Knowledge Discovery and Pattern Extraction

Learn the science of extracting reliable knowledge from data. Design rigorous experiments and quantify their uncertainty. Find patterns with similarity search, clustering and graph analysis, and know when the results can be trusted.

CS Master Course | 2027

Sessions

Twelve sessions plus the semester project.

  1. Counting

    • Sum and product rules: the fundamental counting principles.
    • Permutations and combinations: when order matters and when it doesn't.
    • Pigeonhole principle: when repetition is unavoidable.

  2. Probability

    • Conditional probability and Bayes' theorem: update beliefs with evidence.
    • Independence, the chain rule and the law of total probability.
    • Random variables: expectation, variance and the key distributions (Bernoulli, Binomial, Poisson, Normal).

  3. The Science of Experimentation I

    • Joint distributions, covariance and correlation.
    • Correlation is not causation: confounders and Simpson's paradox.
    • The Beta distribution, sums of random variables and the Central Limit Theorem.
    • Sampling and bootstrapping: standard error and resampling.

  4. The Science of Experimentation II

    • Descriptive statistics that lie: mean vs. median, skewed distributions, outliers.
    • The evaluation equation: reported score = true score + bias + noise.
    • Confidence intervals, significance, and the misuse of p-values.
    • Train/validation/test methodology and A/B testing.

  5. Optimizing in the Dark: What Everybody Gets Wrong — but Not You

    • The winner's curse: why your best result is probably wrong.
    • Data leakage and multiple comparisons.
    • Sample size and power: how many samples you actually need.
    • The organizational cost of bad measurement.

  6. A Common Quest: Finding Similarities

    • Distance metrics: Jaccard, cosine, Euclidean, each with the representation it fits.
    • Near duplicates at scale: shingling, MinHash and locality-sensitive hashing (LSH).
    • Nearest neighbors and recommendations.
    • Clustering: k-means and DBSCAN, their assumptions and how to evaluate them.

  7. Creating Useful Representations

    • The representation is the modeling choice before the model: what it preserves, compresses and throws away.
    • Embeddings for words, documents, users and items.
    • Graph representations and graph embeddings.
    • Choose a representation based on what should count as similar or related.

  8. Graphs and Graph Metrics

    • Graph data models: directed, weighted, bipartite. Adjacency matrices and edge lists.
    • Centrality: degree, betweenness, closeness, eigenvector. PageRank.
    • Structural properties: paths, connected components, diameter, clustering coefficient.

  9. Graph Clustering

    • Community detection: what a community is, intuitively and formally.
    • Modularity (Louvain, Leiden), label propagation and spectral clustering.
    • Evaluate communities without ground truth.

  10. Graph Neural Networks

    • From random walks to learned node embeddings.
    • Message passing: GCN, GraphSAGE, GAT.
    • When GNNs help, and when simpler methods suffice.

  11. Knowledge Modeling, Querying and Inference

    • Knowledge graphs: entities, relations, triples. Completion as link prediction.
    • Knowledge graph embeddings and multi-hop queries in vector space.
    • GNN recommenders and relational deep learning over multi-table databases.
    • Toward foundation models for knowledge graph reasoning.

  12. Conversational “X”

    • Conversation as a control surface: steer underspecified tasks through dialogue.
    • Conversational extraction, clustering and exploration, with humans in the loop.
    • Evaluation and decision support without fixed ground truth.