We are given the dataset below, where every row shows the probability of an instance belonging to the three classes y1, y2, and y3. Using the least confident query strategy, which instance should you query first?

y1

y2

y3

Instance 1

0.01

0.9

0.09

Instance 2

0.1

0.5

0.4

Instance 3

0.6

0.2

0.2

Instance 4

0.45

0.51

0.04

Question

We are given the dataset below, where every row shows the probability of an instance belonging  to the three classes y1, y2, and y3. Using the least confident query strategy, which instance should you query first?

y1

y2

y3

Instance 1

0.01

0.9

0.09

Instance 2

0.1

0.5

0.4

Instance 3

0.6

0.2

Instance 4

0.45

0.51

0.04

BlackTom AI · Accepted Answer

Let's start by restating what the problem asks: we have four instances, each with predicted probabilities for three classes y1, y2, and y3, and we want to select the instance to query first using the least confident query strategy.

Option review in turn:
- Instance 4: The probabilities are [0.45, 0.51, 0.04]. The highest probability here is 0.51 (for y2), so the model is most confident about this instance with 51% certainty. This leaves relatively little uncertainty, suggesting it is not the least confident choice.
- Instance 3: The probabilities are [0.6, 0.2, 0.2]. The top probability is 0.6 (for y1). Here the model shows a reasonable level of confidence (60%), making it not the least confident option either. The remaining classes have much smaller probabilities, but the max is still moderately high.
- Instance 2: The probabilities are [0.1, 0.5, 0.4]. The largest probability is 0.5 (for y2). This indicates the model is only moderately confident, and has ambiguity among the top two choices (y2 at 0.5, and y3 at 0.4).
- Instance 1: The probabilities are [0.01, 0.9, 0.09]. The maximum probability is 0.9 (for y2), which shows very high confidence for this instance, so it is clearly not the least confident.

Now, the core criterion: least confident query strategy selects the instance with the smallest maximum predicted probability across classes, i.e., the smallest model confidence.
- Instance 4 has max 0.51
- Instance 3 has max 0.6
- Instance 2 has max 0.5
- Instance 1 has max 0.9
Among these, the smallest maximum probability is 0.5 for Instance 2. Therefore, Instance 2 is the least confidently predicted instance and should be queried first.

Putting it together, the reasoning points to Instance 2 as the correct choice because it yields the lowest peak probability among the three classes, signaling the highest uncertainty under the least confident criterion.

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