Questions tagged [mean-squared-error]

For questions related to the mean squared error (MSE) function, which is often used to solve regression problems.

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In variational autoencoders, why do people use MSE for the loss?

In VAEs, we try to maximize the ELBO = $\mathbb{E}_q [\log\ p(x|z)] + D_{KL}(q(z \mid x), p(z))$, but I see that many implement the first term as the MSE of the image and its reconstruction. Here's a ...
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"Porpoising" in latter stages of validation loss and MSE charts in Keras

Performing a prediction of a continuous y target using Keras, the simple structure of the code revolves around; ...
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What error should I use for RNN?

I'm relatively new to machine learning, and I don't know what error I should use for an RNN. I want to use a simple Elman RNN to predict the cases of Covid-19 there will be in a hospital for the next ...
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Would either $L_1$ or $L_2$ regularisation lower the MSE on the training and test data?

Consider linear regression. The mean squared error (MSE) is 120.5 for the training dataset. We've reached the minimum for the training data. Is it possible that by applying Lasso (L1 regularization) ...
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How do I prove that the MSE is zero when all predictions are equal to the corresponding labels?

In the back-propogation algorithm, the error term is: $$ E=\frac{1}{2}\sum_k(\hat{y}_k - y_k)^2, $$ where $\hat{y}_k$ is a vector of outputs from the network, $y_k$ is the vector of correct labels (...
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What is the meaning of these equations in Noise2Noise paper?

I am trying to understand what is meant by following equations in the Noise2Noise paper by Nvidia. What is meant by the equation in this image? What is $\mathbb{E}_y\{y\}$? And how should I try to ...
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What is the definition of a loss function in the context of neural networks?

I have read what the loss function is, but I am not sure if I have understood it. For each neuron in the output layer, the loss function is usually equal to the square of the difference value of the ...
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4 votes
2 answers
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What is the advantage of using cross entropy loss & softmax?

I am trying to do the standard MNIST dataset image recognition test with a standard feed forward NN, but my network failed pretty badly. Now I have debugged it quite a lot and found & fixed some ...
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How can a learning rate that is too large cause the output of the network (and the error) to go to infinity?

It happened to my neural network, when I use a learning rate of <0.2 everything works fine, but when I try something above 0.4 I start getting "nan" errors because the output of my ...
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Why do we calculate the mean squared error loss to improve the value approximation in Advantage Actor-Critic Algorithm?

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How MSE should be appliead with multi target deep network?

I'm having a problem understanding how the MSE should be used when working with a multidimensional target, e.g 3 dimensiones. (My outputs are continuois values, not categorical) Let us say I have a ...
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What does it mean if classification error is equal between two networks but the MSE is different?

I'm experimenting with training a feedforward neural network using a genetic algorithm and I've done a few tests using both the mean squared error and classification error functions as fitness ...
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How to implement Mean square error loss function in mini batch GD

I have a vectorized implementation of the neural network in c++. I successfully solve the classification problems of Fashion MNIST and CIFAR. Now I am modifying my code to do the Linear regression. I ...
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4 answers
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Is it normal to have the root mean squared error greater on the test dataset than on the training dataset?

I am new to deep learning. I am training a model and I am getting a root mean squared error (RMSE) greater on the test dataset than on the training dataset. What could be the reason behind this? Is ...
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2 votes
2 answers
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How to determine the target value when using ReLU as activation function?

Consider the following simple neural network with only one neuron. The input is $x_1$ and $y_2$, where $-250 < x < 250$ and $-250 < y < 250$ The weights of the only neuron are $w_1$ and $...
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3 answers
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In which cases is the categorical cross-entropy better than the mean squared error?

In my code, I usually use the mean squared error (MSE), but the TensorFlow tutorials always use the categorical cross-entropy (CCE). Is the CCE loss function better than MSE? Or is it better only in ...
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How to express accuracy of a regression ANN that uses MSE loss function?

I have a regression MLP network with all input values between 0 and 1, and am using MSE for the loss function. The minimum MSE over the validation sample set comes to 0.019. So how to express the '...
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What are the advantages of the Kullback-Leibler over the MSE/RMSE?

I've recently encountered different articles that are recommending to use the KL divergence instead of the MSE/RMSE (as the loss function), when trying to learn a probability distribution, but none of ...
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7 votes
3 answers
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How is it possible that the MSE used to train neural networks with gradient descent has multiple local minima?

We often train neural networks by optimizing the mean squared error (MSE), which is an equation of a parabola $y=x^2$, with gradient descent. We also say that weight adjustment in a neural network by ...
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  • 193
3 votes
1 answer
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Why is the "square error function" sometimes defined with the constant 1/2 and sometimes with the constant 1/m?

Depending on the source, I find people using different variations of the "squared error function". How come that be? Here, it is defined as $$ E_{\text {total }}=\sum \frac{1}{2}(\text {...
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2 votes
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Is it a good idea to train a CNN to detect the hydration value (percentage) in skin images and evaluate it with the MSE?

I have a large dataset of skin images, each one associated with a hydration value (percentage). Now I'm looking into predicting the hydration value from an image. My thinking: train a CNN on the ...
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