<p>Active learning involves choosing which point to query for a label -- as opposed to passive learning, where the example-label pairs are drawn from a distribution without any control of the learner.</p>
<p>See the paper
Active Nearest-Neighbor Learning in Metric Spaces
Aryeh Kontorovich, Sivan Sabato, Ruth Urner; JMLR 18(195):1−38, 2018.
<a href="https://www.jmlr.org/papers/v18/16-499.html" rel="nofollow noreferrer">https://www.jmlr.org/papers/v18/16-499.html</a></p>
<p>for a detailed discussion</p>

CC BY-SA 4.0
2024-05-07T12:03:16.013Z
Thank you @Aryeh, I understand that the distribution controls learning in the passive setting but that's only for the pool-based active learning. However, as I understand in streaming-based active learning, the model should perform well in high-probability mass regions. If the queries do not take care of those regions (distribution is unknown), how can we ensure that the model won't make a mistake on a freshly sampled point from the distribution?
Guesttilunderstandingnature
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2024-05-07T16:07:17.777Z
can you link to a paper where this model is rigorously defined?
Aryeh
CC BY-SA 4.0
2024-05-07T16:39:36.693Z
Paper https://jmlr.org/papers/v13/dekel12b.html: Selective Sampling and Active Learning from Single and Multiple Teachers by Ofer Dekel, Claudio Gentile, Karthik Sridharan. This Paper: https://proceedings.neurips.cc/paper/2007/file/8f85517967795eeef66c225f7883bdcb-Paper.pdf is more classic in active learning and describes my confusion, where the setting is explained rigorously in section 2.1, and my confusion appears in the first line of Algorithm 1 (Input) : A general agnostic active learning algorithm by Sanjoy Dasgupta, Daniel Hsu and Claire Monteleoni
Guesttilunderstandingnature
CC BY-SA 4.0
2024-05-06T17:35:46.887Z
2024-05-06T17:35:46.887Z
Aryeh
<p>I would like to understand intuitively what it means to sample from a distribution <span class="math-container">$\mathcal{D}$</span>. 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.</p>
<p>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 <span class="math-container">$\mathcal{D}$</span> (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?</p>
<p>In some papers (e.g, this <a href="https://%20jmlr.org/papers/volume13/el-yaniv12a/el-yaniv12a.pdf" rel="nofollow noreferrer">paper</a>) authors write <span class="math-container">$x \sim \mathcal{D}$</span> to say we use iid sampling from the distribution. In the sequential setting, when sampling <span class="math-container">$x_t$</span> at time step <span class="math-container">$t$</span> and <span class="math-container">$x_t'$</span> at time step <span class="math-container">$t'$</span> such that <span class="math-container">$t &lt; t'$</span>, does it mean <span class="math-container">$\underset{x \sim \mathcal{D}}{\mathbb{P}}[x = x_t] &gt; \underset{x \sim \mathcal{D}}{\mathbb{P}}[x = x_{t'}]$</span>? In other words, in the sequential setting, do we guarantee that we always sample from high-probability regions at first?</p>
<p>I would be grateful to receive any insights.</p>

CC BY-SA 4.0
2024-05-05T21:27:29.837Z
@J..yB..y this paper https://www.jmlr.org/papers/volume13/el-yaniv12a/el-yaniv12a.pdf page 3 in section 2 third line (saw the same sentence in different forms in many active learning papers ).
Guesttilunderstandingnature
CC BY-SA 4.0
2024-05-05T23:05:17.860Z
Put it in the question!
J.y B.y
<machine-learning>
The true meaning of sampling from a distribution in the context of active learning
Guesttilunderstandingnature
# The true meaning of sampling from a distribution in the context of active learning

(Asked by: username_0 on 2024-05-03)

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](https://%20jmlr.org/papers/volume13/el-yaniv12a/el-yaniv12a.pdf)) 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.

**Tags:** machine-learning

> **Comments:**
> **username_0**: @J..yB..y this paper https://www.jmlr.org/papers/volume13/el-yaniv12a/el-yaniv12a.pdf page 3 in section 2 third line (saw the same sentence in different forms in many active learning papers ).  
> **username_1**: Put it in the question!  

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## 1 answers

### Answer by username_2 on 2024-05-06. Score: 4 | Accepted answer

Active learning involves choosing which point to query for a label -- as opposed to passive learning, where the example-label pairs are drawn from a distribution without any control of the learner.

See the paper
Active Nearest-Neighbor Learning in Metric Spaces
username_2 Kontorovich, Sivan Sabato, Ruth Urner; JMLR 18(195):1−38, 2018.
<https://www.jmlr.org/papers/v18/16-499.html>

for a detailed discussion

> **Comments:**
> **username_0**: Thank you @username_2, I understand that the distribution controls learning in the passive setting but that's only for the pool-based active learning. However, as I understand in streaming-based active learning, the model should perform well in high-probability mass regions. If the queries do not take care of those regions (distribution is unknown), how can we ensure that the model won't make a mistake on a freshly sampled point from the distribution?  
> **username_2**: can you link to a paper where this model is rigorously defined?  
> **username_0**: Paper https://jmlr.org/papers/v13/dekel12b.html: Selective Sampling and Active Learning from Single and Multiple Teachers by Ofer Dekel, Claudio Gentile, Karthik Sridharan. This Paper: https://proceedings.neurips.cc/paper/2007/file/8f85517967795eeef66c225f7883bdcb-Paper.pdf is more classic in active learning and describes my confusion, where the setting is explained rigorously in section 2.1, and my confusion appears in the first line of Algorithm 1 (Input) : A general agnostic active learning algorithm by Sanjoy Dasgupta, Daniel Hsu and Claire Monteleoni  

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