Bias and variance

deviation ： Deviation refers to the difference between the result of model training and the real value .

explain ： Deviation measures the deviation between the expected prediction and the real result of the learning algorithm , Immediately draw the fitting ability of learning algorithm itself . If the deviation is too large , We need to shrink it , That is to reduce the difference between the real value , The effect of this training will be better .

variance ： Variance refers to the difference between the results obtained from different training sets . Expectation prediction is for the same sample under different training sets （ Test set ） The predicted value of is taken as the mean , Instead of taking the average of the predicted values of all samples in a training .

explain ： Variance measures the change of learning performance caused by the change of training set of the same size , Immediately draws the impact of data perturbation .

（1） Define expectations as :                       

among   As the training set Medium On the model Output , Tag the model in the dataset , by The true mark of .

（2） The calculation formula of variance is ：                

( Every x Calculate the expectation based on the difference between the obtained value and the average value , Different D You will get different variances , See the generalization of the model by observing the change of variance )

（3） The calculation formula of deviation is ：                  

（ First seek x Expectations of predicted values , Recalculate with actual value y Difference ）

For deviations and variances , It can be estimated that . A model , Use different data sets for modeling , Test on a test set , Get a series of predicted values , The variance of the predicted value is the required variance , The difference between the mean value of the predicted value and the real value is a deviation .

Here is an example of my calculation