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Bayesian Classifiers

Master probabilistic classification from fundamental decision theory to advanced Bayesian networks. Learn how to make optimal decisions under uncertainty with real-world applications from medical diagnosis to spam detection.

Bayesian Decision Theory & Bayes' Theorem
Module 1
Understand the probabilistic framework for decision-making. Learn conditional risk, Bayes decision rule, Bayes optimal classifier, and the fundamental Bayes' theorem. Compare discriminative vs generative models with medical diagnosis and email spam examples.

Topics Covered:

Conditional Risk & Decision Rules
Bayes Optimal Classifier
Discriminative vs Generative Models
Bayes' Theorem Components
Posterior, Prior, Likelihood
Medical Diagnosis Examples
Maximum Likelihood Estimation
Module 2
Master parameter estimation using maximum likelihood. Learn likelihood functions, log-likelihood to avoid underflow, and apply MLE to Gaussian and Bernoulli distributions with wine quality prediction examples.

Topics Covered:

Likelihood Function
Log-Likelihood
Parameter Estimation
Gaussian Distribution MLE
Bernoulli Distribution MLE
Wine Quality Example
Naïve Bayes Classifier
Module 3
Learn the simplest yet powerful Bayesian classifier. Understand attribute independence assumption, probability estimation for discrete and continuous attributes, Laplacian correction, and complete step-by-step calculations with watermelon dataset 3.0 and text classification examples.

Topics Covered:

Attribute Independence Assumption
Discrete & Continuous Probability Estimation
Gaussian Distribution for Continuous Attributes
Laplacian Correction
Watermelon Dataset 3.0 Example
Text Classification Applications
Semi-Naïve Bayes Classifiers
Module 4
Relax the strict independence assumption with semi-naive approaches. Master ODE, SPODE, TAN, and AODE methods. Learn dependency relationship modeling and apply to customer segmentation with dependency diagrams.

Topics Covered:

One-Dependent Estimator (ODE)
SPODE (Super-Parent ODE)
TAN (Tree Augmented Naïve Bayes)
AODE (Averaged ODE)
Dependency Relationship Diagrams
Customer Segmentation Example
Bayesian Networks
Module 5
Explore probabilistic graphical models for complex dependencies. Learn DAG structure, conditional probability tables (CPT), conditional independence, D-separation, structure learning with AIC/BIC/MDL, and inference methods with medical diagnosis network examples.

Topics Covered:

DAG Structure & CPT
Conditional Independence
D-separation & Moral Graph
Structure Learning (AIC, BIC, MDL)
Exact & Approximate Inference
Medical Diagnosis Networks
EM Algorithm & Approximate Inference
Module 6
Handle latent variables and missing data with the EM algorithm. Learn E-step and M-step, Gibbs sampling, variational inference, ELBO, KL divergence, and plate notation with missing data handling examples.

Topics Covered:

EM Algorithm (E-step & M-step)
Marginal Likelihood
Gibbs Sampling
Variational Inference
ELBO & KL Divergence
Plate Notation & Missing Data

Suggested Learning Paths

Foundation Path

Start with probabilistic fundamentals

  • Bayesian Decision Theory
  • Maximum Likelihood Estimation
  • Naive Bayes

Advanced Path

Master complex probabilistic models

  • Semi-Naive Bayes
  • Bayesian Networks
  • EM Algorithm

Complete Path

Comprehensive understanding of Bayesian methods

  • All Modules
  • Real-World Applications
  • Inference Methods

Why Learn Bayesian Classifiers?

Probabilistic Foundation

Bayesian methods provide a rigorous probabilistic framework for decision-making under uncertainty, essential for understanding modern machine learning.

Interpretable Predictions

Bayesian classifiers provide probability estimates for each class, not just predictions, enabling risk assessment and decision-making in critical applications like medical diagnosis.

Handles Missing Data

Bayesian methods naturally handle missing data and latent variables through the EM algorithm and probabilistic inference, making them robust for real-world datasets.

Fast & Efficient

Naive Bayes classifiers are extremely fast for both training and prediction, making them ideal for real-time applications like spam detection and text classification.

Models Complex Dependencies

Bayesian networks can model complex conditional dependencies between variables, enabling sophisticated reasoning in domains like medical diagnosis and risk assessment.

Industry Applications

Widely used in spam filtering, medical diagnosis, recommendation systems, and natural language processing. Essential knowledge for any data scientist working with probabilistic models.

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