AI:Regression Problems - Revision history

Hdridder: /* Linear regression with 1 variable (Univariate linear regression) */

2019-05-26T13:34:18Z

Linear regression with 1 variable (Univariate linear regression)

← Older revision		Revision as of 13:34, 26 May 2019
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	==Linear regression with 1 variable (Univariate linear regression)==		==Linear regression with 1 variable (Univariate linear regression)==

			There is some [[linear algebra]] involved.

	;h(x) = θ<sub>(0)</sub> + θ<sub>(1)</sub>*x		;h(x) = θ<sub>(0)</sub> + θ<sub>(1)</sub>*x
	:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication tables θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4		:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication tables θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4

Hdridder: /* Linear regression with 1 variable (Univariate linear regression) */

2019-04-28T14:53:00Z

Linear regression with 1 variable (Univariate linear regression)

← Older revision		Revision as of 14:53, 28 April 2019
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	;h(x) = θ<sub>(0)</sub> + θ<sub>(1)</sub>*x		;h(x) = θ<sub>(0)</sub> + θ<sub>(1)</sub>*x
	:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication tables θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4		:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication tables θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4
	The aim of the learning algorithm is to choose θ(0) and θ(1) so that the result for all input values is as close as possible to the given output values. ~~For this we use~~ a 'Squared error cost function' like:		The aim of the learning algorithm is to choose θ(0) and θ(1) so that the result for all input values is as close as possible to the given output values. The mean difference is calculated by a 'Squared error cost function' like:

	<math>J(\theta^{(0)},\theta^{(1)}) = \frac{1}{2}m*\sum_{i=1}^m (h( x^{(i)}) - y^{(i)})^2</math>		<math>J(\theta^{(0)},\theta^{(1)}) = \frac{1}{2}m*\sum_{i=1}^m (h( x^{(i)}) - y^{(i)})^2</math>

Hdridder: Hdridder moved page Supervised Learning to AI:Regression Problems

2019-04-28T09:33:05Z

Hdridder moved page Supervised Learning to AI:Regression Problems

← Older revision		Revision as of 09:33, 28 April 2019
(No difference)

Hdridder at 18:36, 24 April 2019

2019-04-24T18:36:37Z

← Older revision		Revision as of 18:36, 24 April 2019
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	A training set has m samples of x's (input variables or features) and the resulting y's (output/target variables)		A training set has m samples of x's (input variables or features) and the resulting y's (output/target variables)

	~~The~~ learning algorithm ~~finds~~ the best matching hypothesis ~~that maps~~ the input to the output values.		For regression problems the learning algorithm needs to find the best matching hypothesis to map the input to the output values.

	The hypothesis (h) can be:		The hypothesis (h) can be:

Hdridder at 14:01, 22 April 2019

2019-04-22T14:01:00Z

← Older revision		Revision as of 14:01, 22 April 2019
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	;h(x) = θ<sub>(0)</sub> + θ<sub>(1)</sub>*x		;h(x) = θ<sub>(0)</sub> + θ<sub>(1)</sub>*x
	:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication tables θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4		:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication tables θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4
	The aim of the learning algorithm is to choose θ(0) and θ(1) so that the result for all input values is as close as possible to the given output values. For this we use a cost function like:		The aim of the learning algorithm is to choose θ(0) and θ(1) so that the result for all input values is as close as possible to the given output values. For this we use a 'Squared error cost function' like:

	<math>J(\theta^{(0)},\theta^{(1)}) = \frac{1}{2}m*\sum_{i=1}^m (h( x^{(i)}) - y^{(i)})^2</math>		<math>J(\theta^{(0)},\theta^{(1)}) = \frac{1}{2}m*\sum_{i=1}^m (h( x^{(i)}) - y^{(i)})^2</math>
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	* m is the number of samples in the data set.		* m is the number of samples in the data set.
	* The square of the difference is taken to force a positive number.		* The square of the difference is taken to force a positive number.
	We need to pick θ so that the outcome of the cost function is as close as possible to 0		We need to pick θ<sub>(0)</sub> and θ<sub>(1)</sub> so that the outcome of the cost function is as close as possible to 0

Hdridder at 13:57, 22 April 2019

2019-04-22T13:57:08Z

← Older revision		Revision as of 13:57, 22 April 2019
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	A training set has m samples of x's (input variables or features) and the resulting y's (output/target variables)		A training set has m samples of x's (input variables or features) and the resulting y's (output/target variables)

	The learning algorithm finds the best matching hypothesis that ~~brings~~ the input to the output values.		The learning algorithm finds the best matching hypothesis that maps the input to the output values.

