cs2007_2024T2_Q1_AN.pdf

Machine Learning Techniques · Quiz 1 · May 2024

Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

Question 117 MCQ · 2.0 marks

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A published solution is not available for this question yet.

Question 118 MCQ · 3.0 marks

[[IMAGE:44b56e54918bfa54_2_7]]

Both k1 and k2 are valid kernels.
k1 is a valid kernel, but k2 is not a valid kernel.
k2 is a valid kernel, but k1 is not a valid kernel.
Neither k1 nor k2 is a valid kernel.

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Question 119 MSQ · 3.0 marks

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A published solution is not available for this question yet.

Question 120 NAT · 3.0 marks

Kernel PCA with a polynomial kernel of degree 3 is run on a dataset of 100 data-points. Let ϕ be the transformation corresponding to this kernel. If the largest eigenvalue of the centered kernel matrix is 10, find the largest eigenvalue of the covariance matrix of the transformed dataset, where ϕ is used to effect the transformation.

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Question 121 NAT · 3.0 marks

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A published solution is not available for this question yet.

Question 122 NAT · 4.0 marks

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A published solution is not available for this question yet.

Question 123 NAT · 4.0 marks

[[IMAGE:44b56e54918bfa54_5_16]]

A published solution is not available for this question yet.

Question 124 NAT · 2.0 marks

[[IMAGE:44b56e54918bfa54_5_17]] Based on the above data, answer the given subquestions.

Find the variance of the dataset along the first principal component.

A published solution is not available for this question yet.

Question 125 NAT · 1.0 marks

[[IMAGE:44b56e54918bfa54_5_17]] Based on the above data, answer the given subquestions.

Find the variance of the dataset along the x-axis.

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Question 126 MCQ · 2.0 marks

[[IMAGE:44b56e54918bfa54_5_17]] Based on the above data, answer the given subquestions.

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A published solution is not available for this question yet.

Question 127 NAT · 2.0 marks

[[IMAGE:44b56e54918bfa54_7_23]] Based on the above data, answer the given subquestions.

If (x1, y1) is the mean of the first cluster after convergence, find the value of x1 + y1.

A published solution is not available for this question yet.

Question 128 NAT · 2.0 marks

[[IMAGE:44b56e54918bfa54_7_23]] Based on the above data, answer the given subquestions.

If (x2, y2) is the mean of the second cluster after convergence, find the value of x2 + y2.

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Question 129 MCQ · 2.0 marks

In the context of Bayesian estimation, consider a Beta prior for the parameter p of a Bernoulli distribution: [[IMAGE:44b56e54918bfa54_8_24]] The dataset has 8 ones and 5 zeros. Based on the above data, answer the given subquestions.

What is the posterior?

Beta(12, 8)
Beta(11, 7)
Br(0.5)
Beta(8, 5)

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Question 130 NAT · 2.0 marks

[[IMAGE:44b56e54918bfa54_9_25]]

A published solution is not available for this question yet.

Question 131 MCQ · 2.5 marks

[[IMAGE:44b56e54918bfa54_9_26]] Based on the above data, answer the given subquestions.

Find the log-likelihood of the dataset under this distribution.

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A published solution is not available for this question yet.

Question 132 NAT · 2.5 marks

[[IMAGE:44b56e54918bfa54_9_26]] Based on the above data, answer the given subquestions.

Consider a dataset that has 25 data-points. The data-point xi and its frequency is given in the following table: [[IMAGE:44b56e54918bfa54_10_31]] In case the table is not clear: the value 0 appears once in the dataset, the value 1 appears four times in the dataset, and so on. Find the maximum likelihood estimate for the parameter λ of the Poisson distribution given this dataset.

A published solution is not available for this question yet.