Gaussian Process Regression - Revision history

Chr: /* result file */

2008-04-23T14:08:11Z

result file

← Older revision		Revision as of 14:08, 23 April 2008
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	Every covariance function has a number of parameters, which have to be determined. If you check this box, a gradient descent optimization technique is executed, which tries to find an optimal set of parameters, which are stored afterwards in a parameter file. If you don´t want to optimize, than the algorithm tries at first to read the parameter file. If this file does not exist than standardparameters are used, which are not optimal.		Every covariance function has a number of parameters, which have to be determined. If you check this box, a gradient descent optimization technique is executed, which tries to find an optimal set of parameters, which are stored afterwards in a parameter file. If you don´t want to optimize, than the algorithm tries at first to read the parameter file. If this file does not exist than standardparameters are used, which are not optimal.
	===result file===		===result file===
−	name of file in which the results ~~should be~~ saved.	+	name of file in which the results are saved.
		+
	==Literature==		==Literature==
	*Rasmussen,C. and C. Williams: Gaussian Processes for Machine Learning; The MIT Press, 2006. ISBN 0-262-18253-X		*Rasmussen,C. and C. Williams: Gaussian Processes for Machine Learning; The MIT Press, 2006. ISBN 0-262-18253-X

Chr: /* mean function */

2008-04-23T14:07:31Z

mean function

← Older revision		Revision as of 14:07, 23 April 2008
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	*Extended Neural Network covariance function: 8		*Extended Neural Network covariance function: 8
	===mean function===		===mean function===
−	A value of one indicates, that a linear regression is applied simulatiously. In many extrapolation cases this will increase prediction performance.	+	A value of one indicates, that a linear regression is applied simulatiously. In many extrapolation cases this will increase prediction performance. A value of zero, skips that part.
		+
	===do optimization===		===do optimization===
	Every covariance function has a number of parameters, which have to be determined. If you check this box, a gradient descent optimization technique is executed, which tries to find an optimal set of parameters, which are stored afterwards in a parameter file. If you don´t want to optimize, than the algorithm tries at first to read the parameter file. If this file does not exist than standardparameters are used, which are not optimal.		Every covariance function has a number of parameters, which have to be determined. If you check this box, a gradient descent optimization technique is executed, which tries to find an optimal set of parameters, which are stored afterwards in a parameter file. If you don´t want to optimize, than the algorithm tries at first to read the parameter file. If this file does not exist than standardparameters are used, which are not optimal.

Chr at 13:22, 23 April 2008

2008-04-23T13:22:24Z

← Older revision		Revision as of 13:22, 23 April 2008
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	* Run the model and enjoy ;)<br>		* Run the model and enjoy ;)<br>
	* To see information about current model execution, choose Logs->Model Info Log<br>		* To see information about current model execution, choose Logs->Model Info Log<br>
−	* The ~~Predictions~~ will be saved in a file named result.txt<br>	+	* The predictions will be saved in a file named result.txt<br>

	==Manual==		==Manual==

Chr at 13:14, 23 April 2008

2008-04-23T13:14:56Z

← Older revision		Revision as of 13:14, 23 April 2008
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	==Download==		==Download==
−	[http://jams.uni-jena.de/jamswiki/uploads/9/9a/Predict.zip zip]	+	[http://jams.uni-jena.de/jamswiki/uploads/9/9a/Predict.zip zip] <br>
	[http://jams.uni-jena.de/jamswiki/uploads/9/9e/Poster.pdf Poster]		[http://jams.uni-jena.de/jamswiki/uploads/9/9e/Poster.pdf Poster]
	==Quick start==		==Quick start==

Chr at 13:14, 23 April 2008

2008-04-23T13:14:47Z

← Older revision		Revision as of 13:14, 23 April 2008
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	==Download==		==Download==
	[http://jams.uni-jena.de/jamswiki/uploads/9/9a/Predict.zip zip]		[http://jams.uni-jena.de/jamswiki/uploads/9/9a/Predict.zip zip]
−		+	[http://jams.uni-jena.de/jamswiki/uploads/9/9e/Poster.pdf Poster]
	==Quick start==		==Quick start==

