Beginning Anomaly Detection Using

 Loss  Functions

 MSE

torch.nn.MSELoss()

If you have questions on the notation for this equation, refer to Chapter 

3

. The 

equation is shown in Figure 

B-28

.

Given input 

θ, the weights, the formula finds the average difference squared between 

the predicted value and the actual value. The parameter h

θ

 represents the model with the 

weight parameter 

θ passed in, so h

θ

(x

i

) would give the predicted value for x

i

 with model’s 

weights 

θ. The parameter y

i

 represents the actual prediction for the data point at index i. 

Lastly, there are n entries in total.

This function has several parameters (two are deprecated):

• 

size_average: (Deprecated in favor of reduction.) The losses are 

averaged over each loss element in the batch by default (True). If 

set to False, then the losses are summed for each minibatch instead. 

Default = True.

appendix B   intro to pytorch

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388

• 

reduce: (Deprecated in favor of reduction.) The losses are averaged 

or summed over observations for each minibatch depending on 

size_average by default (True). If set to False, then it returns a loss per 

batch element and ignores size_average. Default = True.

• 

reduction: A string value to specify the type of reduction to be done. 

Choose between ‘none’, ‘elementwise_mean’, or ‘sum’. ‘none’ means 

no reduction is applied, ‘elementwise_mean’ will divide the sum of 

the output by the number of elements in the output, and ‘sum’ will 

just sum the output. Default = ’elementwise_mean’. Note: specifying 

either size_average or reduce will override this parameter.

This loss metric can be used in autoencoders to help evaluate the difference between 

the reconstructed output and the original. In the case of anomaly detection, this metric 

can be used to separate the anomalies from the normal data points, since anomalies 

have a higher reconstruction error.