quiz.json

{
  "questions": [
    {
      "stage": "pre",
      "question": "What is the 'curse of dimensionality'?",
      "options": ["High-dimensional data takes too long to download", "As dimensions grow, distances become meaningless, volume concentrates in corners, and you need exponentially more data", "Neural networks cannot process data with more than 100 features", "High-dimensional data always contains noise"],
      "correct": 1,
      "explanation": "In high dimensions, all pairwise distances converge to similar values, data points spread to corners, and maintaining sample density requires exponentially more data. Dimensionality reduction counteracts these effects."
    },
    {
      "stage": "pre",
      "question": "What does PCA find?",
      "options": ["The most important features by name", "The orthogonal directions of maximum variance in the data", "Clusters of similar data points", "The optimal number of features to keep"],
      "correct": 1,
      "explanation": "PCA computes the eigenvectors of the covariance matrix, which are orthogonal directions ranked by how much data variance they capture. The first principal component points along the direction of maximum spread."
    },
    {
      "stage": "post",
      "question": "After running PCA on 784-dimensional MNIST data with k=50 components, you find 95% of variance is captured. What does this tell you?",
      "options": ["Only 50 pixels matter in each image", "The data effectively lives in a ~50-dimensional subspace; the remaining 734 dimensions are mostly noise or redundancy", "95% of images belong to the same class", "The model will achieve 95% accuracy"],
      "correct": 1,
      "explanation": "95% explained variance with 50 components means the essential structure of 784-dimensional data is captured by just 50 directions. The rest carries only 5% of the variation -- mostly noise."
    },
    {
      "stage": "post",
      "question": "Why should you NOT use t-SNE as preprocessing before training a classifier?",
      "options": ["t-SNE is too slow for large datasets", "t-SNE is designed for visualization only: it distorts global distances, is stochastic, and the output coordinates have no consistent meaning across runs", "t-SNE reduces data to exactly 2 dimensions which is too few", "t-SNE requires the labels to be known in advance"],
      "correct": 1,
      "explanation": "t-SNE preserves local neighborhoods but distorts global structure. Distances between clusters are meaningless, and different runs produce different layouts. Use PCA for preprocessing and t-SNE/UMAP only for visualization."
    },
    {
      "stage": "post",
      "question": "When would you choose kernel PCA over standard PCA?",
      "options": ["When you have more samples than features", "When the data lies on a nonlinear manifold that standard PCA cannot separate, like concentric circles", "When you need the fastest possible computation", "When you want interpretable principal components"],
      "correct": 1,
      "explanation": "Standard PCA finds linear subspaces. If data has nonlinear structure (e.g., two concentric rings), PCA projects both onto the same line. Kernel PCA maps data to a higher-dimensional space where the structure becomes linear."
    }
  ]
}