Chr at 10:03, 23 April 2008

2008-04-23T10:03:15Z

← Older revision		Revision as of 10:03, 23 April 2008
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	NOTICE: you shouldn´t enable both boxes at the same time.		NOTICE: you shouldn´t enable both boxes at the same time.
	===reduced training size===		===reduced training size===
−	If you have a large number of datasets, training will be computationally extremly expensive. It is also possible, that you will be running out of memory. ~~Thats~~ why you can reduce the number of datasets used for training. The procedure which is used for this reduction tries to select datasets which are as different as possible. If you do not want to reduce your number of datasets, simply choose a number which is larger than the amount of datasets you have.	+	If you have a large number of datasets, training will be computationally extremly expensive. It is also possible, that you will be running out of memory. That is why you can reduce the number of datasets used for training. The procedure which is used for this reduction tries to select datasets which are as different as possible. If you do not want to reduce your number of datasets, simply choose a number which is larger than the amount of datasets you have.
	==covariance function==		==covariance function==
	Covariance Function which is used for regression. The following values are possible:		Covariance Function which is used for regression. The following values are possible:
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	name of file in which the results should be saved.		name of file in which the results should be saved.
	==Literature==		==Literature==
−	*~~Carl Edward~~ Rasmussen ~~and Christopher K~~. I. Williams: Gaussian Processes for Machine Learning; The MIT Press, 2006. ISBN 0-262-18253-X	+	*Rasmussen,C. and C. Williams: Gaussian Processes for Machine Learning; The MIT Press, 2006. ISBN 0-262-18253-X
−	*	+	*Scholkopf, B. and A. Smola: Learning with Kernels: Support Vector Machines, Regularization, Optimization and Beyond. MIT Press Cambridge, MA, USA, 2001
		+	*Stein, M. Interpolation of Spatial Data: Some Theory for Kriging. Springer, 1999.
		+	*Blight, B. and L. Ott.: A Bayesian approach to model inadequacy for polynomial regression. Biometrika, 62(1):79, 1975.
		+	*Berger, J. O. S: Statistical Decision Theory and Bayesian Analysis. Spring, New York. 1985

