimation and statistical learning theory, including maximum likelihood estimation, Fisher information, and generalization analysis based on risk and concentration bounds.
• Probabilistic PCA (pPCA) (k5) Students can derive the probabilistic PCA model and its assumptions. They can implement the method in Python, apply it to data and interpret the results.
• Variational Autoencoders (VAE) (k5) Students can derive the VAE objective using the evidence lower bound (ELBO). They can implement and train a VAE in Python and analyze the resulting latent representations.
• Diffusion Models (k5) Students can explain the forward and reverse diffusion processes and derive the training objective of diffusion models. They can implement a diffusion model in Python and analyse the generated results.
• Optimization and Learning Dynamics (k5) Students understand optimization methods used for training machine learning models such as stochastic gradient descent. They can explain how learning dynamics influence the solutions obtained by learning algorithms and analyse their impact on model behaviour and generalization.
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Students acquire a theoretical understanding of how machine learning methods can be analysed, modified, and applied with respect to generalization, inference, representation, and learning dynamics. They gain knowledge of advanced concepts such as Vapnik-Chervonenkis dimension, probabilistic PCA, variational autoencoders, and diffusion models.
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