GANs, VAEs, and Diffusion Probabilistic Models (DDPM/DDIM).
For a small example, a toy dataset clusters near -2 and +2. Compare a single Gaussian with a mixture and inspect which can represent both modes without averaging them away.
A team wants realistic tabular data for testing. Define utility and privacy goals, train on scoped data, compare marginals and relationships, and test memorization risk.
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Predict how one control changes the Generative Models result.
The starter deliberately follows a tempting but flawed assumption: Selecting samples by eye
Check: Your saved hypothesis predicts a direction, the experiment tests it, and the result changes or supports your explanation.
Explanations after each answer · 80% to pass · Generative Models
Chapter 1 of 4 · Core
Generative Adversarial Networks (Goodfellow et al., 2014) frame generative modeling as a game-theoretic competition between two networks: a Generator that maps a low-dimensional noise vector to the data space, and a Discriminator that outputs the probability that a sample came from the empirical data distribution rather than the generated distribution .
The system is optimized by solving a zero-sum, two-player minimax objective:
Mathematical Proof of the Optimal Discriminator : For any fixed generator , we want to find the discriminator that maximizes the objective . We can express the expectation terms as continuous integrals: Using the change of variables under the push-forward measure , this becomes: To maximize this integral with respect to at each point , we differentiate the integrand with respect to : Substituting and , we obtain the unique optimal discriminator:
Jensen-Shannon Divergence Convergence Bound: Substituting back into the minimax objective: where is the Jensen-Shannon divergence. This proves that the global minimum of the minimax game is achieved if and only if , where .
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Primary sources and free technical reading for Generative Models.