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).

For example: if we have to calculate the probability of taking a blue ball from the second bag out of three different bags of balls,.
an email) consisting of m words.
.

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-.