Those two are different.

EM measures the joint log-likelihood. If x is an instance, and p(x) is the estimated density for the instance, then log(p(x)) is what's used to calculate the joint log-likelihood.

In contrast, the conditional log-likelihood is based on the conditional probability of the observed class value y given the instance x, so it is based on log(p(y|x)).

Cheers,
Eibe

On Fri, Dec 22, 2017 at 7:57 PM, Valerio jus <valeriojus@gmail.com> wrote:
Thanks a lot, Eibe.


It's the scheme's negative conditional loglikelihood (aka log loss), computed from the class probabilities of the test instances using base-2 logarithm.

Kindly I have this observation and need your valuable opinion about it. I observed the appearance of the term "Log likelihood" in a cluster method like EM. Therefore, how similiar this "Log likelihood" to the one you mentioned (ie., loglikelihood or log loss). Are the two terms refer to one thing? 

Valerio 

The negative conditional loglikelihood on the training data is what logistic regression minimizes. You can view logistic regression as empirical risk minimization if you measure risk using log loss, and you consider logistic regression models as your set of hyotheses.

Cheers,
Eibe

On Thu, Dec 21, 2017 at 10:00 PM, Valerio jus <valeriojus@gmail.com> wrote:
Dear Eibe, 

Thanks for the detaild reply.

1- However, in your opinion, can the "Class complexity | scheme " of entropy help us in finding/computing the "Empirical risk minimization"?

2- How can one interpret the "Class complexity | scheme" ?(how to use it for the sake of scheme evaluation?)

Thanks.

Valerio

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