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📗 (Fall 2014 Midterm Q12, Fall 2013 Final Q4, Spring 2017 Final Q2) A linear SVM has \(w\) = and \(b\) = . Which of the following points is predicted positive (label 1)?
📗 Choices:
📗 (Fall 2014 Midterm Q14) Suppose an SVM has \(w\) = and \(b\) = . What is the actual distance between the two planes defined by \(w^\top x + b = -1\) and \(w^\top x + b = 1\).
📗 Answer: .
📗 (Fall 2014 Midterm Q15, Fall 2013 Final Q7, Fall 2011 Midterm Q9) If \(K\left(x, x'\right)\) is a kernel with induced feature representation \(\varphi\left(x\right)\) = , and \(G\left(x, x'\right)\) is another kernel with induced feature representation \(\theta\left(x\right)\) = , then it is known that \(H\left(x, x'\right) = a K\left(x, x'\right) + b G\left(x, x'\right)\), \(a\) = , \(b\) = is also a kernel. What is the induced feature representation of \(H\) for this \(x\)?
📗 Hint: Fall 2014 Midterm Q15 gives you the formula: basically summing two kernels is equivalent to concatenating the corresponding feature vectors, but please try to convince yourself this is correct (see the last quiz question for Lecture 5).
📗 Answer (comma separated vector): .
📗 (Fall 2014 Midterm Q13, Fall 2012 Final Q7) Recall a linear SVM with slack variables has the objective function \(\dfrac{1}{2} w^\top w + C \displaystyle\sum_{i=1}^{n} \varepsilon_{i}\). What is the optimal \(w\) when the trade-off parameter \(C\) is 0? The training data contains only points with label 0 and with label 1. Only enter the weights, no bias.
📗 Answer (comma separated vector): .
📗 (Fall 2010 Final Q14) Consider a small dataset with \(n\) points, where each point in a dimensional space. For which values of \(n\), there exists a dataset such that, no matter what binary label we give to each point, a linear SVM can perfectly classify the resulting dataset.
📗 Hint: the largest such \(n\) is called the Vapnik-Chervonenkis (VC) dimension. The VC dimension for linear classifiers (for example SVM) is the dimension of the space plus 1. The following is an example in 2D with 3 points: no matter what binary label we give to each point, a line can always separate the two classes: note that it is not the case with 4 points (remember the XOR example).
📗 Choices:
📗 (Fall 2011 Midterm Q7) Given a weight vector \(w\) = , consider the line defined by \(w^\top x\) = . Along this line, there is a point that is the closest to the origin. How far is that point to the origin in Euclidean distance?
📗 Answer: .
📗 (Fall 2011 Midterm Q8, Fall 2009 Final Q1) Let \(w\) = and \(b\) = . For the point \(x\) = , \(y\) = , what is the smallest slack value \(\xi\) for it to satisfy the margin constraint?
📗 Answer: .
📗 (Fall 2019 Final Q10) A linear SVM with with weights \(w_{1}, w_{2}, b\) is trained on the following data set: \(x_{1}\) = , \(y_{1}\) = and \(x_{2}\) = , \(y_{2}\) = . The attributes are two dimensional \(\left(x_{1}, x_{2}\right)\) and the label \(y\) is binary. The classification rule is \(\hat{y} = 1_{\left\{w_{1} x_{1} + w_{2} x_{2} + b \geq 0\right\}}\). Assuming \(b\) = , what is \(\left(w_{1}, w_{2}\right)\)?
📗 Hint: draw the line then figure out its equation using one point on the line and its slope.
📗 This is survey question. What is the highest numbered programming course you took (CS300, CS320, CS400, etc) and do you think that course prepared you for P1? If not, please explain.
📗 Answer: .
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📗 Answer: .
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