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Data split influences the bias-variance curve for linear regression

0

$begingroup$

I have always heard about the importance of plotting bias-variance curve to see what complexity to pick.

So, I did the same when I wanted to pick an optimal parameter for ridge regularization with linear regression (fixed polynomial degree at 3). The curve is the least square cost function of the parameter lambda of regularization. However, the whole curve and minimum kept changing significantly each time I changed the random state of my split function (using one to three ratio for cross-validation).

How can I solve this problem and what value should I pick?

python cross-validation variance bias ridge-regression

share|improve this question

edited Mar 30 at 7:33

Damini Jain

1136

asked Mar 29 at 17:27

Iheb96Iheb96

11

$endgroup$

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  $begingroup$
  What do you mean by bias variance curve here? That is not a plot of the loss w.r.t. lambda.
  $endgroup$
  – Sean Owen
  Mar 30 at 8:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @SeanOwen Wasn't the bias-variance tradeoff curve of error w.r.t the model complexity which can be polynomial degree in linear regression or regularization ? If i am wrong how to pick the best value of lambda
  $endgroup$
  – Iheb96
  Mar 30 at 8:58
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I think you are talking about stats.stackexchange.com/questions/256141/… but that explains what linear regression automatically minimizes. Your plot of error vs hyperparam isnt quite that but anyway. Different lambda and min error are to some degree expected especially if your data is small and using only 2/3 to train.
  $endgroup$
  – Sean Owen
  Mar 30 at 13:43
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @SeanOwen The data base is around 1300 row and 80 feature. What would be the wise choice lambda to pick instead of a random value?
  $endgroup$
  – Iheb96
  Mar 31 at 13:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  For each value of lambda, you'd evaluate the error on the validation set with the same split and choose the lambda with lowest error. You can augment this by averaging the validation error across different splits, or k-fold splits of the data set.
  $endgroup$
  – Sean Owen
  Mar 31 at 16:33
  

  
  
  
  

add a comment | 

0

$begingroup$

I have always heard about the importance of plotting bias-variance curve to see what complexity to pick.

So, I did the same when I wanted to pick an optimal parameter for ridge regularization with linear regression (fixed polynomial degree at 3). The curve is the least square cost function of the parameter lambda of regularization. However, the whole curve and minimum kept changing significantly each time I changed the random state of my split function (using one to three ratio for cross-validation).

How can I solve this problem and what value should I pick?

python cross-validation variance bias ridge-regression

share|improve this question

edited Mar 30 at 7:33

Damini Jain

1136

asked Mar 29 at 17:27

Iheb96Iheb96

11

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What do you mean by bias variance curve here? That is not a plot of the loss w.r.t. lambda.
  $endgroup$
  – Sean Owen
  Mar 30 at 8:38
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @SeanOwen Wasn't the bias-variance tradeoff curve of error w.r.t the model complexity which can be polynomial degree in linear regression or regularization ? If i am wrong how to pick the best value of lambda
  $endgroup$
  – Iheb96
  Mar 30 at 8:58
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I think you are talking about stats.stackexchange.com/questions/256141/… but that explains what linear regression automatically minimizes. Your plot of error vs hyperparam isnt quite that but anyway. Different lambda and min error are to some degree expected especially if your data is small and using only 2/3 to train.
  $endgroup$
  – Sean Owen
  Mar 30 at 13:43
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @SeanOwen The data base is around 1300 row and 80 feature. What would be the wise choice lambda to pick instead of a random value?
  $endgroup$
  – Iheb96
  Mar 31 at 13:41
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  For each value of lambda, you'd evaluate the error on the validation set with the same split and choose the lambda with lowest error. You can augment this by averaging the validation error across different splits, or k-fold splits of the data set.
  $endgroup$
  – Sean Owen
  Mar 31 at 16:33
  

  
  
  
  

add a comment | 

$begingroup$

I have always heard about the importance of plotting bias-variance curve to see what complexity to pick.

So, I did the same when I wanted to pick an optimal parameter for ridge regularization with linear regression (fixed polynomial degree at 3). The curve is the least square cost function of the parameter lambda of regularization. However, the whole curve and minimum kept changing significantly each time I changed the random state of my split function (using one to three ratio for cross-validation).

How can I solve this problem and what value should I pick?

python cross-validation variance bias ridge-regression

share|improve this question

edited Mar 30 at 7:33

Damini Jain

1136

asked Mar 29 at 17:27

Iheb96Iheb96

11

$endgroup$

share|improve this question

edited Mar 30 at 7:33

Damini Jain

1136

asked Mar 29 at 17:27

Iheb96Iheb96

11

share|improve this question

edited Mar 30 at 7:33

Damini Jain

1136

asked Mar 29 at 17:27

Iheb96Iheb96

11

edited Mar 30 at 7:33

Damini Jain

1136

edited Mar 30 at 7:33

Damini Jain

1136

asked Mar 29 at 17:27

Iheb96Iheb96

11

asked Mar 29 at 17:27

Iheb96Iheb96

11