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In particular see "Chapter 4: Artificial Neural Networks" (in particular pp. 96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural ...
In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a model inspired by the structure and function of biological neural networks in animal brains. [1] [2] An ANN consists of connected units or nodes called artificial neurons, which loosely model the neurons in the brain. Artificial ...
A widely used type of composition is the nonlinear weighted sum, where () = (()), where (commonly referred to as the activation function [3]) is some predefined function, such as the hyperbolic tangent, sigmoid function, softmax function, or rectifier function. The important characteristic of the activation function is that it provides a smooth ...
Backpropagation computes the gradient of a loss function with respect to the weights of the network for a single input–output example, and does so efficiently, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this can be derived through ...
A seventh order polynomial function was fit to the training data. In the right column, the function is tested on data sampled from the underlying joint probability distribution of x and y. In the top row, the function is fit on a sample dataset of 10 datapoints. In the bottom row, the function is fit on a sample dataset of 100 datapoints.
Plot of three variants of the hinge loss as a function of z = ty: the "ordinary" variant (blue), its square (green), and the piece-wise smooth version by Rennie and Srebro (red). The y-axis is the l(y) hinge loss, and the x-axis is the parameter t
Empirical risk minimization for a classification problem with a 0-1 loss function is known to be an NP-hard problem even for a relatively simple class of functions such as linear classifiers. [5] Nevertheless, it can be solved efficiently when the minimal empirical risk is zero, i.e., data is linearly separable .