Sigmoid function
Topic of Neural units, part of Statistical learning
Sigmoid function
| Type | Topic |
| Taught in | Neural units |
| Part | Statistical learning |
| Questions using it | 9 |
The logistic function g(z)=1/(1+e^{-z}), which maps the real line onto (0,1). It is a smooth stand-in for a threshold, its derivative is g(z)\{1-g(z)\}, and a sigmoid output with no hidden layer is a logistic regression.
In Neural units
From Neural units
Two activations are used here. The threshold, the McCulloch–Pitts decision, and the logistic sigmoid are
f(\mathrm{net})= \begin{cases} 0, & \mathrm{net}<0,\\ 1, & \mathrm{net}\ge 0, \end{cases} \qquad g(z)=\frac{1}{1+e^{-z}}.
Used in
- Taught in Neural units
- Also used in Introduction to generalised linear models · Smooth means · Logistic regression · Ensembles, random forests, and boosting · Backpropagation · Networks in practice · Random slopes, and a binary mixed model
- Questions that use it (9) — Linear hidden units (answer) · A gradient by hand · Saturation · One backpropagation update (answer) · Initial weights (answer) · Softmax gradient · Complexity and early stopping · Q42 (answer) · Question 20 (answer)
- All 7 questions on Neural units
See also
Artificial neuron · Perceptron · Activation function · Hidden layer · Binary logistic regression · Local minima, plateaus, and symmetry · One hidden layer approximates continuous functions · Softmax is multinomial logistic regression