How Can the Logit Function Be Modified for a Specific Output Range?

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SUMMARY

The discussion focuses on modifying the logistic function, specifically the sigmoid function represented as f(z) = 1/(1+exp(-z)), to ensure that if z > 0.5, then f > 0.5, and if z < 0.5, then f < 0.5. Participants suggest shifting the input by replacing z with z - 0.5 to achieve the desired output range. The conversation clarifies the terminology, confirming that the function in question is indeed the sigmoid function, commonly used in neural networks and fuzzy control systems.

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adan
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Hi,
I am looking for changing the logit f(z) = 1/(1+exp(-z)), where z range is [-inf,+inf]. I want to adapt it as follows:
if z > 0.5 then f > 0.5
z < 0.5 then f < 0.5

Thanks
 
Last edited:
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Hi,
If I understand you well, you want to shift the graph to the right by 0.5. So replace ##z## by ##z-0.5##

1624359059346.png
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BvU said:
Hi,
If I understand you well, you want to shift the graph to the right by 0.5. So replace ##z## by ##z-0.5##

View attachment 284871##\ ##
Thank you so much!
 
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adan said:
I am looking for changing the logit f(z) = 1/(1+exp(-z))
Do you mean logistic function? That is apparently how @BvU interpreted this. I don't believe there is such a thing as a "logit" function.
 
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Me too... :rolleyes:

Never too old to learn 😎

##\ ##
 
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Actually, the ##f## in this thread is the sigmoid function. Vaguely remember it's used in neural networks and fuzzy control.

##\ ##
 
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adan said:
Hi,
I am looking for changing the logit f(z) = 1/(1+exp(-z)), where z range is [-inf,+inf]. I want to adapt it as follows:
if z > 0.5 then f > 0.5
z < 0.5 then f < 0.5

Thanks
Just a technicality : Why are you using #[\-infty, \infty]#, i.e., are you considering #\pm \infty # as actual inputs?
 
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