| (*)• Estimation and Statistical Learning Theory (k5) Students are able to apply methods from estimation and statistical learning theory. They can calculate quantities such as the mean, variance, Fisher Information and the Likelihood function of a given probability distribution and perform a maximum likelihood estimation.
• Probabilistic PCA (pPCA) (k5) Students understand the assumptions of pPCA and can derive the model equations. They can implement the method in Python, apply it to data and interpret the results.
• Variational Autoencoders (VAE) (k5) Students understand the assumptions of the VAE model and can derive its loss function using the evidence lower bound (ELBO). They can implement a VAE model and training in Python, apply it to a dataset and analyze the training results.
• Neural Ordinary Differential Equations (nODE) (k5) Students can solve basic ordinary differential equations by hand and derive the loss function of a nODE using the adjoint method. They can implement a nODE in Python using manually derived gradients or an automatic differentiation engine.
• Diffusion models (k5) Students understand the forward and backward diffusion process and can derive the optimization objective of a diffusion model using the evidence lower bound (ELBO). They can implement a diffusion model and training in Python, apply it to a dataset and analyze the training results.
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(*)Students acquire a theoretical understanding of advanced machine learning methods such as probabilistic PCA, variational autoencoders, and diffusion models and gain practical knowledge of implementing and training these models on real datasets
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