Past year questions
Machine Learning Techniques (BSCS2007) PYQs
57 verified past-year questions tagged to real concepts, week by week. A few samples below — the full bank, filterable by type and difficulty, is in the app.
Distribution by week
Sample questions
Let x = [x₁, x₂]ᵀ and y = [y₁, y₂]ᵀ be two vectors in ℝ². Let k₁ and k₂ be two functions defined from ℝ² × ℝ² → ℝ:
k₁(x, y) = x₁y₁ + x₂y₂ + x₁x₂y₁y₂ k₂(x, y) = x₁y₁ + x₂y₂ + x₁x₂y₁y₂ + 1
Which of the following statements is true?
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.
Consider a covariance matrix C for a mean-centered dataset in ℝ³. After performing standard PCA, the three principal components turn out to be:
[1, 0, 0]ᵀ, [0, 1, 0]ᵀ, [0, 0, 1]ᵀ
Which of the following statements are true? You can assume that C is not the zero matrix.
C is a diagonal matrix.
The diagonal entries of C are non-negative.
The diagonal entries of C are strictly greater than zero.
C has to be the identity matrix.
C is a matrix of the form kI, where k > 0 and I is the identity matrix.
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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