Howtosignalprocessing
- What is the log-likelihood in logistic regression?
- What is the mathematical derivation of logistic regression?
- What is the derivative of the logistic function?
- Can we use gradient descent for logistic regression?
What is the log-likelihood in logistic regression?
The log-likelihood value of a regression model is a way to measure the goodness of fit for a model. The higher the value of the log-likelihood, the better a model fits a dataset. The log-likelihood value for a given model can range from negative infinity to positive infinity.
What is the mathematical derivation of logistic regression?
In simple words: “Take the normal regression equation, apply the logit L , and you'll get out the logistic regression” (provided the criterion is binary). L(t)=ln(f(t)1−f(t))=b0+b1x L ( t ) = l n ( f ( t ) 1 − f ( t ) ) = b 0 + b 1 x .
What is the derivative of the logistic function?
The logistic function is g(x)=11+e−x, and it's derivative is g′(x)=(1−g(x))g(x).
Can we use gradient descent for logistic regression?
Surprisingly, the update rule is the same as the one derived by using the sum of the squared errors in linear regression. As a result, we can use the same gradient descent formula for logistic regression as well.
