Machine Learning Techniques Quiz 2: 24 March 2024 (January 2024 term)

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

Consider a regression problem where you are tasked with predicting the sale prices of houses based on their square footage. You decide to experiment with two different models:

The training dataset consists of information on 200 houses, and you use the models to make predictions on a test dataset of 50 houses. The Mean Squared Error (MSE) is chosen as the evaluation metric.
Based on the above data, answer the given subquestions.

Considering the specific context of predicting house prices based on square footage, which model is more likely to provide accurate predictions on the training dataset?

Consider a regression problem where you are tasked with predicting the sale prices of houses based on their square footage. You decide to experiment with two different models:

The training dataset consists of information on 200 houses, and you use the models to make predictions on a test dataset of 50 houses. The Mean Squared Error (MSE) is chosen as the evaluation metric.
Based on the above data, answer the given subquestions.

Identify the factors that could influence the model’s performance on the training dataset in this housing price prediction scenario. Select all correct statements:

Consider a naive Bayes model is trained on the following data matrix $X$ of shape $(d, n)$ and corresponding label vector $y$:

$X = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 0 \end{bmatrix} \quad y = \begin{bmatrix} 1 & 0 & 1 & 1 \end{bmatrix}^T$

Assume that $\hat{p}$ and $\hat{p}_j^{y_i}$ are estimates for $P(y = 1)$ and $P(f_j = 1 | y = y_i)$, respectively. Here, $f_i;\ i = 1, 2, 3$ is the $i^{th}$ feature.

These parameters are estimated using MLE.

Based on the above data, answer the given subquestions.

Consider a naive Bayes model is trained on the following data matrix $X$ of shape $(d, n)$ and corresponding label vector $y$:

$X = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 0 \end{bmatrix} \quad y = \begin{bmatrix} 1 & 0 & 1 & 1 \end{bmatrix}^T$

Assume that $\hat{p}$ and $\hat{p}_j^{y_i}$ are estimates for $P(y = 1)$ and $P(f_j = 1 | y = y_i)$, respectively. Here, $f_i;\ i = 1, 2, 3$ is the $i^{th}$ feature.

These parameters are estimated using MLE.

Based on the above data, answer the given subquestions.

Consider a dataset with the following data points and the target variable:

The linear regression model is given by $y = w_0 + w_1 x$. Assume that the Leave-One-Out Cross-Validation technique is applied.

Based on the above data, answer the given subquestions.

Consider a dataset with the following data points and the target variable:

The linear regression model is given by $y = w_0 + w_1 x$. Assume that the Leave-One-Out Cross-Validation technique is applied.

Based on the above data, answer the given subquestions.

What will be the predicted value for the left-out data point?

Given a design matrix $X \in \mathbb{R}^{d \times n}$ and a target vector $Y \in \mathbb{R}^{n \times 1}$, where $d$ represents the number of features, $n$ represents the number of data points, and the data is defined as:

$X = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$

$Y = \begin{bmatrix} 3 \\ 5 \end{bmatrix}$

Calculate the coefficients $\beta$ for Ridge regression with $\lambda = 1$.

Consider the following data-points in a binary classification problem. w is the weight vector corresponding to a linear classifier. The labels are +1 and −1.

Which of the following statements are true?

Select all true statements.