Is the negative log likelihood convex?

Is the negative log likelihood convex?

log-likelihood is convex (i.e. by equating gradient to 0, which is the optimality criterion for a convex function).

Is higher log-likelihood better?

Many procedures use the log of the likelihood, rather than the likelihood itself, because it is easier to work with. The log likelihood (i.e., the log of the likelihood) will always be negative, with higher values (closer to zero) indicating a better fitting model.

Is the log-likelihood concave?

It can be shown that when f is convex and log-concave, the log-likelihood is concave.

Why is the log-likelihood concave?

If you happen to know that the first term happens to be a concave function (any function of the form f(w)=Aw+b is called an affine function, and it is concave), and that the second term is a negative log-sum-exp of an affine function (which also happens to be concave), you get that the log likelihood is concave.

Can a log likelihood function be a negative cross?

So yes, it is possible that you end up with a negative value for log-likelihood (for discrete variables it will always be so). Thanks for contributing an answer to Cross Validated!

Is the natural logarithm function positive or negative?

The natural logarithm function is negative for values less than one and positive for values greater than one. So yes, it is possible that you end up with a negative value for log-likelihood (for discrete variables it will always be so).

Which is the first derivative of the log likelihood function?

The first derivative of the log-likelihood function is called Fisher’s score function, and is denoted by u(θ) = ∂logL(θ;y) ∂θ. (A.7) Note that the score is a vector of first partial derivatives, one for each element of θ. If the log-likelihood is concave, one can find the maximum likelihood

What does negative log likelihood mean in azure ml?

No missing data. Edit 2 Possible Explanation – ( click here ): Apparently, Linear Regression and Boosted Trees in Azure ML don’t calculate the Negative Log-Likelihood metric – and that could be the reason that NLL is infinity or undefined in both cases.