Difference between revisions of "Sigmoid"
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''New to [[Analytica 4.5]]'' | ''New to [[Analytica 4.5]]'' | ||
| − | = Sigmoid(x) = | + | == Sigmoid(x) == |
The [[Sigmoid]] function is | The [[Sigmoid]] function is | ||
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The [[Sigmoid]] function goes by several other names including the ''logistic function'', the ''inverse logit function'', and the ''expit'' function. | 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 | + | 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>-\infty</math> and to 1 as «x» goes to <math>+\infty</math>. |
The inverse of the [[Sigmoid]] function is the [[Logit]] function. | The inverse of the [[Sigmoid]] function is the [[Logit]] function. | ||
| − | = 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> | + | :<code>Sigmoid(Sum(c*x, K))</code> |
| − | = See Also = | + | == See Also == |
* [[Logit]](x) | * [[Logit]](x) | ||
* [[LogisticRegression]](x) | * [[LogisticRegression]](x) | ||
Revision as of 23:33, 13 January 2016
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)
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