Which of the following satisfies the support vectors? Suppose the linear model, h, is known, and the true label y is in {−1,1}.

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BlackTom AI · Accepted Answer

The question is asking which condition identifies support vectors for a linear model h when the true label is y ∈ {−1, 1}.
First, recall how the SVM margin works: for a given example (x, y), the functional margin is y · h(x) = y · (w^T x + b).
In the hard-margin SVM formulation, the support vectors are precisely those points that lie exactly on the margin, which satisfies y · h(x) = 1. Points with y · h(x) > 1 lie outside the margin and are correctly classified with a margin beyond the boundary, while points with y · h(x) < 1 lie inside the margin and are not supporting the margin boundary.
So the condition y h(x) = 1 characterizes the support vectors (under the classic hard-margin interpretation). If soft-margin/SVM with slack variables were in play, the boundary would be y · h(x) ≥ 1 for points not strictly inside the margin, but the core identifying condition for being on the margin remains y h(x) = 1 for the support vectors.

Given the provided answer option yh=1, this aligns with the standard criterion for support vectors on the margin in many SVM formulations. However, without the other options to compare, we can’t evaluate alternative statements.

In summary, the key idea is: a training example is a support vector when its label multiplied by the model output equals 1, i.e., y · h(x) = 1, which places it exactly on the decision boundary of the margin.

Machine Learning: Fundamentals and Applications Quiz 7 SVM

Which of the following satisfies the support vectors? Suppose the linear model, h, is known, and the true label y is in {−1,1}.

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