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GO Classes DPP | ML | LOSS-FUNCTION

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3 3 votes

Consider the following data:

\[
\begin{array}{|l|l|}
\hline
g(x) & y \\
\hline
+30 & +1 \\
\hline
-20 & -1 \\
\hline
-1 & -1 \\
\hline
+1 & +1 \\
\hline
\end{array}
\]

Which of the following will be true?

  1. The values of $0-1$ loss and squared loss will be the same, which will be equal to zero.
     
  2. The values of 0-1 loss and squared loss will be the same, which will be equal to some large positive quantity.
     
  3. The value of 0-1 loss will be zero, while the value of squared loss will be some large positive quantity.
     
  4. The value of squared loss will be zero, while the value of $0-1$ loss will be some large positive quantity.

1 Answer

0 0 votes

\[
\begin{array}{|l|l|l|l|l|}
\hline
g(x) & y & \operatorname{sign}(g(x)) & \text{0-1 loss} & \text{Squared loss } [g(x)-y]^2 \\
\hline
+30 & +1 & +1 & 0 & 29^2 \\
\hline
-20 & -1 & -1 & 0 & 19^2 \\
\hline
-1 & -1 & -1 & 0 & 0 \\
\hline
+1 & +1 & +1 & 0 & 0 \\
\hline
\end{array}
\]

The value of $0-1$ loss is zero, while the value of squared loss is a large positive quantity. 

Hence, option (C) is correct.

• edited by
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