Beginning Anomaly Detection Using

 Loss  Functions

In the examples, y_true is the true label and y_pred is the predicted label.

 Mean Squared Error

keras.losses.mean_squared_error(y_true, y_pred)

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

3

. See the 

equation in Figure 

A-15

.

Figure A-15.  The equation for mean squared error

Appendix A   intro to KerAs

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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

) gives 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 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.