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If a vector of predictions is generated from a sample of data points on all variables, and is the vector of observed values of the variable being predicted, with ^ being the predicted values (e.g. as from a least-squares fit), then the within-sample MSE of the predictor is computed as
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When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows.
Depending on the complexity of the model being simulated, the learning rule of the network can be as simple as an XOR gate or mean squared error, or as complex as the result of a system of differential equations. The learning rule is one of the factors which decides how fast or how accurately the neural network can be developed.
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Download as PDF; Printable version; In other projects ... based on their research in single-layer neural networks ... is the mean square error, and it is minimized by ...
Folding activation functions are extensively used in the pooling layers in convolutional neural networks, and in output layers of multiclass classification networks. These activations perform aggregation over the inputs, such as taking the mean, minimum or maximum. In multiclass classification the softmax activation is often used.
Rprop can result in very large weight increments or decrements if the gradients are large, which is a problem when using mini-batches as opposed to full batches. RMSprop addresses this problem by keeping the moving average of the squared gradients for each weight and dividing the gradient by the square root of the mean square. [citation needed]