# Out-of-sample likelihood example

I'm an amateur in statistics. I was reading a paper in which it is mentioned that

A model gives high out-of-sample likelihood.

What does that mean? What is exactly "High-out-of-sample likelihood"? What would be the simple explaination of it?

For other folks who might have an answer, the relevant quote from the paper is as follows:

The objective is to learn a good model $f(w_{t} ,\dots ,w_{t−n+1}) = \hat{P}(w_t|w_{t−1})$, in the sense that it gives high out-of-sample likelihood

After skimming the relevant section of the paper you linked, I think you could rephrase the author's comment (in plain English, avoiding stats jargon as much as possible) as follows:

"A good model is one that is consistent with the data we actually observe"

Two important concepts to understand here.

• Training data vs. real-world (out-of-sample) data:

• Training data is used to fit the model initially. That's different from the the 'real-world' data you really need the model to handle. The author seems to be referring to this real-world data when he/she uses the term out-of-sample data.
• Likelihood:

• When fitting a model, you want to know "how plausible is this model?". To fit the model, you maximize this "plausibility", which is represented by the likelihood of seeing the data, given the model.
• This is a tricky concept - it's not the likelihood of the model being "right", but is still a measure of how well the data "matches" the model.

So the author is saying that we want to learn a "good model" in the sense that it is the most plausible model for the real world data we encounter.