How to interpret loss and accuracy for a machine learning model

Question

When I trained my neural network with Theano or Tensorflow  they will report a variable called  loss  per epoch   How should I interpret this variable  Higher loss is better or worse  or what does it mean for the final performance  accuracy  of my neural network

User · Answer

They are two different metrics to evaluate your model's performance usually being used in different phases.

Loss is often used in the training process to find the "best" parameter values for your model (e.g. weights in neural network). It is what you try to optimize in the training by updating weights.

Accuracy is more from an applied perspective. Once you find the optimized parameters above, you use this metrics to evaluate how accurate your model's prediction is compared to the true data.

Let us use a toy classification example. You want to predict gender from one's weight and height. You have 3 data, they are as follows:(0 stands for male, 1 stands for female)

y1 = 0, x1_w = 50kg, x2_h = 160cm;

y2 = 0, x2_w = 60kg, x2_h = 170cm;

y3 = 1, x3_w = 55kg, x3_h = 175cm;

You use a simple logistic regression model that is y = 1/(1+exp-(b1*x_w+b2*x_h))

How do you find b1 and b2? you define a loss first and use optimization method to minimize the loss in an iterative way by updating b1 and b2.

In our example, a typical loss for this binary classification problem can be: (a minus sign should be added in front of the summation sign)

We don't know what b1 and b2 should be. Let us make a random guess say b1 = 0.1 and b2 = -0.03. Then what is our loss now?

$\hat{y}_1 = \frac{1}{ 1 + e^{ -(0.1 \cdot 50 - 0.03 \cdot 160) } } = 0.549834 = 0.55$

$\hat{y}_2 = \frac{1}{ 1 + e^{ -(0.1 \cdot 60 - 0.03 \cdot 170) } } = 0.7109495 = 0.71$

$\hat{y}_3 = \frac{1}{ 1 + e^{ -(0.1 \cdot 55 - 0.03 \cdot 175) } } = 0.5621765 = 0.56$

so the loss is

$-\log(1-0.55) -\log(1-0.71) - \log(0.56) \simeq 2.6162$

Then you learning algorithm (e.g. gradient descent) will find a way to update b1 and b2 to decrease the loss.

What if b1=0.1 and b2=-0.03 is the final b1 and b2 (output from gradient descent), what is the accuracy now?

Let's assume if y_hat >= 0.5, we decide our prediction is female(1). otherwise it would be 0. Therefore, our algorithm predict y1 = 1, y2 = 1 and y3 = 1. What is our accuracy? We make wrong prediction on y1 and y2 and make correct one on y3. So now our accuracy is 1/3 = 33.33%

PS: In Amir's answer, back-propagation is said to be an optimization method in NN. I think it would be treated as a way to find gradient for weights in NN. Common optimization method in NN are GradientDescent and Adam.

User · Answer

The lower the loss  the better a model  unless the model has over-fitted to the training data   The loss is calculated on training and validation and its interperation is how well the model is doing for these two sets  Unlike accuracy  loss is not a percentage  It is a summation of the errors made for each example in training or validation sets  In the case of neural networks  the loss is usually negative log-likelihood and residual sum of squares for classification and regression respectively  Then naturally  the main objective in a learning model is to reduce  minimize  the loss function s value with respect to the model s parameters by changing the weight vector values through different optimization methods  such as backpropagation in neural networks  Loss value implies how well or poorly a certain model behaves after each iteration of optimization  Ideally  one would expect the reduction of loss after each  or several  iteration s   The accuracy of a model is usually determined after the model parameters are learned and fixed and no learning is taking place  Then the test samples are fed to the model and the number of mistakes  zero-one loss  the model makes are recorded  after comparison to the true targets  Then the percentage of misclassification is calculated  For example  if the number of test samples is 1000 and model classifies 952 of those correctly  then the model s accuracy is 95 2    There are also some subtleties while reducing the loss value  For instance  you may run into the problem of over-fitting in which the model  quot memorizes quot  the training examples and becomes kind of ineffective for the test set  Over-fitting also occurs in cases where you do not employ a regularization  you have a very complex model  the number of free parameters W is large  or the number of data points N is very low

User · Answer

Just to clarify the Training Validation Test data sets  The training set is used to perform the initial training of the model  initializing the weights of the neural network  The validation set is used after the neural network has been trained  It is used for tuning the network s hyperparameters  and comparing how changes to them affect the predictive accuracy of the model  Whereas the training set can be thought of as being used to build the neural network s gate weights  the validation set allows fine tuning of the parameters or architecture of the neural network model  It s useful as it allows repeatable comparison of these different parameters architectures against the same data and networks weights  to observe how parameter architecture changes affect the predictive power of the network  Then the test set is used only to test the predictive accuracy of the trained neural network on previously unseen data  after training and parameter architecture selection with the training and validation data sets

[machine-learning] How to interpret "loss" and "accuracy" for a machine learning model

Examples related to machine-learning

Examples related to neural-network

Examples related to mathematical-optimization

Examples related to deep-learning

Examples related to objective-function