Coursera: Machine Learning (Week 3) Quiz - Logistic Regression | Andrew NG

 

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1.Logistic Regression

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1. Suppose that you have trained a logistic regression classifier, and it outputs on a new example a prediction  = 0.2. This means (check all that apply):
   •  Our estimate for P(y = 1|x; θ) is 0.8.
   •  Our estimate for P(y = 0|x; θ) is 0.8.
   •  Our estimate for P(y = 1|x; θ) is 0.2.
   •  Our estimate for P(y = 0|x; θ) is 0.2.

2. Suppose you have the following training set, and fit a logistic regression classifier .
   
   
   Which of the following are true? Check all that apply.
   •  Adding polynomial features (e.g., instead using 
   •  At the optimal value of θ (e.g., found by fminunc), we will have J(θ) ≥ 0.
   •  Adding polynomial features (e.g., instead using ) would increase J(θ) because we are now summing over more terms.
   •  If we train gradient descent for enough iterations, for some examples  in the training set it is possible to obtain .
   • 
     

3. For logistic regression, the gradient is given by . Which of these is a correct gradient descent update for logistic regression with a learning rate of  ? Check all that apply.
   •   (simultaneously update for all j). ANSWER
   •  .
   •   (simultaneously update for all j). ANSWER
   •   (simultaneously update for all j).
   • 
     

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4. Which of the following statements are true? Check all that apply.
   •  The one-vs-all technique allows you to use logistic regression for problems in which each  comes from a fixed, discrete set of values.
   •  For logistic regression, sometimes gradient descent will converge to a local minimum (and fail to find the global minimum). This is the reason we prefer more advanced optimization algorithms such as fminunc (conjugate gradient/BFGS/L-BFGS/etc).
   •  The cost function  for logistic regression trained with  examples is always greater than or equal to zero.
   •  Since we train one classifier when there are two classes, we train two classifiers when there are three classes (and we do one-vs-all classification).
   • 5.Suppose you train a logistic classifier . Suppose , , . Which of the following figures represents the decision boundary found by your classifier?
     •   Figure:
        ANSWER
     •   Figure:
       
       
     •   Figure:
       
       
     •   Figure:
       
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