	The hypothesis can be:		The hypothesis (h) can be:

	==Linear regression with 1 variable (Univariate linear regression)==		==Linear regression with 1 variable (Univariate linear regression)==
	;h(x) = θ(0) + θ(1)*x		;h(x) = θ<sub>(0)</sub> + θ<sub>(1)</sub>*x
	:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication ~~table~~ θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4		:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication tables θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4
	The aim of the learning algorithm is to choose θ(0) and θ(1) so that the result for all input values is as close as possible to the given output values.		The aim of the learning algorithm is to choose θ(0) and θ(1) so that the result for all input values is as close as possible to the given output values. For this we use a cost function like:

	;J(θ(0),θ(1)) = ~~0.5m~~ * ~~∑<sup>~~m~~</sup><sub>i</sub>~~( h( x(i) ) = y(i) )~~²~~		<math>J(\theta^{(0)},\theta^{(1)}) = \frac{1}{2}m*\sum_{i=1}^m (h( x^{(i)}) - y^{(i)})^2</math>

	~~<math>J~~(~~\theta^{(0~~)~~},\theta^{~~(1)~~}) = \frac{1}{2}~~m*~~\sum_{i=1}^m (h( x^{(i)}) - y^{(i)})^2</math>~~		This means that for each sample in the dataset we calculate the square value of the difference between the output of our hypothesis(h) and the actual value in the training set(y). We sum it all up and multiply by half the number of rows in the dataset.
			* m is the number of samples in the data set.
			* The square of the difference is taken to force a positive number.
			We need to pick θ so that the outcome of the cost function is as close as possible to 0

Hdridder at 20:32, 8 April 2019

2019-04-08T20:32:44Z

← Older revision		Revision as of 20:32, 8 April 2019
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	;J(θ(0),θ(1)) = 0.5m * ∑<sup>m</sup><sub>i</sub>( h( x(i) ) = y(i) )²		;J(θ(0),θ(1)) = 0.5m * ∑<sup>m</sup><sub>i</sub>( h( x(i) ) = y(i) )²

	~~<nowiki>~~<math>\sum_{i=1} k²</math~~></nowiki~~>		<math>J(\theta^{(0)},\theta^{(1)}) = \frac{1}{2}m*\sum_{i=1}^m (h( x^{(i)}) - y^{(i)})^2</math>

Hdridder: /* Linear regression with 1 variable (Univariate linear regression) */

2019-04-08T19:11:58Z

Linear regression with 1 variable (Univariate linear regression)

← Older revision		Revision as of 19:11, 8 April 2019
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	;J(θ(0),θ(1)) = 0.5m * ∑<sup>m</sup><sub>i</sub>( h( x(i) ) = y(i) )²		;J(θ(0),θ(1)) = 0.5m * ∑<sup>m</sup><sub>i</sub>( h( x(i) ) = y(i) )²

	sum_{i=1}~~^m k^2~~		<nowiki><math>\sum_{i=1} k²</math></nowiki>

Hdridder at 19:04, 8 April 2019

2019-04-08T19:04:07Z

← Older revision		Revision as of 19:04, 8 April 2019
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	;J(θ(0),θ(1)) = 0.5m * ∑<sup>m</sup><sub>i</sub>( h( x(i) ) = y(i) )²		;J(θ(0),θ(1)) = 0.5m * ∑<sup>m</sup><sub>i</sub>( h( x(i) ) = y(i) )²

	\sum_{i=1}^m k^2		sum_{i=1}^m k^2

Hdridder: Created page with "Category:AI Learning from a training set. A training set has m samples of x's (input variables or features) and the resulting y's (output/target variables) The learning..."

2019-04-06T20:07:43Z

Created page with "Category:AI Learning from a training set. A training set has m samples of x's (input variables or features) and the resulting y's (output/target variables) The learning..."

New page

[[Category:AI]]

Learning from a training set.
A training set has m samples of x's (input variables or features) and the resulting y's (output/target variables)

The learning algorithm finds the best matching hypothesis that brings the input to the output values.

The hypothesis can be:

==Linear regression with 1 variable (Univariate linear regression)==
;h(x) = θ(0) + θ(1)*x
:θ are the hypothesis parameters, it is the weight a feature gets. For the multiplication table θ is just the table you are working on. So for the table of 4, in the above formula θ(1) = 4
The aim of the learning algorithm is to choose θ(0) and θ(1) so that the result for all input values is as close as possible to the given output values.

;J(θ(0),θ(1)) = 0.5m * ∑<sup>m</sup><sub>i</sub>( h( x(i) ) = y(i) )²

\sum_{i=1}^m k^2