Probabilistic Programming and Data Structures

  1. Probabilistic Data Structures Theory
    1. Fundamental Principles
      1. Randomization in Data Structures
        1. Hash Functions
          1. Universal Hashing
            1. Cryptographic Hash Functions
              1. Non-Cryptographic Hash Functions
              2. Randomized Algorithms
                1. Probabilistic Analysis
                2. Space-Time Tradeoffs
                  1. Memory Efficiency Goals
                    1. Query Time Optimization
                      1. Approximation Quality
                      2. Error Analysis Framework
                        1. False Positive Rates
                          1. False Negative Rates
                            1. Estimation Error Bounds
                              1. Confidence Intervals
                              2. Streaming Data Model
                                1. Single-Pass Constraints
                                  1. Limited Memory Assumptions
                                    1. Online Algorithm Design
                                  2. Mathematical Foundations
                                    1. Concentration Inequalities
                                      1. Markov's Inequality
                                        1. Chebyshev's Inequality
                                          1. Chernoff Bounds
                                            1. Hoeffding's Inequality
                                              1. McDiarmid's Inequality
                                              2. Hash Function Analysis
                                                1. Collision Probability
                                                  1. Load Balancing Properties
                                                    1. Independence Assumptions
                                                    2. Sketching Theory
                                                      1. Linear Sketches
                                                        1. Johnson-Lindenstrauss Lemma
                                                          1. Dimensionality Reduction

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                                                      5. Model Development and Validation

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                                                      7. Membership and Set Operations