Regression, Regularization and Gradient-Based Learning Previous Year Questions (PYQs) for GATE DA: 4+ Solved Questions with Step-by-Step Solutions

Consider that Linear Ridge Regression is being used to learn a prediction function $y_{pred}=w^{T}x$, where $w,x\in {\mathbb{R}}^2$ and Mean Absolute Error (MAE) is used to measure the prediction error. A weight of 0.20 is associated with the regularizer.

At an intermediate step of the training process, assume that the parameter $w=[-3.00,4.00{]}^T$. In the next step, for the input $x=[1.00,2.00{]}^T$, the predicted value of $y$ is noted. Let the relation between $x=[x_1,x_2{]}^T$ and the true value of $y$ be $y_{true}=x_1+x_2$.

The value of the overall regularized loss function for this instance is _______ . (Rounded off to two decimal places)

Consider that for a supervised learning task, the objective function being minimized is $f_w(x)=wx$, where $x\in \mathbb{R}$ is the input and $w\in \mathbb{R}$ is the parameter. Stochastic Gradient Descent with learning rate of 0.10 is used for parameter updates.

Suppose that at the end of iteration $i$, the value of $w$ becomes 10.00.

Let $x=10.00$ be the input for iteration $(i+1)$.

The value of $w$ at the end of iteration $(i+1)$ is __________ . (Rounded off to two decimal places)

Given data $\{(-1,1),(2,-5),(3,5)\}$ of the form $(x,y)$, we fit a model $y=wx$ using linear least-squares regression. The optimal value of $w$ is
(Round off to three decimal places)