What is meant by "the number of examples is reduced", and why is this the case? I am currently studying the paper Learning and Evaluating Classifiers under Sample Selection Bias by Bianca Zadrozny. In section 3.2. Logistic Regression, the author says the following:

3.2. Logistic regression
In logistic regression, we use maximum likelihood to find the parameter vector $\beta$ of the following model:
$$P(y = 1 \mid x) = \dfrac{1}{1 + \exp(\beta_0 + \beta_1 x_1 + \dots + \beta_n x_n)}$$
With sample selection bias we will instead fit:
$$P(y = 1 \mid x, s = 1) = \dfrac{1}{1 + \exp(\beta_0 + \beta_1 x_1 + \dots + \beta_n x_n)}$$
However, because we are assuming that $y$ is independent of $s$ given $x$ we have that $P(y = 1 \mid x, s = 1) = P(y = 1 \mid x)$. Thus, logistic regression is not affected by sample selection bias, except for the fact that the number of examples is reduced. Asymptotically, as long as $P(s = 1 \mid x)$ is greater than zero for all $x$, the results on a selected sample approach the results on a random sample. In fact, this is true for any learner that models $P(y \mid x)$ directly. These are all local learners.

This part is unclear to me:

However, because we are assuming that $y$ is independent of $s$ given $x$ we have that $P(y = 1 \mid x, s = 1) = P(y = 1 \mid x)$. Thus, logistic regression is not affected by sample selection bias, except for the fact that the number of examples is reduced.

What is meant by &quot;the number of examples is reduced&quot;, and why is this the case?
I think what he means is that, while distribution $P(y  \mid x,s)$ has three variables, $P(y  \mid x)$ has two variables. The number of parameters required to describe a distribution (or samples to approximate it) grows exponentially with the number of variables (for more info see for instance Ian goodfellow, .. deep learning&quot;).