Читать книгу Machine Learning for Tomographic Imaging - Professor Ge Wang - Страница 51

The loss function is critical to guide the process of training an artificial neural network. The loss is used to measure the discrepancy between a predicted value yˆ and the corresponding label y. It is a non-negative function, whose minimization drives the performance of the network reaching convergence in the training stage. Training a neural network is to update the network parameters so that yˆ approaches y as closely as possible by some certain measure. The local slope or more general gradient by which the loss value changes at a current parametric setting will tell us how to update the parameters for a reduced loss. That is, we use the loss function to compute a clue by which we refine our parameters. The loss function is defined in terms of labels as follows:

L(θ)=1n∑i=1nLy(i),fx(i),θ,(3.17)

where [x(i)=x1i,x2i,…,xmi]∈Rm denotes a training sample, y(i) denotes the corresponding label or a gold standard, θ is a set of parameters to be learned, and f(·) is the model function. The loss function can take a variety of forms as the definition of discrepancy is not unique. Next, we introduce several commonly used loss functions.