Probabilistic Programming and Data Structures

  1. Frequency Estimation and Heavy Hitters
    1. Problem Definition
      1. Heavy Hitters Problem
        1. Frequency Estimation
          1. Top-K Queries
            1. Streaming Constraints
            2. Count-Min Sketch
              1. Data Structure Design
                1. Two-Dimensional Counter Array
                  1. Hash Function Family
                  2. Operations
                    1. Update Procedure
                      1. Point Query
                        1. Range Query
                        2. Error Analysis
                          1. Overestimation Bounds
                            1. Probability Guarantees
                              1. Parameter Selection
                              2. Extensions
                                1. Count-Min-Log Sketch
                                  1. Conservative Update
                                    1. Merging Sketches
                                  2. Count Sketch
                                    1. Signed Hash Functions
                                      1. Median Estimation
                                        1. Frequency Recovery
                                          1. Comparison with Count-Min
                                          2. Misra-Gries Algorithm
                                            1. Counter Management
                                              1. Decrement Strategy
                                                1. Frequency Guarantees
                                                  1. Space Complexity
                                                  2. Space-Saving Algorithm
                                                    1. Stream-Summary Structure
                                                      1. Counter Replacement
                                                        1. Error Bounds
                                                          1. Implementation Details
                                                          2. Lossy Counting
                                                            1. Bucket-Based Approach
                                                              1. Error Parameter
                                                                1. Support Threshold
                                                                  1. Memory Management

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                                                                8. Cardinality Estimation

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                                                                10. Similarity and Distance Estimation