What does Negative Log Likelihood mean? I have a data set which has continuous independent variables and a continuous dependent variable. To predict the dependent variable using the independent variables, I've run an ensemble of regression models and tried to compare them against each other. Here are the results for reference:



I can interpret what the R-squared value / Coefficient of determination for each of those models means. However, I can't understand what the Negative Log Likelihood means. Especially, why is it Infinity for Linear Regression and Boosted Decision Tree, and a finite value for a Decision Forest Regression?

Edit:
Data Description: The data that went into these three models is all continuous independent variables and a continuous dependent variable. There are a total of 542 observations and 26 variables. 
These 542 variables are split 70 - 30 to get training and testing datasets. Therefore, the training dataset has 379 observations and 26 variables; the testing dataset has 163 observations and 26 variables.
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.
Likelihood function is the product of probability distribution function, assuming each observation is independent. However, we usually work on a logarithmic scale, because the PDF terms are now additive. If you don't understand what I've said, just remember the higher the value it is, the more likely your model fits the model. Google for maximum likelihood estimation if you're interested.

Obviously, your input data is bad. You should give your model a proper data set. While I don't have your data set, we can take a look at the likelihood function for linear regression:

 

You will get infinity if the likelihood function is zero or undefined (that's because log(0) is invalid). Look at the equation, most likely your sample standard deviation is zero. If it's zero, the last term will be undefined. Have you given a data set that you copied and pasted the same data over rows?

Boosted trees should also be undefined if your sample deviation is zero. However, decision tree is estimated based on impurity and won't crash here. 

Summary: please check and double check your data.

EDIT I think you just had a bug. Linear regression will always give you something here. Have you fitted the models in R with the same dataset? –