HyperReal

Advanced Cardinality Estimation for Privacy-Preserving Analytics

HLL-based Audience Extrapolation Compatible with Online Measurement

Overview

This documentation explores advanced cardinality estimation algorithms, focusing on HyperLogLog (HLL) and HyperReal (HR) sketching techniques for privacy-preserving analytics. These methods enable accurate audience measurement and cross-platform deduplication without exposing individual user data.

Problem Statement

For RAM or PRIVACY reasons we cannot:

  • Count unique hashed users directly
  • Count unique hashed users by demographic attributes
  • Join hashed users across providers (e.g., Google and Facebook)
  • Join hashed users across platforms within the same provider

Goal: Deduplicate audiences between census (online) and panel (TV) data without direct links, both at total and demographic levels.

Key Innovation

HyperReal provides an unbiased alternative to HyperLogLog, enabling more accurate cardinality estimation while maintaining the same privacy and memory efficiency benefits.

Documentation Sections

🔬

Fundamentals of Methodology

Understanding hashing properties, uniform distribution, and the mathematical foundations underlying HLL sketches.

Mathematical foundations and core concepts

📈

Algorithm Evolution

From Flajolet-Martin (1985) to HyperLogLog (2007) - the complete evolution of cardinality estimation algorithms.

Historical development and algorithmic improvements

🎯

HyperLogLog Sketches

Deep dive into HyperLogLog implementation, bias correction, and range corrections with practical code examples.

Industry standard algorithm implementation

⚡

HyperReal Algorithm

The unbiased alternative to HLL - mathematical foundations, implementation, and performance comparisons.

Next-generation unbiased cardinality estimation

🔍

Extended Algorithms

Enhanced HLL and HR with demographic tracking capabilities for attribute-aware cardinality estimation.

Demographic-aware cardinality estimation

📺

Panel to HyperReal

Converting TV panel data to HyperReal sketches using naive and fast association methods.

TV audience measurement integration

🔄

Sketch Operations

Merging sketches for union and intersection operations, enabling cross-platform analytics.

Cross-platform data integration

📊

Simulations & Results

Comprehensive performance analysis using NYC parking violations dataset with accuracy and memory comparisons.

Real-world performance validation

💻

Implementation Guide

Complete Python implementations with code examples, best practices, and optimization techniques.

Production-ready code and best practices

🎯

Real-World Applications

Privacy-preserving audience measurement, cross-platform deduplication, and scalable analytics solutions.

Industry use cases and deployment patterns

📦

CardinalityKit Package

Professional Python toolkit with clean APIs, comprehensive examples, and production-ready implementations.

Complete software package and documentation