Test RMSE of polynomial regression drops when using more variables?
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I am testing polynomial regression for a data set of 50 variables and a sample size of 5000. I ordered the coefficients of the linear model from high to low and then made different models using the p most explanatory variables. The RMSE values of these models are shown in the following figures. For polynomial regression of degree=2 everything seems to be normal, but for degree=3 something strange happens. (The dotted line shows the location of minimum RMSE)
I cannot understand why the test RMSE drops when using more than 27 variables? It seems to start underfitting rather than overfitting with more variables. Interestingly, this happens at the same time as the training RMSE becomes around 1e-14. Meanwhile, the adjused R-squared shows the following strange behaviour at that moment:
Am I using just too many dimensions for this polynomial regression? Or is there another reason why this is happening? I would love to understand what is going on. I will quickly move on to better algorithms, but I just wanted to make a benchmark for my ML project. Thanks in advance!
machine-learning regression supervised-learning model-selection
asked 12 mins ago
SalmonSalmon
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I am testing polynomial regression for a data set of 50 variables and a sample size of 5000. I ordered the coefficients of the linear model from high to low and then made different models using the p most explanatory variables. The RMSE values of these models are shown in the following figures. For polynomial regression of degree=2 everything seems to be normal, but for degree=3 something strange happens. (The dotted line shows the location of minimum RMSE)
I cannot understand why the test RMSE drops when using more than 27 variables? It seems to start underfitting rather than overfitting with more variables. Interestingly, this happens at the same time as the training RMSE becomes around 1e-14. Meanwhile, the adjused R-squared shows the following strange behaviour at that moment:
Am I using just too many dimensions for this polynomial regression? Or is there another reason why this is happening? I would love to understand what is going on. I will quickly move on to better algorithms, but I just wanted to make a benchmark for my ML project. Thanks in advance!
machine-learning regression supervised-learning model-selection
asked 12 mins ago
SalmonSalmon
1
New contributor
Salmon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
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I am testing polynomial regression for a data set of 50 variables and a sample size of 5000. I ordered the coefficients of the linear model from high to low and then made different models using the p most explanatory variables. The RMSE values of these models are shown in the following figures. For polynomial regression of degree=2 everything seems to be normal, but for degree=3 something strange happens. (The dotted line shows the location of minimum RMSE)
I cannot understand why the test RMSE drops when using more than 27 variables? It seems to start underfitting rather than overfitting with more variables. Interestingly, this happens at the same time as the training RMSE becomes around 1e-14. Meanwhile, the adjused R-squared shows the following strange behaviour at that moment:
Am I using just too many dimensions for this polynomial regression? Or is there another reason why this is happening? I would love to understand what is going on. I will quickly move on to better algorithms, but I just wanted to make a benchmark for my ML project. Thanks in advance!
machine-learning regression supervised-learning model-selection
asked 12 mins ago
SalmonSalmon
1
New contributor
Salmon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I am testing polynomial regression for a data set of 50 variables and a sample size of 5000. I ordered the coefficients of the linear model from high to low and then made different models using the p most explanatory variables. The RMSE values of these models are shown in the following figures. For polynomial regression of degree=2 everything seems to be normal, but for degree=3 something strange happens. (The dotted line shows the location of minimum RMSE)
I cannot understand why the test RMSE drops when using more than 27 variables? It seems to start underfitting rather than overfitting with more variables. Interestingly, this happens at the same time as the training RMSE becomes around 1e-14. Meanwhile, the adjused R-squared shows the following strange behaviour at that moment:
Am I using just too many dimensions for this polynomial regression? Or is there another reason why this is happening? I would love to understand what is going on. I will quickly move on to better algorithms, but I just wanted to make a benchmark for my ML project. Thanks in advance!
machine-learning regression supervised-learning model-selection
machine-learning regression supervised-learning model-selection
asked 12 mins ago
SalmonSalmon
1
New contributor
Salmon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 12 mins ago
SalmonSalmon
1
New contributor
Salmon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 12 mins ago
SalmonSalmon
1
New contributor
Salmon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 12 mins ago
SalmonSalmon
1
asked 12 mins ago
SalmonSalmon
1
1
New contributor
Salmon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Salmon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Salmon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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