Bayesian network - Revision history

Rice at 18:55, 24 May 2024

2024-05-24T18:55:06Z

← Older revision		Revision as of 18:55, 24 May 2024
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	By relaxing some assumptions, [[Naive Bayes]] reduces the computational complexity.		By relaxing some assumptions, [[Naive Bayes]] reduces the computational complexity.

			= Training =

			After the structure of a Bayesian network is defined, its parameters (the conditional probabilities) are estimated by training data. The model structure is then refined and the parameters updated again.

			= Data-driven learning =

			Instead of using domain knowledge, one can use learning algorithms to automatically learn the dependencies between the variables using data.

			An example algorithm is BIC.

	= Analysis =		= Analysis =

Rice at 18:44, 24 May 2024

2024-05-24T18:44:19Z

@@ Line 2: / Line 2: @@
 The '''Bayesian network''' is a network probabilistic, graphical model that describes dependencies.
 = Properties =
@@ Line 33: / Line 27: @@
 Bayesian networks are interpretable.
-However, they are computationally expensive on higher dimensional data.
+However, they are computationally expensive on higher dimensional data. We need to compute a large number of combinations of feature input probabilities. This is also the motivation behind [[Naive Bayes]]

Rice: /* Joint probability */

2024-05-24T18:36:37Z

Joint probability

← Older revision		Revision as of 18:36, 24 May 2024
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	</math>		</math>

	By relaxing some assumptions, [[~~Naiive~~ Bayes]] reduces the computational complexity.		By relaxing some assumptions, [[Naive Bayes]] reduces the computational complexity.

	= Analysis =		= Analysis =

Rice at 06:07, 24 May 2024

2024-05-24T06:07:42Z

← Older revision		Revision as of 06:07, 24 May 2024
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	By relaxing some assumptions, [[Naiive Bayes]] reduces the computational complexity.		By relaxing some assumptions, [[Naiive Bayes]] reduces the computational complexity.

			= Analysis =

			Bayesian networks are interpretable.

			However, they are computationally expensive on higher dimensional data.

Rice: /* Application */

2024-05-24T06:06:45Z

Application

← Older revision		Revision as of 06:06, 24 May 2024
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	Bayesian networks have applications in machine learning tasks that deal with dependent features.		Bayesian networks have applications in machine learning tasks that deal with dependent features.

	An example is ~~[[Part-of-speech]]~~, where ~~words are grammatically classified in~~ a ~~string. This involves a complex network of dependencies between object, subject, verbs, nouns, etc. that can be modeled and optimized with a Bayesian network~~.		An example is weather forecasting, where weather at each given time is strongly dependent on weather at a previous time.

	= Properties =		= Properties =

Rice: /* DAG */

2024-05-24T06:03:02Z

DAG

← Older revision		Revision as of 06:03, 24 May 2024
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	Each edge identifies a causal relation, usually temporal: something that happened in the future cannot cause something to happen in the past. As such, the graph is ''acyclic''.		Each edge identifies a causal relation, usually temporal: something that happened in the future cannot cause something to happen in the past. As such, the graph is ''acyclic''.

			Each node is a conditional probability: Given that the parents happen, what is the probability of the node event happening.

	= Joint probability =		= Joint probability =

Rice at 05:56, 24 May 2024

2024-05-24T05:56:16Z

← Older revision		Revision as of 05:56, 24 May 2024
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	P(x_1, x_2,\ldots,x_n)=\prod_{i=1}^nP(x_i\|Parents(x_i))		P(x_1, x_2,\ldots,x_n)=\prod_{i=1}^nP(x_i\|Parents(x_i))
	</math>		</math>

			By relaxing some assumptions, [[Naiive Bayes]] reduces the computational complexity.

Rice at 05:54, 24 May 2024

2024-05-24T05:54:58Z

← Older revision		Revision as of 05:54, 24 May 2024
Line 16:		Line 16:

	Each edge identifies a causal relation, usually temporal: something that happened in the future cannot cause something to happen in the past. As such, the graph is ''acyclic''.		Each edge identifies a causal relation, usually temporal: something that happened in the future cannot cause something to happen in the past. As such, the graph is ''acyclic''.

			= Joint probability =

			Bayesian networks are primarily used to calculate the ''joint probability'' of an event given its dependencies. This can be done with the following formula

			<math>
			P(x_1, x_2,\ldots,x_n)=\prod_{i=1}^nP(x_i\|Parents(x_i))
			</math>

Rice at 05:51, 24 May 2024

2024-05-24T05:51:52Z

← Older revision		Revision as of 05:51, 24 May 2024
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	An example is [[Part-of-speech]], where words are grammatically classified in a string. This involves a complex network of dependencies between object, subject, verbs, nouns, etc. that can be modeled and optimized with a Bayesian network.		An example is [[Part-of-speech]], where words are grammatically classified in a string. This involves a complex network of dependencies between object, subject, verbs, nouns, etc. that can be modeled and optimized with a Bayesian network.

			= Properties =

			== DAG ==

			Bayesian networks are directed, acyclic [[graph]]s.

			Each edge identifies a causal relation, usually temporal: something that happened in the future cannot cause something to happen in the past. As such, the graph is ''acyclic''.

Rice: Created page with "Category:Machine Learning The '''Bayesian network''' is a network probabilistic, graphical model that describes dependencies. = Application = Bayesian networks have applications in machine learning tasks that deal with dependent features. An example is Part-of-speech, where words are grammatically classified in a string. This involves a complex network of dependencies between object, subject, verbs, nouns, etc. that can be modeled and optimized with a Bayesia..."

2024-05-24T05:44:59Z

Created page with "Category:Machine Learning The '''Bayesian network''' is a network probabilistic, graphical model that describes dependencies. = Application = Bayesian networks have applications in machine learning tasks that deal with dependent features. An example is Part-of-speech, where words are grammatically classified in a string. This involves a complex network of dependencies between object, subject, verbs, nouns, etc. that can be modeled and optimized with a Bayesia..."

New page

[[Category:Machine Learning]]

The '''Bayesian network''' is a network probabilistic, graphical model that describes dependencies.

= Application =

Bayesian networks have applications in machine learning tasks that deal with dependent features.

An example is [[Part-of-speech]], where words are grammatically classified in a string. This involves a complex network of dependencies between object, subject, verbs, nouns, etc. that can be modeled and optimized with a Bayesian network.