Difference between revisions of "Sigmoid"

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[[Category:Functions that operate on complex numbers]]
 
[[Category:Functions that operate on complex numbers]]
  
''New to [[Analytica 4.5]]''
 
  
 
== Sigmoid(x) ==
 
== Sigmoid(x) ==
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== Library ==
 
== Library ==
 
 
Advanced Math Functions
 
Advanced Math Functions
  
 
== Uses ==
 
== Uses ==
 
 
Since the [[Logit]] function is the ''link function'' in generalized linear regression that results in [[LogisticRegression|logistic regression]], the [[Sigmoid]] function is used to apply the coefficients of [[LogisticRegression|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:
 
Since the [[Logit]] function is the ''link function'' in generalized linear regression that results in [[LogisticRegression|logistic regression]], the [[Sigmoid]] function is used to apply the coefficients of [[LogisticRegression|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:
 
:<code>Sigmoid(Sum(c*x, K))</code>
 
:<code>Sigmoid(Sum(c*x, K))</code>
 +
 +
==History==
 +
[[Sigmoid]] was introduced in [[Analytica 4.5]].
  
 
== See Also ==
 
== See Also ==
 
 
* [[Logit]](x)
 
* [[Logit]](x)
 
* [[LogisticRegression]](x)
 
* [[LogisticRegression]](x)

Revision as of 23:13, 21 January 2016


Sigmoid(x)

The Sigmoid function is

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

SigmoidGraph.png

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))

History

Sigmoid was introduced in Analytica 4.5.

See Also

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