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Machine Learning Techniques, End Term
For a given dataset, a 1-Nearest Neighbor (1-NN) and a 3-Nearest Neighbor (3-NN) classifier are applied. Which classifier is likely to exhibit a higher Leave-One-Out Cross Validation (LOOCV) error? In case of tie-breaker, assign a positive class (+) to the data point.
For a given dataset, a 1-Nearest Neighbor (1-NN) and a 3-Nearest Neighbor (3-NN) classifier are applied. Which classifier is likely to exhibit a higher Leave-One-Out Cross Validation (LOOCV) error? In case of tie-breaker, assign a positive class (+) to the data point. Scatter plot of labeled positive (+) and negative (-) data points Consider the following three weight vectors obtained by minimizing the ridge regression objective with penalty parameters $\lambda = 0.1, 10, 50$. $\theta_1 = \begin{bmatrix} 0.5 & 0.56 & 2.5 \end{bmatrix}^T$\ $\theta_2 = \begin{bmatrix} 0.05 & 0.1 & 1.23 \end{bmatrix}^T$\ $\theta_3 = \begin{bmatrix} 1.2 & 0.84 & 3.15 \end{bmatrix}^T$ Select the most appropriate match for each weight vector corresponding to penalty parameter $\lambda$ from the following options: Consider the following dataset with two features and the corresponding labels: | $x_1$ | $x_2$ | $y$ | |---|---|---| | 1 | 0 | 1.5 | | 2 | 2 | 4 | | 3 | 0 | 4.5 | | 4 | 2 | 7 | Fit the linear regression model $y = w_1 x_1 + w_2 x_2$ using the normal equation obtained from the squared error loss. **Hint:** The normal equation for linear regression is: $$w = (XX^T)^{-1} X y$$