Chr at 09:54, 23 April 2008

2008-04-23T09:54:44Z

← Older revision		Revision as of 09:54, 23 April 2008
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	==Manual==		==Manual==
−	After starting JAMS you will see a window like ~~that~~ in figure 1.	+	After starting JAMS you will see a window like the one in figure 1.
	[[Image:Window prediction.jpg\|thumb\|Figure 1]]		[[Image:Window prediction.jpg\|thumb\|Figure 1]]
	There are some model attributes and parameters which can be changed.		There are some model attributes and parameters which can be changed.
	===data file===		===data file===
	The data file is a simple text file. It contains all time series, which should be used for training, validation and verification. The datafile has a table like structure.		The data file is a simple text file. It contains all time series, which should be used for training, validation and verification. The datafile has a table like structure.
−	Each row consists of all relevant measurements at time t, which are represented as tab seperated floating point numbers. It is important that every row has the same number of elements. The value, which ~~should~~ be predicted, must be the last element in each row. In cases in which this value is unknown, simply write an arbitary number in that column, but remember that you should not use them in the training process. A simple data file will look like that:	+	Each row consists of all relevant measurements at time t, which are represented as tab seperated floating point numbers. It is important that every row has the same number of elements. The value, which is supposed to be predicted, must be the last element in each row. In cases in which this value is unknown, simply write an arbitary number in that column, but remember that you should not use them in the training process. A simple data file will look like that:
	1.0 0.0 0.5 11.1 -0.1		1.0 0.0 0.5 11.1 -0.1
	0.0 0.2 0.3 11.0 -0.5		0.0 0.2 0.3 11.0 -0.5
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	7.1.2007 3.0 5.2 1.0 13.6 0.0		7.1.2007 3.0 5.2 1.0 13.6 0.0
	8.1.2007 0.8 1.1 0.5 13.6 -0.7		8.1.2007 0.8 1.1 0.5 13.6 -0.7
−	~~so gaps~~ should look like that:	+	Gaps should look like that:
	3;4		3;4
	===enable crossvalidation===		===enable crossvalidation===
	If you check this box, a crossvalidation is performed. You can specify the number of crossvalidation iterations in the textfield below.		If you check this box, a crossvalidation is performed. You can specify the number of crossvalidation iterations in the textfield below.
	===enable splitvalidation===		===enable splitvalidation===
−	If you check this box, a ~~splitalidation~~ is performed. You can specify the number of datasets which are used for training in the textfield below. The remaining datasets are used for validation.<br>	+	If you check this box, a splitvalidation is performed. You can specify the number of datasets which are used for training in the textfield below. The remaining datasets are used for validation.<br>
	NOTICE: you shouldn´t enable both boxes at the same time.		NOTICE: you shouldn´t enable both boxes at the same time.
	===reduced training size===		===reduced training size===
−	If you have a large number of datasets, training will be computationally extremly expensive. It is also possible, that you will running out of memory. Thats why you can reduce the number of datasets used for training. The procedure which is used for this reduction tries to select datasets which are as different as possible. If you ~~don´t~~ want to reduce your number of datasets, simply choose a number which is larger than the amount of datasets you have.	+	If you have a large number of datasets, training will be computationally extremly expensive. It is also possible, that you will be running out of memory. Thats why you can reduce the number of datasets used for training. The procedure which is used for this reduction tries to select datasets which are as different as possible. If you do not want to reduce your number of datasets, simply choose a number which is larger than the amount of datasets you have.
	==covariance function==		==covariance function==
	Covariance Function which is used for regression. The following values are possible:		Covariance Function which is used for regression. The following values are possible:
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	name of file in which the results should be saved.		name of file in which the results should be saved.
	==Literature==		==Literature==
		+	*Carl Edward Rasmussen and Christopher K. I. Williams: Gaussian Processes for Machine Learning; The MIT Press, 2006. ISBN 0-262-18253-X
		+	*

Chr at 09:47, 23 April 2008

2008-04-23T09:47:02Z

← Older revision		Revision as of 09:47, 23 April 2008
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	==Abstract==		==Abstract==
−	During the last decade the number of publications on the field of kernel machines has increased enormously. Widely known are studies on Support Vector Machines (SVM), much activity was also spent on applying Gaussian processes to problems on the area of machine learning. This method represents an universal and practical approach to learning with kernel machines. Because of its solid statistical foundation learning with Gaussian processes has advantages over other empirical approaches concerning interpretability of model predictions. It also offers an established framework for model selection and subsequent model setup.	+	During the last decade the number of publications on the field of kernel machines has increased enormously. Widely known are studies on Support Vector Machines (SVM), much activity was also spent on applying Gaussian processes to problems on the area of machine learning. This method represents a universal and practical approach to learning with kernel machines. Because of its solid statistical foundation learning with Gaussian processes has advantages over other empirical approaches concerning interpretability of model predictions. It also offers an established framework for model selection and subsequent model setup.

