What is the difference between Loss and RMSE when do regression task using the Deep Learning Tool Box?

I'm doing a regression task using Deep Learning Tool Box, and the Training Progress showing two classes of curves namely RMSE and Loss.

What is the difference between? I cann't find detailed description In the Help document.

[Shreya Bhatia]

Hi Zongwei, May I know the nature of your project? I am doing a similar regression project that I am doing to predict the gait cycle % of when a person is climbing stairs. I am using RNN for it. My regression values are linearly continuous between 0 and 100%. Do let me know your approach?

Answer 1

[Deepak Kumar]

Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). Residuals are a measure of how far from the regression line data points are; RMSE is a measure of how spread out these residuals are. In other words, it tells you how concentrated the data is around the line of best fit.

A loss function is a measure of how good a prediction model does in terms of being able to predict the expected outcome.

To know more about RMSE and Loss refer to following links:

https://www.statisticshowto.datasciencecentral.com/rmse/

https://towardsdatascience.com/common-loss-functions-in-machine-learning-46af0ffc4d23

[Zongwei Yao]

Thanks very much for the reply.

The 2nd hyperlink introduces 3 common loss functions for regression task, namely MSE, MAE, and MBE.

Which one is used in Deep learning toolbox?

My task is regress mass data from images, similar with the tutoral "Train Convolutional Neural Network for Regression" ——https://www.mathworks.com/help/deeplearning/examples/train-a-convolutional-neural-network-for-regression.html?searchHighlight=regression%20using%20convolutional&s_tid=doc_srchtitle

The labels in my task are range from 0 to 1.

My results show the RMSE is about 0.13 while the loss is about 0.007.

So I'm wondering what is the defination of the loss function? How can I evaluate the quality of the results?

[Deepak Kumar]

MSE gives the most accurate results so you can go with MSE.

In terms of RMSE, the lower the better. RMSE values of 0.1 below is very satisfactory.

In your case. RMSE and loss seems fine.

For more info about acceptable value of loss and errors , follow :

https://www.researchgate.net/post/What_is_the_Acceptable_MSE_value_and_Coefficient_of_determinationR2

Link for loss function:

https://www.youtube.com/watch?v=7YQBh0gFZ00

[Zongwei Yao]

Thanks for the lovely advice.

I watched the video and understood the defination of cross-entropy for classification task,.

I'm wondering does the cross-entropy works for regression case as the same? How the probability is calculated?

[Deepak Kumar]

https://www.quora.com/Can-we-use-cross-entropy-to-solve-the-regression-problem

[Zongwei Yao]

Thanks again！

[Ernst Kloppenburg]

@Deepak Kumar I tried to find an answer for the question "what is RMSE vs. Loss in Matlab DL toolbox" myself and ended up here. For me it is about the output of "trainNetwork" for a regression problem:

|========================================================================================|

| Epoch | Iteration | Time Elapsed | Mini-batch | Mini-batch | Base Learning |

| | | (hh:mm:ss) | RMSE | Loss | Rate |

|========================================================================================|

| 1 | 1 | 00:00:00 | 0.95 | 0.5 | 0.0100 |

Unfortunately none of your answers actually answers the original question. Could you give pointers to relevant sections in the toolbox documentation? Or could you give an answers in terms of formulae?

Specifically, I am puzzled because the documentation says that the training loss for a regression problem is RMSE. Then why do the two "Mini-batch..." columns in the output show different values?

[Ilya Kuprov]

Same problem here. What exactly (as in, please provide the equation) is "loss"?