GATE Data Science & AI

Let $D=\left\{x^{(1)}, \ldots ., x^{(n)}\right\}$ be a dataset of $n$ observations where each $x^i \in \mathbb{R}^{100}$. It is given that $\sum_{i=1}^n x^{(\mathrm{i})}=0$ The cov...

Consider designing a linear classifier $$ y=\operatorname{sign}(f(x ; w ; b)), f(x ; w, b)=w^{\mathrm{T}} x+b $$ on a dataset $$ \begin{aligned} & D=\left\{\left(x_1, y_1\right),\l...

Let $C_1$ and $C_2$ be two sets of objects. Let $D(x, y)$ be a measure of dissimilarity between two objects $x$ and $y$. Consider the following definitions of dissimilarity between...

Let $\left\{x_1, x_2, \ldots ., x_n\right\}$ be a set of linearly independent vectors in $\mathbb{R}^n$. Let the $(\mathrm{i}, \mathrm{j})$ - th element of matrix $A \in \mathbb{R}...

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

Let $x_1, x_2, x_3, x_4, x_5$ be a system of orthonormal vectors in $\mathbb{R}^{10}$. Consider the matrix $A=x_1 x_1^T+\ldots . .+x_5 x_5^T$. Which of the following statements is/...

(Round off to three decimal places) The naive Bayes classifier is used to solve a two-class classification problem with class labels $y_1, y_2$. Suppose the prior probabilities are...

Consider a two-class problem in $R^d$ with class labels red and green. Let $\mu_{\text {red }}$ and $\mu_{\text {green }}$ be the means of the two classes. Given test sample $x \in...

Which of the following statements is/are correct about the rectified linear unit (ReLU) activation function defined as $\operatorname{ReLU}(x)=\max (x, 0)$, where $\mathrm{x} \in \...

Consider designing a linear binary classifier $f(x)=\operatorname{sign} g\left(w^T x+b\right), x \in \mathbb{R}^2$ on the following training data: Class -1: $\left\{\binom{2}{0},\b...