##### Question Answer the following machine-learning / deep-learning concept questions. Where useful, include the formula, the intuition, and a small worked example. 1. **PCA:** What do the eigenvectors of the covariance matrix represent, and how do they relate to principal components and explained variance? 2. **Decision trees:** Define Gini impurity, show how to compute it for a node, and explain how it is used to choose splits. 3. **Reinforcement learning:** Write the Bellman equation (both the expectation form for a fixed policy and the optimality form for V* / Q*) and explain its role in policy evaluation and improvement. 4. **Regularization – dropout:** What is dropout, how does it behave at training vs. inference time, and why does it act as a regularizer? 5. **Training stability:** What is gradient clipping, when is it useful, and how do residual (skip) connections in ResNets help mitigate the vanishing-gradient problem? 6. **Optimization landscape:** Why are deep-learning objectives typically non-convex, and what are the practical implications for optimization (e.g., local minima vs. saddle points)? 7. **Transformers:** Describe scaled dot-product attention and multi-head attention, and explain why the dot products are scaled by 1/√d_k.