Sorry to have been so silent - finishing a book will do that to you!

Here's one comment... my wife just got back home and it's dinnertime so I'll have to continue tomorrow:

> The most common way to work with collected data is to split it into a **training set** and a **test set**. (Sometimes there is a division into three sets, the third being a **validation set** which is used when the model has meta-parameters as a test set to find the best values for them.) The training and validation sets are used in the process of determining the best model parameters, while the test set – which is not used in any way in determining the best model parameters – is then used to see how effective the model is likely to be on new, unseen data.

It's a bit confusing to introduce the third, optional "validation set" before you've said what the "training set" and "test set" are. You introduce this "validation set" and say it's "used as a test set" before you even say what a test said is. Then you say "the training and validation sets are..." giving some feature common to both those two, even though you just said the validation set is used as a test set, making it sound like _those_ two are similar. Then you say something about the test set.

Don't feel bad, this sort of convoluted circular exposition is typical of people trying to explain things they understand too well! It always helps to replace the terms one is trying to explain by meaningless symbols like **X**, **Y** and **Z**, since they'll be meaningless to the people reading the explanation:

> The most common way to work with collected data is to split it into a **X** and a **Y**. (Sometimes there is a division into three sets, the third being a **Z** which is used when the model has meta-parameters as a Y to find the best values for them.) The X and Z are used in the process of determining the best model parameters, while the Y – which is not used in any way in determining the best model parameters – is then used to see how effective the model is likely to be on new, unseen data.

I recommend something more like this:

> The most common way to work with collected data is to split it into a **training set** and a **test set**. The training set lets us choose the best model parameters. The test set – which is not used in any way in determining the best model parameters – is then used to see how effective the model is likely to be on new, unseen data. (Sometimes there is a more elaborate division into three sets, the third being a **validation set** which is used when the model has "meta-parameters", in order to... something or other, preferably not including the phrase "test set".)

It would be great to say what a "meta-parameter" is... or simply leave out this "validation set" stuff, which may be too much for a beginner who is trying to absorb all this information for the first time. I don't really know how a "meta-parameter" differs from a parameter, though I know that most kinds of abstract thing come along with a "meta-things".

Anyway, it looks great as far as I've gotten. More later!