CS 451 Quiz 4
Linear Regression with Multiple Variables
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Notation and conventions
Note: x_k denotes subscript k; x^k denotes superscript k (or exponentiation). Recall that we use 'm' for the number of training examples, and 'n' for the number of features.
Check all that are true
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In input vector x^(i)_j, i denotes training example i, and j denotes feature j
The parameter vector theta has n+1 elements since we always add a constant feature x_0 = 1
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Vectorization
Check all that are true
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Recall that both theta and x are column vectors, and that x' denotes the transpose of x.
The hypothesis h_theta(x) can be computed in vectorized form as theta' * x
theta' * x = x' * theta
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Gradient descent
In the above multivariate gradient descent algorithm, the loop "for j := 0...n" should be executed
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sequentially
in parallel, i.e. simultaneously
Feature scaling
Feature scaling guarantees convergence, but may slow down the convergence rate
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True
False
Which are valid ways of performing feature scaling? Check all that apply.
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subtract the mean, then divide by the range
divide by the range, then add the mean
subtract the mean, then divide by the standard deviation
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Learning rate
If the learning rate alpha is too small, the cost may increase in some iterations
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True
False
Plotting the cost vs. the number of iterations is a good way of checking whether gradient descent converges
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True
False
Polynomial regression
To fit a polynomial to our input data, we can use the standard multivariate linear regression algorithm; we just create additional features, e.g. x2 = x1^2 and x3 = x1^3.
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True
False
Normal equation
Instead of using the iterative gradient descent method, the minimum cost can also be found analytically by solving the normal equation
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True
False
Using the normal equation is the only practical way to minimize J for large n (say, n > 1,000,000) , since gradient descent will be too slow.
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True
False
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