Bayesian classifiers are statistical classifiers based on Bayes' theorem. They make predictions by calculating the probability of each possible outcome given the evidence or observed features. The naive Bayes classifier assumes independence between features given the class, allowing it to quickly determine the highest probability class. Bayesian classifiers have advantages of being powerful, efficient, and simple, though their independence assumption may not always hold. They are commonly applied to problems like spam filtering, natural language processing, and pattern recognition.

1. Bayesian Classifier
Gang Tao

2. Algebraic Geometry
Complex Analysis factal Differential equation
Geometry
Dynamical System
Combinatorial Mathematics
Statistics
Computational mathematics

3. Bayes Theorem

5. Bayes Theorem

6. Diachronic Interpretation
H -> Hypothesis
D -> Data
P(H) -> Prior Probability
P(H|D) -> Posterior Probability
P(D|H) -> Likelihood
P(D) -> Normalizing Constant

7. Bayes Theorem
Original Belief Observation+ = New Belief

8. Bayes and Occam’s Razor

9. “All Models are wrong, but
some of them are better than
the others”

10. Model Complexity

11. Naive Bayes
“Naive” because it is based on independence
assumption
All the attributes are conditional independent
given the class

12. Naive Bayes Classifier

13. How to build a Bayesian Classifier
for prediction
Prepare Data
Features
Extraction
Select
Distribution
Model
Calculate the
Probability for
each attributes
Multiply All
Probabilities
Label with
highest
Probability

14. Advantage VS. Disadvantage
Powerful
Efficient in Space and Time
Incremental Trainer
Simple
Independant Assumption
Probability are not relevant

15. Application of Bayesian Classifier
Spam Email Filter
Natural Language Processing
Word Segmentation
Spell Checking
Machine Translation
Pattern Recognition

16. Thank You