Register

GO Classes DPP | ML | PERCEPTRON

253 views
1 1 vote

Assume that the Perceptron algorithm is applied to a data set in which the maximum of the lengths of the data points is $4$ and the value of the margin ( $\gamma$ ) of the optimal separator is $1$ . If the algorithm has made $10$ mistakes at some point in the execution of the algorithm, which of the following can be valid squared length(s) of the weight vector obtained in the $11$th iteration?

  1. $90$
     
  2. $150$
     
  3. $190$
     
  4. $180$

1 Answer

0 0 votes
The number of mistakes after $t$ updates to the weight vector is:

$$
\gamma^2 t^t \leq\left\|w^t\right\|^2 \leq t R^2
$$

For $t=11$, we have:

$$
121 \leq\left\|w^{11}\right\|^2 \leq 11 \times 16
$$

From this, we get:

$$
121 \leq\left\|w^{11}\right\|^2 \leq 176
$$

From the options given, we see that $\left\|w^{11}\right\|^2=150$ is valid.
Voting & Accepting an answer helps improve the community
Answer:
← Previous · GO Classes DPP | ML ...Next → · GO Classes DPP | ML ...
← Previous in category · GO Classes DPP | ML ...Next in category → · GO Classes DPP | ML ...
Position:
Show:

Related questions

1 1 vote
1 1 answer
327
327 views
GO Classes asked Oct 7, 2025
327 views
GO Classes DPP | ML | PERCEPTRON
Consider the following data set with three data points:$$\left(\left[\begin{array}{l}2 \\2\end{array}\right],+1\right),\left(\left[\begin{array}{c}2 \\-2\end{array}\right...
2 2 votes
1 1 answer
256
256 views
GO Classes asked Oct 7, 2025
256 views
GO Classes DPP | ML | PERCEPTRON
Consider the following data set:\[\begin{array}{|c|c|c|}\hlinef_1 & f_2 & y \\\hline-1 & -1 & -1 \\0 & 1 & +1 \\1 & 0 & +1 \\1 & 1 & +1 \\\hline\end{array}\]If the Percep...
1 1 vote
1 1 answer
351
351 views
GO Classes asked Oct 7, 2025
351 views
GO Classes DPP | ML | NAÏVE BAYES
A binary classification dataset has 1000 data points belonging to $\{0,1\}^2$. A naive Bayes algorithm was run on the same dataset that results in the following estimate:...
0 0 votes
1 1 answer
287
287 views
GO Classes asked Oct 7, 2025
287 views
GO Classes DPP | ML | NAÏVE BAYES
A binary classification dataset has 1000 data points belonging to $\{0,1\}^2$. A naive Bayes algorithm was run on the same dataset that results in the following estimate:...