I would like to understand intuitively what it means to sample from a distribution $\mathcal{D}$. It may sound like a dumb question, but I can't find an answer anywhere, a colleague recommended sharing the question with this cs community as there are many brilliant researchers with nice intuitions.
In the context of active learning, we sample from regions of the input space where the probability mass is high and hope to learn the model on those regions. How does it happen in practice when we don't know the underlying distribution $\mathcal{D}$ (stream-based active learning), but only have access to a finite dataset sampled from the distribution (pool-based active learning)? Is streaming-based active learning not feasible in practice?
In some papers (e.g, this paper) authors write $x \sim \mathcal{D}$ to say we use iid sampling from the distribution. In the sequential setting, when sampling $x_t$ at time step $t$ and $x_t'$ at time step $t'$ such that $t < t'$, does it mean $\underset{x \sim \mathcal{D}}{\mathbb{P}}[x = x_t] > \underset{x \sim \mathcal{D}}{\mathbb{P}}[x = x_{t'}]$? In other words, in the sequential setting, do we guarantee that we always sample from high-probability regions at first?
I would be grateful to receive any insights.
