Sigmoid

New to Analytica 4.5

Sigmoid(x)

The Sigmoid function is

[math]\displaystyle{ Sigmoid(x) = {1\over{1+\exp(-x)}} }[/math]

The Sigmoid function goes by several other names including the logistic function, the inverse logit function, and the expit function.

There are other functions that are also sigmoidal in shape, most notably the ArcTan and Tanh functions. These other sigmoidal fucntions differ in their asymptotic values. The Sigmoid(x) function goes to 0 as x goes to [math]\displaystyle{ -\infty }[/math] and to 1 as x goes to [math]\displaystyle{ +\infty }[/math].

The inverse of the Sigmoid function is the Logit function.

Library

Advanced Math Functions

Uses

Since the Logit function is the link function in generalized linear regression that results in logistic regression, the Sigmoid function is used to apply the coefficients of logistic regression to make predictions. So if c are the coefficients returned by the LogisticRegression function, where c is a vector indexed by K, and x is a new data point (also indexed by K), then the predicted probability for x is computed using:

Sigmoid( Sum( c*x, K ) )

See Also

• Logit(x)
• LogisticRegression(x)