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edit approved Aug 31, 2013 at 20:38
Comp_Warrior
edit approved Aug 31, 2013 at 20:38
Comp_Warrior
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Problem with singular covariance matrices when doing gaussianGaussian process regression

I'm working with gaussianGaussian process regression. Currently I start testing differntdifferent covariance functions and compositions to see what type of data they could describe best. I made an own implementation in Java.

My problem: Most of the covariance funtionsfunctions I use result in a singular covariance matrix which is not invertableinvertible.

  1. Should'tShouldn't the proposed covariance functions/estimators produce only invertableinvertible matrices?

  2. Are there methods or hints for regularizing the matrices? Or can that be done by using other values or ranges as inputs? May the introduction of error terms would help as well? Most problems I get with integer $x$ inputs to the brownianBrownian motion covariance function $k(x,x') = \min(x,x')$. When I am using this the matrix it is always singular.

Thank you

Problem with singular covariance matrices when doing gaussian process regression

I'm working with gaussian process regression. Currently I start testing differnt covariance functions and compositions to see what type of data they could describe best. I made an own implementation in Java.

My problem: Most of the covariance funtions I use result in a singular covariance matrix which is not invertable.

  1. Should't the proposed covariance functions/estimators produce only invertable matrices?

  2. Are there methods or hints for regularizing the matrices? Or can that be done by using other values or ranges as inputs? May the introduction of error terms would help as well? Most problems I get with integer $x$ inputs to the brownian motion covariance function $k(x,x') = \min(x,x')$. When I am using this the matrix it is always singular.

Thank you

Problem with singular covariance matrices when doing Gaussian process regression

I'm working with Gaussian process regression. Currently I start testing different covariance functions and compositions to see what type of data they could describe best. I made an own implementation in Java.

My problem: Most of the covariance functions I use result in a singular covariance matrix which is not invertible.

  1. Shouldn't the proposed covariance functions/estimators produce only invertible matrices?

  2. Are there methods or hints for regularizing the matrices? Or can that be done by using other values or ranges as inputs? May the introduction of error terms would help as well? Most problems I get with integer $x$ inputs to the Brownian motion covariance function $k(x,x') = \min(x,x')$. When I am using this the matrix it is always singular.

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user88
user88

Problem with singular covariance matrices when doing gaussian process covariance function singular matrixregression

i'm,I'm working with gaussian process regression. Currently iI start testing differnt covariance functions and compositions to see what type of data they could describe best. I made an own implementation in javaJava.

My Problem:My problem: Most of the covariance funtions iI use, result in a singular covariance matrix which is not invertable.

Question 1: Should't the proposed covariance functions/estimators produce only invertable matrices?

Question 2: Are there methods or hints for regularizing the matrices? Or can that be done by using other values or ranges as inputs? May the introduction of error terms would help as well ? Most Problems i get with interger x inputs to the brownian motion cov function k(x,x') = min(x,x'). When i am using this the matrix is always singular.

  1. Should't the proposed covariance functions/estimators produce only invertable matrices?

  2. Are there methods or hints for regularizing the matrices? Or can that be done by using other values or ranges as inputs? May the introduction of error terms would help as well? Most problems I get with integer $x$ inputs to the brownian motion covariance function $k(x,x') = \min(x,x')$. When I am using this the matrix it is always singular.

Thank you

gaussian process covariance function singular matrix

i'm, working with gaussian process regression. Currently i start testing differnt covariance functions and compositions to see what type of data they could describe best. I made an own implementation in java.

My Problem: Most of the covariance funtions i use, result in a singular covariance matrix which is not invertable.

Question 1: Should't the proposed covariance functions/estimators produce only invertable matrices?

Question 2: Are there methods or hints for regularizing the matrices? Or can that be done by using other values or ranges as inputs? May the introduction of error terms would help as well ? Most Problems i get with interger x inputs to the brownian motion cov function k(x,x') = min(x,x'). When i am using this the matrix is always singular.

Thank you

Problem with singular covariance matrices when doing gaussian process regression

I'm working with gaussian process regression. Currently I start testing differnt covariance functions and compositions to see what type of data they could describe best. I made an own implementation in Java.

My problem: Most of the covariance funtions I use result in a singular covariance matrix which is not invertable.

  1. Should't the proposed covariance functions/estimators produce only invertable matrices?

  2. Are there methods or hints for regularizing the matrices? Or can that be done by using other values or ranges as inputs? May the introduction of error terms would help as well? Most problems I get with integer $x$ inputs to the brownian motion covariance function $k(x,x') = \min(x,x')$. When I am using this the matrix it is always singular.

Thank you

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Andreas
Andreas
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gaussian process covariance function singular matrix

i'm, working with gaussian process regression. Currently i start testing differnt covariance functions and compositions to see what type of data they could describe best. I made an own implementation in java.

My Problem: Most of the covariance funtions i use, result in a singular covariance matrix which is not invertable.

Question 1: Should't the proposed covariance functions/estimators produce only invertable matrices?

Question 2: Are there methods or hints for regularizing the matrices? Or can that be done by using other values or ranges as inputs? May the introduction of error terms would help as well ? Most Problems i get with interger x inputs to the brownian motion cov function k(x,x') = min(x,x'). When i am using this the matrix is always singular.

Thank you