Hi,
in todays lecture it is said you can use linear regression to do a binary classification, basically to map your predictor to desired y={0,1}
you classify this way :
if $$ f(x)>0.5 \text{ you predict 1, else 0.} $$
my question is the following, can we assume that the real value of f(x) tells us something about the confidence of f in it's prediction?
basically, if you have f(x) =0.6 you are predicting 1 with less confidence than if you have f(x)=0.99
In principle you can use linear regression for classification, but for reasons explained in lecture 5b this is problematic.
Nevertheless,
if you have \(f(x)=0.6\) you are predicting 1 with less confidence than if you have \(f(x)=0.99\)
This is correct.
can we assume that the real value of \(f(x)\) tells us something about the confidence of \(f\) in it's prediction?
This is an issue in least-squares linear regression as the output is unbounded \((-\infty, \infty)\).
Therefore, logistic regression, with the bounded sigmoid function (aka logistic function) will always give an output in the interval \([0,1]\). In this case, the logistic classifier output value can be interpreted as a confidence estimate.
(tip: use the buttons in the forum editor to encapsulate your formulas; this way they will always correctly display.)
binary classification using linear regression
Hi,
in todays lecture it is said you can use linear regression to do a binary classification, basically to map your predictor to desired y={0,1}
you classify this way :
if $$ f(x)>0.5 \text{ you predict 1, else 0.} $$
my question is the following, can we assume that the real value of f(x) tells us something about the confidence of f in it's prediction?
basically, if you have f(x) =0.6 you are predicting 1 with less confidence than if you have f(x)=0.99
In principle you can use linear regression for classification, but for reasons explained in lecture 5b this is problematic.
Nevertheless,
This is correct.
This is an issue in least-squares linear regression as the output is unbounded \((-\infty, \infty)\).
Therefore, logistic regression, with the bounded sigmoid function (aka logistic function) will always give an output in the interval \([0,1]\). In this case, the logistic classifier output value can be interpreted as a confidence estimate.
(tip: use the buttons in the forum editor to encapsulate your formulas; this way they will always correctly display.)
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