Recent questions and answers in Machine Learning

Using monthly stock averages, $x_1, x_2, \ldots x_n$, you run linear regression without regularization to estimate some future stock value $y$. However, your test error r...

Consider the contour map shown below.If a person were walking straight from point $A$ to point $B$, would s/he be walking uphill or downhill? Is the slope steeper at poin...

Consider the convex function $f(z) = z^2$ . Let $\alpha$ be our learning rate in gradient descent. For which values of $\alpha$ will $lim_{t \rightarrow \infty} f(z^{(t)}...

If the step size is dynamic, $\eta = \frac{1}{t}$, and $w^{(1)} = 0$, find the expression for $w^{(t)}$ after $t$ steps of SGD.$w^{(t)}= \frac{1}{n} \sum_{i=1}^n \frac{1}...

Which of the following is true, given the optimal learning rate?Batch gradient descent is always guaranteed to converge to the global optimum of a loss function.Stochasti...

Good practices to avoid overfitting include:  Using a two part cost function which includes a regularizer to penalize model complexity.Using a good optimizer to minimize ...

Consider the least squares regression model, $\hat{\mathbb{Y}}=\mathbb{X} \theta$. Assume that $\mathbb{X}$ and $\mathbb{Y}$ refer to the design matrix and true response ...

Consider the least squares regression model, $\hat{\mathbb{Y}}=\mathbb{X} \theta$. Assume that $\mathbb{X}$ and $\mathbb{Y}$ refer to the design matrix and true response ...

In a LASSO Regression, if the regularization parameter $\lambda$ is very high, which of the following is true? The model can shrink the coefficients of uninformative feat...

Consider the dataset with six datapoints: $\{(x_1, y_1), (x_2, y_2),.., (x_6,y_6)\}$ where $x_1 = \begin{bmatrix}1 \\ 0\end{bmatrix}, x_2 = \begin{bmatrix}0 \\ 1\end{bmat...

In the context of Slack Soft Margin SVM (Support Vector Machine), which of the following expressions can describe the slack variable $\xi^{(i)}$? $ \xi^{(i)} = \begin{ca...

What is the value of $\alpha_n$ for the circled data point ? $\alpha_n=0$$\alpha_n=C$$0<\alpha_n<C$Can be anything i.e. $0 \leq \alpha_n \leq C$

Suppose we have a training dataset of 90 points, and a test set of 30 points, and want to know which $\lambda$ value is best for a ridge regression model. Our candidate h...

$\text { Suppose you have this data set with one real-valued input and one real-valued output. }$I.What is the mean squared leave one out cross validation error of using ...

Peanut wants to train a model to accurately classify different types of animals from images. After training and testing his model, he observes that the model has high tra...

Parth now decides to use only the two most important features, $X_1$ , and $X_2$, in the dataset to predict weekly watch time. Given below is the scatterplot of the two f...

Suppose we are given three datasets $A, B$, and $C \in \mathbb{R}^{100 \times 2}$ i.e. each dataset consists of 100 data points in two dimensions. We visualize the datase...

Answer the same questions for the following dataset:$$\begin{bmatrix} 1 & 1 \\ 1.5 & 1.5 \\ -2 & 2 \\ 4 & -4 \\ 6 & -6 \\ 2 & 2 \end{bmatrix}$$What are the first $v_1$ a...

Which of the options are correct, select all that apply?You are solving a binary classification task, and the final two layers in your network are a ReLU activation follo...

Which of the options are correct, select all that apply ?Maximum value of local gradient when sigmoid is used as an activation function is 0.5.Minimum value of local grad...

Which of the following algorithms is used for Reinforcement learning?Naive BayesPrincipal Component AnalysisFast Forest QuantileQ-learning

Kevin is trying to fit a simple linear regression model $\hat{y}=\theta_0+\theta_1 x$ on a dataset with 900 observations.After determining $\hat{\theta_0}$ and $\hat{\the...

Consider the following two regularized linear regression objectives:$$L_1(w)=\sum_{i=1}^{n}(y_i-w^T x_i)^2+\lambda\sum_{j=1}^{8}w^2_j$$$$L_2(w)=\sum_{i=1}^{n}(y_i-w^T x_i...

Consider just the general shape of the following plots.For each of the following possible interpretations of the quantities being plotted on the $X$ and $Y$ axes, indicat...

   

Consider the following two statements S1 and S2 about linear separability.$S1 :$ If we take any data set that is not linearly separable and remove a feature, it is still ...

Suppose a linear regression model is trained using$$X \in \mathbb{R}^{N \times d}, \quad t \in \mathbb{R}^{N} .$$Now the dataset is duplicated to form$$X^{\prime}=\left[\...

In logistic regression, we predict Class 1 when$$\sigma\left(\mathbf{w}^{T} \mathbf{x}+b\right)>0.5$$What is the equation of the decision boundary?A. $\mathbf{w}^{T} \mat...