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Interactive 3D/PAC Learning
Hypothesis Class |H|
|H| ≈ 1kln|H|=6.9
101M
Target accuracy ε
ε = 0.10error ≤ 10%
0.010.50
Confidence δ
Required Samples
n ≥99
Achievable ε:0.100
PAC formula: n ≥ (1/ε)(ln|H| + ln(1/δ))
With n samples, you are (1-δ) confident the learned hypothesis has error ≤ ε.
Insight: Larger |H| needs exponentially more samples. Tighter ε requires 1/ε times more data. The three curves show how confidence level δ shifts the required n.

PAC Learning - Interactive Visualization

PAC (Probably Approximately Correct) learning answers: how many training examples do we need for a model to generalize? The sample complexity n ≥ (1/ε)(ln|H| + ln(1/δ)) grows with accuracy requirement (1/ε), confidence (1/δ), and hypothesis class size (|H|). This visualization shows how sample complexity curves change with these parameters.

  • See sample complexity n as a function of accuracy ε
  • Adjust hypothesis class size |H| to see impact on sample needs
  • Compare curves for different confidence levels δ
  • Understand the fundamental theorem of learning: finite VC dim → PAC learnable
  • Foundation for generalization bounds and model complexity analysis

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.