Statistical Machine Learning Quiz

A scalar

• A scalar

• A matrix of size m X n

• A vector of size m X 1

• A vector of size n X 1

Which of the following is true about eigenvalues and eigenvectors?

• Eigenvalues are always real numbers

• Eigenvectors are always orthogonal

• Eigenvectors remain in the same direction after a transformation

• Eigenvalues are always positive

Orthogonality between two vectors implies that their dot product is:

• Greater than zero

• Equal to zero

• Less than zero

• Equal to one

The determinant of a matrix is useful for:

• Checking if a matrix is invertible

• Finding eigenvalues

• Calculating matrix rank

• All of the above

The gradient descent algorithm minimizes a function by moving in the direction of:

• Zero gradient

• Increasing gradient

• Negative gradient

• Positive gradient

Bayes' rule relates which two probabilities?

• Prior and posterior probabilities

• Conditional and marginal probabilities

• Joint and marginal probabilities

• None of the above

The prior probability in Bayes' rule represents:

• Probability before evidence is considered

• Probability after evidence is considered

• Conditional probability of evidence given the hypothesis

• Likelihood of the hypothesis given evidence

In Gaussian distributions, approximately what percentage of the data lies within one standard deviation from the mean?

• 50%

• 68%

• 95%

• 99%

A key assumption of Gaussian distributions is that:

• Data is uniformly distributed

• Data is normally distributed around a mean

• All data points are independent

• None of the above

What is the primary role of loss functions in machine learning?

• Maximizing accuracy

• Estimating the error between predicted and actual values

• Optimizing the algorithm's runtime

• None of the above