Data Compression and Machine Learning

Introduction

There is a deep and fascinating connection between machine learning and data compression. Both fields rely on recognizing and exploiting patterns in data:

✅ Machine learning predicts future data based on past data.
✅ Data compression reduces data size by representing it efficiently, relying on predictability within the data.

The Core Idea

A system that predicts the posterior probabilities of a sequence given its entire history can be used for optimal data compression.

If you can predict the next symbol accurately, you can compress data efficiently using arithmetic coding, which assigns shorter codes to more probable symbols.

Why Prediction Enables Compression

When you predict the probability distribution of the next symbol, you know which outcomes are likely. Arithmetic coding then compresses the sequence near the theoretical entropy limit by: ✅ Assigning fewer bits to likely symbols.
✅ Assigning more bits to rare symbols.

A perfect predictor would achieve optimal compression, demonstrating how learning patterns in data (machine learning) enables efficient compression.

Why Compression Enables Prediction

Conversely:

An optimal compressor can be used for prediction by finding the symbol that compresses best, given the previous history.

If you know which symbol would lead to the smallest compressed size, it implies that this symbol is the most probable, effectively making a prediction.

Thus: ✅ Compression and prediction are two sides of the same coin.

Compression as a Benchmark for Intelligence

Since: ✅ A good compressor needs to understand and capture all patterns and regularities in data.
✅ Intelligence, in part, is the ability to discover patterns and make predictions.

Using data compression as a benchmark for general intelligence has been proposed: ✅ The better you compress data, the better you understand it.
✅ Compression forces models to find meaningful representations.

Practical Example: Language Models

Large language models like GPT can: ✅ Predict the next word in a sequence accurately.
✅ Generate highly compressible output when used with arithmetic coding.

This demonstrates: ✅ The stronger the model’s understanding (learning patterns), the better the potential compression.

Key Takeaways

✅ Prediction and compression are fundamentally linked.
✅ Machine learning models that predict well can compress well, and vice versa.
✅ Compression efficiency can serve as a measure of a system’s understanding of data, connecting to the notion of intelligence.

What’s Next?

✅ Explore arithmetic coding and entropy in the context of compression.
✅ Experiment with using a language model for compressing text data.
✅ Continue your structured learning on superml.org.

Join the SuperML Community to discuss data compression, prediction, and their connection to building intelligent systems.

Happy Learning! 📦🤖