The document discusses key concepts in machine learning theory such as sample complexity, computational complexity, and mistake bounds. It focuses on analyzing the performance of broad classes of learning algorithms characterized by their hypothesis space. Specific topics covered include probably approximately correct (PAC) learning, sample complexity for finite vs infinite hypothesis spaces, and mistake bounds for algorithms like HALVING and weighted majority. The goal is to understand how many training examples and computational steps are needed for a learner to converge to a successful hypothesis.

1. Swapna.C

2. 1.Introduction
It is possible to set quantitative bounds on these
measures, depending on attributes of the learning
problem such as:
 The size or complexity of the hypothesis space
considered by the learner.
 The accuracy to which the target concept must be
approximated.
 The probability that the learner will output a
successful hypothesis.
 The manner in which training examples are presented
to the learner.

3.  Main focus on broad classes of learning algorithms
characterized by the hypothesis. Our goal is to answer
questions:
 Sample complexity: How many training examples are
need for a learner to converge to a successsful
hypothesis?
 Computational complexity: How much
computational effort is needed for a learner to
converge (with high probability) to a successful
hypothesis?
 Mistake bound: How many training examples will
the learner misclassify before converging to a
successful hypothesis?

4. 2.PROBABLY LEARNING AN APPROXIMATELY
CORRECT HYPOTHESIS
 A particular setting for the learning problem called
the probably approximately correct (PAC) learning
model.
 2.1 The Problem Setting:

5. 2.3 PAC Learnability

6. 3 SAMPLE COMPLEXITY FOR
FINITE HYPOTHESIS SPACES

7. 3.1 Agnostic Learning and
Inconsistent Hypotheses

8. 3.2 Conjunctions of Boolean
Literals Are PAC-Learnable

9. 3.3 PAC-Learnability of Other
Concept Classes
 3.3.1 UNBIASED LEARNERS:

10. 3.3.2 K-TERM DNF AND K-CNF
CONCEPTS

11. 4 SAMPLE COMPLEXITY FOR
INFINITE HYPOTHESIS SPACES

12. 4.1 Shattering a Set of Instances

13. 4.2 The Vapnik-Chervonenkis
Dimension

14. 4.3 Sample Complexity and the VC
Dimension

15. 4.4 VC Dimension for Neural
Networks

16. 5 THE MISTAKE BOUND MODEL OF
LEARNING

17. 5.2 Mistake Bound for the
HALVINGA lgorithm

18. 5.3 Optimal Mistake Bounds

19. 5.4 WEIGHTED-MAJORITAYlg
orithm