The random variable y is being transformed according to the measurement mapping: z = Cy + \epsilon, where: - z \in \mathbb{R}^d, - C \in \mathbb{R}^{d \times n}, - \epsilon \sim \mathcal{N}(0, \sigma^2 I_d) is independent Gaussian (measurement) noise. Which of the following represents the conditional probability distribution p(z \mid y)?

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Machine Learning Foundations · End Term · 13 Apr 2025 · January 2025 term · Set QDD3

Question 2: The random variable y is being transformed according to t…

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The random variable $y$ is being transformed according to the measurement mapping:

$z = Cy + \epsilon,$

where:

$z \in \mathbb{R}^d$ ,
$C \in \mathbb{R}^{d \times n}$ ,
$\epsilon \sim \mathcal{N}(0, \sigma^2 I_d)$ is independent Gaussian (measurement) noise.

Which of the following represents the conditional probability distribution $p(z \mid y)$ ?

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Question 2 of 14 in the IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 13 Apr 2025, in the January 2025 term (IIT M DIPLOMA AN EXAM QDD3 13 Apr 2025). It carries 3 marks.

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