Probably Approximately Correct (PAC)
Learning Model
- Machine Learning -
Presented By -
Khrishtina Dutta (22/525)
Nabajit Chouhan (22/526)
Rashmi Choudhury (22/527)
Subungsa Boro (22/528)
Susankar Borgohain (22/530)
Contents –
1. Introduction to PAC Learning
2. Key Concepts in PAC
3. PAC Learning Definition
4. Example of PAC Learning
5. PAC Learnability
6. Strengths & Limitations
7. Variants of PAC Learning
8. Real-World Applications
9. Conclusion
Introduction to PAC Learning
What is PAC Learning?
• A theoretical framework in machine learning introduced by Leslie
Valiant in 1984.
• Defines conditions under which a learning algorithm can generalize
from limited data.
Why is it important?
• Helps understand the feasibility of learning tasks.
• Provides a foundation for evaluating algorithm efficiency.
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Key Concepts in PAC Learning
Concept Class (C): A set of functions (hypotheses) that can be learned.
Hypothesis (h): A function that approximates the target concept.
Distribution (D): The probability distribution of data.
Error (ε): The maximum tolerable error rate.
Confidence (δ): The probability that the hypothesis is PAC-learnable.
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PAC Learning Definition
PAC Learning (Probably Approximately Correct Learning) is a way to
describe how well a machine learning algorithm can learn a concept
from examples.
It means that if we give the algorithm enough training data, it will:
• Probably (with high confidence)
• Find an answer that is approximately correct (meaning it makes very
few mistakes).
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Example of PAC Learning
Consider a binary classification problem:
• Concept Class: Identifying if an email is spam or not.
• Hypothesis: A learned model that predicts spam.
• Error (ε): Acceptable misclassification rate (e.g., 5%).
• Confidence (δ): 95% probability that the model performs well.
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PAC Learnability
Conditions for PAC Learnability:
• Finite Hypothesis Space: If the concept class is small, learning is
easier.
• Polynomial Sample Complexity: The required number of samples
should be manageable.
• Efficient Learning Algorithm: There must be a way to find a good
hypothesis in polynomial time.
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Strengths & Limitations
Strengths:
• Provides a mathematical foundation for learning theory.
• Helps in designing better machine learning algorithms.
Limitations:
• Assumes data follows a fixed distribution.
• May not always account for real-world complexities like noise and
changing environments.
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Variants of PAC Learning
Weak vs. Strong PAC Learning:
• Weak PAC: The algorithm achieves an error slightly less than 1/2.
• Strong PAC: The algorithm achieves an error close to 0.
Agnostic PAC Learning:
• Accounts for noise and cases where the target function is not in
the hypothesis class.
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Real-World Applications
• Spam Email Detection
• Medical Diagnosis
• Speech Recognition
• Autonomous Driving
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Conclusion
• PAC Learning provides a structured way to evaluate learning models.
• It defines conditions under which a model can generalize efficiently.
• While theoretical, it has practical applications in AI and ML.
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