**The technique is easiest to understand when described using binary or categorical input values. **

**tween naive Bayes and logistic regression is that logistic regression is a discrimina-tive classiﬁer while naive Bayes is a generative classiﬁer. **

**EECS E6720 Bayesian Models for Machine Learning Columbia University, Fall 2016 Lecture 1, 9/8/2016 Instructor: John Paisley Bayes rule pops out of basic manipulations of probability distributions. . **

**. **

**It is based on the Bayes Theorem. **

**e. The attribute conditional independence assumption of naive Bayes essentially ignores attribute dependencies and is often violated. . **

**Bayes**’ theorem states the following.

**This is possible because we will be computing P(djc)P(c) P(d) for each possible class. The better that metric reflects label similarity, the better the classified will be. 3 Naive Bayes as a Special Case of Bayes Networks A Bayes Network is a directed graph that represent a family of probability distributions. **

**g. 3 Total Probability Formula (review) 3. **

**. **

**Different types of classification •Exemplar-based: transfer category labels from examples with most similar features •What similarity function? What parameters? •Linear classifier: confidence in positive label is a weighted sum of features •What are the weights? •Non-linear classifier: predictions based on more complex function of. **

**. These exemplify two ways of doing classiﬁcation. **

**9. Training the Naive Bayes classisifer corresponds to estimating $\vec{\theta}_{jc}$ for all $j$ and $c$ and storing them in the respective conditional probability tables (CPT). **

**.**

**Bayes** theorem plays a critical role in probabilistic learning and **classification**.

**The multinomial view: Let us assume we have d possible words in our dictionary. **

**Usingthisassumptionsimpliﬁesthepredictionalgorithm. So, for now, let's pretend the Naive Bayes assumption holds. This is the basic concept of Bayesian Learning;. **

**On the other hand, although a Bayesian network can represent arbitrary attribute dependencies, learning an optimal Bayesian network classifier from data is intractable. Note: This tutorial assumes that you are using Python 3. . . Naive Bayes Classifier REVIEW: Bayesian Methods Our focus this lecture: Learning and classification methods based on probability theory. . **

**. **

**KNN and Naive Bayes are widely used Machine Learning algorithms. e. **

**Different types of classification •Exemplar-based: transfer category labels from examples with most similar features •What similarity function? What parameters? •Linear classifier: confidence in positive label is a weighted sum of features •What are the weights? •Non-linear classifier: predictions based on more complex function of. **

**. **

**A Naïve Bayes classifier is an algorithm that uses Bayes' theorem to classify objects. **

** In-lecture:** Section 2 and Section 4.

**if ~y(= y 1;y 2;:::;y i;:::;y M) where each y i is binary-, discrete-, or continuous-. **

BayesClassiﬁer 3 1.