Rice: /* How it works */

2024-05-24T19:18:02Z

How it works

← Older revision		Revision as of 19:18, 24 May 2024
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	P(C\|X_1,X_2,X_3)\propto P(X_1\|C)P(X_2\|C)P(X_3\|C)		P(C\|X_1,X_2,X_3)\propto P(X_1\|C)P(X_2\|C)P(X_3\|C)
	</math>		</math>

			We can divide P(C\|X) over P(notC\|X) to avoid calculating P(X1,X2,X3). We can then apply a log to avoid zero denominators.

Rice: Created page with "Category:Machine Learning '''Naive Bayes''' is an approach to Bayesian networks that simplify the computation of joint probability of an outcome based on high dimensional features. = Motivation = Consider binary classification output C is dependent on binary features X1~X3. By Bayes theorem, we can compute C's probability based on the features with Bayes' theorem: $P(C|X_1,X_2,X_3)=\frac{P(X_1,X_2,X_3|C)P(C)}{P(X_1,X_2,X_3)}$ This, in turn,..."

2024-05-24T18:50:29Z

Created page with "Category:Machine Learning '''Naive Bayes''' is an approach to Bayesian networks that simplify the computation of joint probability of an outcome based on high dimensional features. = Motivation = Consider binary classification output C is dependent on binary features X1~X3. By Bayes theorem, we can compute C's probability based on the features with Bayes' theorem: <math> P(C|X_1,X_2,X_3)=\frac{P(X_1,X_2,X_3|C)P(C)}{P(X_1,X_2,X_3)} </math> This, in turn,..."

New page

[[Category:Machine Learning]]

'''Naive Bayes''' is an approach to [[Bayesian network]]s that simplify the computation of joint probability of an outcome based on high dimensional features.

= Motivation =

Consider binary classification output C is dependent on binary features X1~X3. By Bayes theorem, we can compute C's probability based on the features with [[Bayes' theorem]]:

<math>
P(C|X_1,X_2,X_3)=\frac{P(X_1,X_2,X_3|C)P(C)}{P(X_1,X_2,X_3)}
</math>

This, in turn, mean that we need to estimate the probability of every combination of features (0 0 0, 0 0 1...). This is computationally expensive.

= How it works =
By assuming that the features are independent, Naive Bayes simplifies the computation to

<math>
P(C|X_1,X_2,X_3)\propto P(X_1|C)P(X_2|C)P(X_3|C)
</math>

Naive Bayes - Revision history

Rice: /* How it works */