Answers.Body: <p>I would say that your intuition is correct: the model associated with the first plot is likely to generalise more than the one associated with the second plot.</p>
  
  <p>In both cases, it doesn't seem that your model has overfitted the training data. Overfitting often occurs when the training error keeps decreasing but the validation error starts to increase. In both your plots, both the training and validation errors keep decreasing (even if slowly, after a while).</p>
  
  <p>Underfitting occurs when your model hasn't learned enough even about your training data. The smaller the training and validation error, the more likely your model has not underfitted, but the value of RMSE depends on the range of your inputs. See e.g. <a href="https://stats.stackexchange.com/q/56302/82135">What are good RMSE values?</a> for more info.</p>
  
  <p>See also this article <a href="https://machinelearningmastery.com/overfitting-and-underfitting-with-machine-learning-algorithms/" rel="nofollow noreferrer">Overfitting and Underfitting With Machine Learning Algorithms</a> for a general overview of the concepts of overfitting and underfitting.</p>
  
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Answers.CreationDate: 2019-05-17T00:46:14.250Z
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Answers.LastEditDate: 2019-05-17T01:00:46.747Z
Answers.UserDisplayName: nbro
Answers.Body: <p>One possibility: If you are using a dropout regularization layer in your network, it is reasonable that the validation error is smaller than the training error. Because usually dropout is activated when training but deactivated when evaluating on the validation set. You get a more smooth (usually means better) function in the latter case.</p>
  
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Body: <p>Below you have the plots of the training and validation errors for two different models. Both plots show the RMSE values for the validation dataset versus the number of training epochs. It is observed that models get lower RMSE value as training progresses.</p>
  
  <p>The model associated with the first plot is performing quite well. The gap is quite narrowed.</p>
  
  <p><a href="https://i.sstatic.net/oMDvC.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/oMDvC.png" alt="First Plot"></a></p>
  
  <p>I think the model associated with this second plot is doing pretty good, but not as well as the other. The gap is much broader. </p>
  
  <p><a href="https://i.sstatic.net/Suc5q.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Suc5q.png" alt="Second Plot"></a></p>
  
  <p>The model of the first plot was trained using a data set containing 1 million of ratings, while the second one used only 100K. I'm implementing the collaborative filtering (CF) algorithm. I am optimising it using SGD.</p>
  
  <p><a href="https://i.sstatic.net/LFPzs.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/LFPzs.png" alt="enter image description here"></a> </p>
  
  <p>Are any of these models overfitting or underfitting?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-05-16T13:59:09.677Z
Comments.Text: What do you mean by "describe both plots in terms of model complexity"? What do you mean by "model complexity"?
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-05-16T15:23:28.597Z
Comments.Text: if it is overfitting or underfitting
Comments.UserDisplayName: NaveganTeX
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-05-17T02:47:22.410Z
Comments.Text: Regarding Model Complexity: (http://www.stats.ox.ac.uk/~sejdinov/teaching/sdmml15/materials/HT15_lecture12-nup.pdf)
Comments.UserDisplayName: NaveganTeX
Tags: <machine-learning><overfitting><recommender-system><cross-validation><underfitting>
Title: Which model is better given their training and validation errors?
UserDisplayName: NaveganTeX
ThreadText: # Which model is better given their training and validation errors?
  
  (Asked by: username_0 on 2019-05-16)
  
  Below you have the plots of the training and validation errors for two different models. Both plots show the RMSE values for the validation dataset versus the number of training epochs. It is observed that models get lower RMSE value as training progresses.
  
  The model associated with the first plot is performing quite well. The gap is quite narrowed.
  
  [![First Plot](https://i.sstatic.net/oMDvC.png)](https://i.sstatic.net/oMDvC.png)
  
  I think the model associated with this second plot is doing pretty good, but not as well as the other. The gap is much broader.
  
  [![Second Plot](https://i.sstatic.net/Suc5q.png)](https://i.sstatic.net/Suc5q.png)
  
  The model of the first plot was trained using a data set containing 1 million of ratings, while the second one used only 100K. I'm implementing the collaborative filtering (CF) algorithm. I am optimising it using SGD.
  
  [![enter image description here](https://i.sstatic.net/LFPzs.png)](https://i.sstatic.net/LFPzs.png)
  
  Are any of these models overfitting or underfitting?
  
  **Tags:** machine-learning, overfitting, recommender-system, cross-validation, underfitting
  > **Comments:**
  > **username_1**: What do you mean by "describe both plots in terms of model complexity"? What do you mean by "model complexity"?  
  > **username_0**: if it is overfitting or underfitting  
  > **username_0**: Regarding Model Complexity: (http://www.stats.ox.ac.uk/~sejdinov/teaching/sdmml15/materials/HT15_lecture12-nup.pdf)  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_1 on 2019-05-17. Score: 1 | Accepted answer
  
  I would say that your intuition is correct: the model associated with the first plot is likely to generalise more than the one associated with the second plot.
  
  In both cases, it doesn't seem that your model has overfitted the training data. Overfitting often occurs when the training error keeps decreasing but the validation error starts to increase. In both your plots, both the training and validation errors keep decreasing (even if slowly, after a while).
  
  Underfitting occurs when your model hasn't learned enough even about your training data. The smaller the training and validation error, the more likely your model has not underfitted, but the value of RMSE depends on the range of your inputs. See e.g. [What are good RMSE values?](https://stats.stackexchange.com/q/56302/82135) for more info.
  
  See also this article [Overfitting and Underfitting With Machine Learning Algorithms](https://machinelearningmastery.com/overfitting-and-underfitting-with-machine-learning-algorithms/) for a general overview of the concepts of overfitting and underfitting.
  
  
  ---
  
  ### Answer by username_2 on 2020-12-18. Score: 0
  
  One possibility: If you are using a dropout regularization layer in your network, it is reasonable that the validation error is smaller than the training error. Because usually dropout is activated when training but deactivated when evaluating on the validation set. You get a more smooth (usually means better) function in the latter case.
  
  
  ---
  
  