	Because of ongoing theoretical and practical developments during the last years, Gaussian processes are nowadays considered as a serious alternative in the area of supervised learning. Because of their promising characteristics these methods are especially suited for Rainfall-Runoff-Modelling. Nevertheless, so far they have not attracted much interest in this domain.		Because of ongoing theoretical and practical developments during the last years, Gaussian processes are nowadays considered as a serious alternative in the area of supervised learning. Because of their promising characteristics these methods are especially suited for Rainfall-Runoff-Modelling. Nevertheless, so far they have not attracted much interest in this domain.
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	*Neural Network covariance function: 6		*Neural Network covariance function: 6
	*Extended Neural Network covariance function: 8		*Extended Neural Network covariance function: 8
−	==	+	===mean function===
		+	A value of one indicates, that a linear regression is applied simulatiously. In many extrapolation cases this will increase prediction performance.
		+	===do optimization===
		+	Every covariance function has a number of parameters, which have to be determined. If you check this box, a gradient descent optimization technique is executed, which tries to find an optimal set of parameters, which are stored afterwards in a parameter file. If you don´t want to optimize, than the algorithm tries at first to read the parameter file. If this file does not exist than standardparameters are used, which are not optimal.
		+	===result file===
		+	name of file in which the results should be saved.
	==Literature==		==Literature==

Chr at 09:36, 23 April 2008

2008-04-23T09:36:00Z

← Older revision		Revision as of 09:36, 23 April 2008
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	If you check this box, a crossvalidation is performed. You can specify the number of crossvalidation iterations in the textfield below.		If you check this box, a crossvalidation is performed. You can specify the number of crossvalidation iterations in the textfield below.
	===enable splitvalidation===		===enable splitvalidation===
−	If you check this box, a splitalidation is performed. You can specify the number of datasets which are used for training in the textfield below. The remaining datasets are used for validation.	+	If you check this box, a splitalidation is performed. You can specify the number of datasets which are used for training in the textfield below. The remaining datasets are used for validation.<br>
		+	NOTICE: you shouldn´t enable both boxes at the same time.
	===reduced training size===		===reduced training size===
−		+	If you have a large number of datasets, training will be computationally extremly expensive. It is also possible, that you will running out of memory. Thats why you can reduce the number of datasets used for training. The procedure which is used for this reduction tries to select datasets which are as different as possible. If you don´t want to reduce your number of datasets, simply choose a number which is larger than the amount of datasets you have.
		+	==covariance function==
		+	Covariance Function which is used for regression. The following values are possible:
		+	*Squared Exponential: 2
		+	*Matérn Class Function: 3
		+	*Rational quadratic: 5
		+	*Neural Network covariance function: 6
		+	*Extended Neural Network covariance function: 8
		+	==
	==Literature==		==Literature==

Chr at 09:26, 23 April 2008

2008-04-23T09:26:25Z

← Older revision		Revision as of 09:26, 23 April 2008
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	3.0 5.2 1.0 13.6 0.0		3.0 5.2 1.0 13.6 0.0
	0.8 1.1 0.5 13.6 -0.7		0.8 1.1 0.5 13.6 -0.7
		+	===input dimension===
		+	Specifies the number of columns -1 in the data file. (e.g 4 in the above case)
		+	===relevant timesteps===
		+	Number of timesteps, which should be used for each prediction. That means if you use a relevant time k = 1, than the prediction is based only on the current time step t. With a relevant time of k = 2, timestep t and t-1 will be used.
		+	===gaps===
		+	If there are gaps in the datafile, than you should add the row before and after the gap here. Each value must be seperated by a ";"
		+	Here is an example of a file with one gap between line 3 and 4
		+	1.1.2007 1.0 0.0 0.5 11.1 -0.1
		+	2.1.2007 0.0 0.2 0.3 11.0 -0.5
		+	3.1.2007 2.3 3.1 1.0 10.5 1.0
		+	6.1.2007 5.0 6.1 4.2 11.5 2.1
		+	7.1.2007 3.0 5.2 1.0 13.6 0.0
		+	8.1.2007 0.8 1.1 0.5 13.6 -0.7
		+	so gaps should look like that:
		+	3;4
		+	===enable crossvalidation===
		+	If you check this box, a crossvalidation is performed. You can specify the number of crossvalidation iterations in the textfield below.
		+	===enable splitvalidation===
		+	If you check this box, a splitalidation is performed. You can specify the number of datasets which are used for training in the textfield below. The remaining datasets are used for validation.
		+	===reduced training size===
		+
	==Literature==		==Literature==