NPTEL Introduction to Machine Learning Week 2 Assignment Answers 2024

1. State True or False:
Typically, linear regression tend to underperform compared to k-nearest neighbor algorithms when dealing with high-dimensional input spaces.

True
False

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2. Given the following dataset, find the uni-variate regression function that best fits the dataset.

f(x)=1×x+4
f(x)=1×x+5
f(x)=1.5×x+3
f(x)=2×x+1

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3. Given a training data set of 500 instances, with each input instance having 6 dimensions and each output being a scalar value, the dimensions of the design matrix used in applying linear regression to this data is

500×6
500×7
500×6²
None of the above

Answer :-

4. Assertion A: Binary encoding is usually preferred over One-hot encoding to represent categorical data (eg. colors, gender etc)
Reason R: Binary encoding is more memory efficient when compared to One-hot encoding

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is not the correct explanation of A
A is true but R is false
A is false but R is true

Answer :-

5. Select the TRUE statement

Subset selection methods are more likely to improve test error by only focussing on the most important features and by reducing variance in the fit.
Subset selection methods are more likely to improve train error by only focussing on the most important features and by reducing variance in the fit.
Subset selection methods are more likely to improve both test and train error by focussing on the most important features and by reducing variance in the fit.
Subset selection methods don’t help in performance gain in any way.

Answer :-

6. Rank the 3 subset selection methods in terms of computational efficiency:

Forward stepwise selection, best subset selection, and forward stagewise regression.
Forward stepwise selection, forward stagewise regression and best subset selection.
Best subset selection, forward stagewise regression and forward stepwise selection.
Best subset selection, forward stepwise selection and forward stagewise regression.

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7. Choose the TRUE statements from the following: (Multiple correct choice)

Ridge regression since it reduces the coefficients of all variables, makes the final fit a lot more interpretable.
Lasso regression since it doesn’t deal with a squared power is easier to optimize than ridge regression.
Ridge regression has a more stable optimization than lasso regression.
Lasso regression is better suited for interpretability than ridge regression.

Answer :-

8. Which of the following statements are TRUE? Let x_i be the i− th datapoint in a dataset of N points. Let v
represent the first principal component of the dataset. (Multiple answer questions)

v=argmax ∑^N_i=1(vTxi)²s.t.|v|=1
v=argmin ∑^N_i=1(v^Txi)²s.t.|v|=1
Scaling at the start of performing PCA is done just for better numerical stability and computational benefits but plays no role in determining the final principal components of a dataset.
The resultant vectors obtained when performing PCA on a dataset can vary based on the scale of the dataset.